context
stringlengths 545
71.9k
| questionsrc
stringlengths 16
10.2k
| question
stringlengths 11
563
|
|---|---|---|
how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
|
it 's a lot of fun . count the flowers . type the missing numbers in the boxes .
|
how do you count by 4 's ?
|
how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
|
how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight .
|
how many legs does a spider have ?
|
how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
|
it 's a lot of fun . count the flowers . type the missing numbers in the boxes .
|
how come we do n't count zero ?
|
how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
|
it 's a lot of fun . count the flowers . type the missing numbers in the boxes .
|
how do you count to 1,000 ?
|
how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
|
let 's keep going . type the missing numbers . it says count the ladybugs .
|
are there numbers smaller than 1 ?
|
how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
|
this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
|
why ca n't you divide by zero ?
|
how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
|
how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight .
|
how do we recognize amount ?
|
how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
|
it 's a lot of fun . count the flowers . type the missing numbers in the boxes .
|
if i count , do fly like counting comet fro tem oomizzomie ?
|
how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
|
it 's a lot of fun . count the flowers . type the missing numbers in the boxes .
|
why we need to count in order so we can count things right ?
|
how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
|
it 's a lot of fun . count the flowers . type the missing numbers in the boxes .
|
do we have to count in order all the time ?
|
how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
|
type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there .
|
what is the largest number so far ?
|
how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
|
how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight .
|
why do mastery challenges only come at certain points ?
|
how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
|
let 's keep going . type the missing numbers . it says count the ladybugs .
|
can u multiply negative numbers ?
|
as we 've talked about in multiple videos , some of the earliest civilizations we have found have been around river valleys , and that is no coincidence because some of the first agriculture emerged around river valleys and the agriculture supported higher population densities and more sedentary populations , and allowed for more specialization . and we have talked about several of these , the ancient egyptians around the nile river , the ancient mesopotamians around the tigris and euphrates . and now we 're gon na talk about the ancient civilization around the indus river . the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization . now to get ourselves acquainted in time , this shows when archaeologists , historians consider to be the main part of the harappan civilization . there 's evidence that people had basic villages , civilizations , agriculture here , as far back as 7,000 bce , and that 's just based on the evidence we have today , but when people refer to the indus valley civilization in particular , they 're usually staring around 3300 bce and in orange right over here , this is the early period , or you could say the early indus valley civilization . now some of the biggest structures and pieces of technology that have been discovered have been right over here , which is often referred to as the mature period for the indus valley civilization , and then it goes into decline . we 'll talk about why it might have gone into decline , although we 're not really sure , and this is called the late . now to put it in context relative to these other civilizations , remember the ancient sumerians were starting to be quite , i guess you could say civilized , by about this period . you start having a lot of intermingling between the acadians and the sumerians as you get into the late third millennium . that 's when you have the empire of sargon the great , the acadian empire . as you get to the end of this mature period right over here , this is close to or around the time of hammurabi , the babylonian empire , and in egypt , if you go back to around 2500 , around this time , that 's when the pyramids were built and you have the egyptian kings , these god-kings that were ruling for most of this period right over here and as we 'll see , there was actually , we believe , a good bit of cultural interchange between the significant civilizations . now just to appreciate how extensive this indus valley civilization was , i will show you this map . and this map , it 's zoomed in of that region around the indus valley that i just showed you . this is a map of most of pakistan here , and these red squares are places where they have found evidence of the civilization . the first place was harappa , right over here , the punjab region of pakistan . and that 's why it 's called the harappan civilization . but as you can see , it 's much more than just around harappa . the largest site is at mohenjo-daro , right over here in the sindh region of pakistan and it 's believed that as many as 40,000 people lived in that city that we now , or that site , that we now call mohenjo-daro . and so far , we have discovered over 1,000 sites in this area and we believe that as many as five million people might have been part of the civilization . now the reason why we think it is a civilization and now , and let me actually keep scrolling around so you appreciate the extent of it . there 's sites in mainly , many in pakistan that you see here . there 's also quite a few in modern-day india right over here , so it 's an extensive network of these sites and the reason why we think it 's one civilization , or at least a connected culture , is that you find a lot of standardization . you find standardization in their weights and measures . in fact , they have a unit of measurement that 's as small as 1.6 millimeters , and the reason why that 's important is you would n't create a unit of measurement of 1.6 millimeters unless you knew how to use something , unless you know how to make things that precise . and one of the things that they made that precise are things like their structures . they had these standard bricks and this brick size and many of these symbols that they used were found throughout these sites . which said we do n't know whether they were controlled by one ruler or one emperor , but there was definitely a lot of cultural interchange to the point that they were using the same size bricks , they were using the same symbols , they were using the same units of measurement . and also , as you can imagine , having a unit of measurement that precise , that small implies that they were great builders . and the evidence we find today says yes , they were . this is a picture of the site at mohenjo-daro in modern-day sindh pakistan , and you can see how tight this brick work is , even by modern standards this is quite good . you 'd need to think of how many things we would build would last 5,000 years in this good , being exposed to the environments . they think this was a public bath . you see a citadel in the background . we 've discovered defensive structures . perhaps most impressively , there is , or most impressive , there 's sewage systems . they think houses had wells , water . so this was a technologically advanced civilization especially for that time . in many ways , more advanced than the other civilizations , the contemporary civilizations that we had talked about . here are some examples of their sculpture or of their art . this is , this one right over here is a picture , it 's called dancing girl , but she 's not dancing , but they think that might be her profession . it 's all speculation by archaeologists today . this they believe is called priest-king , once again , it 's all speculation . this is an example of the types of seals they made . this is their jewelry , once again , this is quite intricate jewelry , and this jewelry was not just discovered in archaeological digs in these various sites . there 's evidence of their jewelry as far as mesopotamia in digs there . and they believe that there was actually a very active maritime trade network between these areas . there 's jewelry discovered in these indus valley civilizations that were based on shells from the arabian peninsula . they have materials from china , so there 's materials from other parts of india , so once again , a very very extensive trade network . these civilizations would have known about them . but as we said , they were extremely , they seemed somewhat organized . even though we ca n't read their writing , in fact i have some examples of their writing here . and you might notice , so this is examples of their writing and you might notice there , this is turned into a somewhat infamous symbol now , because of the nazis , this is a swastika . but the swastika was one of the symbols they used , it 's a symbol in hinduism , it 's considered a symbol of good luck . it 's something that the nazis kind of usurped and turned it into a very negative thing , but it does show this connection between that indus valley or that harappan civilization and modern cultures that are in india and things like the hindu religion . although once again , we do not know a ton about their religion because their language has n't survived and we can not decipher their actual writing . but because of their organization and the consistency , or relative consistency amongst these different sites that are so far flung , this is a large distance even on modern day terms , but especially if we 're talking about four or five thousand years ago . because of that , we think that , okay , there must have been at least decent government administration or organization at a city-state level , although we 're unsure whether there was a connected empire , whether you had an organization beyond that or they all just decided to take each other 's standards and symbols and brick sizes and things like that . now , one of the key mysteries of the indus valley civilization is why did it end ? it seemed to be this thriving civilization , perhaps the most extensive one . in other videos , i talk about right now , the oldest wheel was discovered in mesopotamia , but some people think that the wheel might have been used even earlier in the indus valley civilization . i talk about this period , as early as 3300 bce , but there 's evidence that the civilization started much earlier . in the site right over here in mehrgarh , right over here in pakistan . they think that humans were having simple villages and agriculture as early , there 's evidence as early as 7000 bce and that site was discovered just in 1974 . we might discover things that take us even further into the past , and when you have a civilization that was around for so long , if there were people there as early as 7000 bce , we 're talking about it was there for thousands of years , but all of a sudden , it starts to decline . there 's evidence of less and less trade going on , less and less sophistication , and then it ends . and it 's one of the mysteries of history , of archaeology today . why did this indus valley civilization end ? some of the older theories were it was maybe it was a foreign invasion , maybe some of the ancestors of the modern indians invaded , or maybe they assimilated it somehow . more current theories do n't think that was the case . they think it might be some form of climate change , that some of the important rivers dried up , made the agriculture much harder . some people think it might have been a natural disaster , it might have been a flood of some kind . but we just do n't know . or the people , for some reason , decided to leave , die , migrate to maybe other parts of the region . but needless to say , it was a significant civilization , and we 're just scratching the surface of what we know about it . we know a lot and we know it was impressive , even though we ca n't read their script and we do n't know as much about it as we know about ancient mesopotamia and the ancient egyptians , but signs are that as more time passes , we 'll realize that it was more and more sophisticated and impressive than maybe we even appreciate today .
|
and it 's one of the mysteries of history , of archaeology today . why did this indus valley civilization end ? some of the older theories were it was maybe it was a foreign invasion , maybe some of the ancestors of the modern indians invaded , or maybe they assimilated it somehow .
|
what does it mean for a civilization to end ?
|
as we 've talked about in multiple videos , some of the earliest civilizations we have found have been around river valleys , and that is no coincidence because some of the first agriculture emerged around river valleys and the agriculture supported higher population densities and more sedentary populations , and allowed for more specialization . and we have talked about several of these , the ancient egyptians around the nile river , the ancient mesopotamians around the tigris and euphrates . and now we 're gon na talk about the ancient civilization around the indus river . the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization . now to get ourselves acquainted in time , this shows when archaeologists , historians consider to be the main part of the harappan civilization . there 's evidence that people had basic villages , civilizations , agriculture here , as far back as 7,000 bce , and that 's just based on the evidence we have today , but when people refer to the indus valley civilization in particular , they 're usually staring around 3300 bce and in orange right over here , this is the early period , or you could say the early indus valley civilization . now some of the biggest structures and pieces of technology that have been discovered have been right over here , which is often referred to as the mature period for the indus valley civilization , and then it goes into decline . we 'll talk about why it might have gone into decline , although we 're not really sure , and this is called the late . now to put it in context relative to these other civilizations , remember the ancient sumerians were starting to be quite , i guess you could say civilized , by about this period . you start having a lot of intermingling between the acadians and the sumerians as you get into the late third millennium . that 's when you have the empire of sargon the great , the acadian empire . as you get to the end of this mature period right over here , this is close to or around the time of hammurabi , the babylonian empire , and in egypt , if you go back to around 2500 , around this time , that 's when the pyramids were built and you have the egyptian kings , these god-kings that were ruling for most of this period right over here and as we 'll see , there was actually , we believe , a good bit of cultural interchange between the significant civilizations . now just to appreciate how extensive this indus valley civilization was , i will show you this map . and this map , it 's zoomed in of that region around the indus valley that i just showed you . this is a map of most of pakistan here , and these red squares are places where they have found evidence of the civilization . the first place was harappa , right over here , the punjab region of pakistan . and that 's why it 's called the harappan civilization . but as you can see , it 's much more than just around harappa . the largest site is at mohenjo-daro , right over here in the sindh region of pakistan and it 's believed that as many as 40,000 people lived in that city that we now , or that site , that we now call mohenjo-daro . and so far , we have discovered over 1,000 sites in this area and we believe that as many as five million people might have been part of the civilization . now the reason why we think it is a civilization and now , and let me actually keep scrolling around so you appreciate the extent of it . there 's sites in mainly , many in pakistan that you see here . there 's also quite a few in modern-day india right over here , so it 's an extensive network of these sites and the reason why we think it 's one civilization , or at least a connected culture , is that you find a lot of standardization . you find standardization in their weights and measures . in fact , they have a unit of measurement that 's as small as 1.6 millimeters , and the reason why that 's important is you would n't create a unit of measurement of 1.6 millimeters unless you knew how to use something , unless you know how to make things that precise . and one of the things that they made that precise are things like their structures . they had these standard bricks and this brick size and many of these symbols that they used were found throughout these sites . which said we do n't know whether they were controlled by one ruler or one emperor , but there was definitely a lot of cultural interchange to the point that they were using the same size bricks , they were using the same symbols , they were using the same units of measurement . and also , as you can imagine , having a unit of measurement that precise , that small implies that they were great builders . and the evidence we find today says yes , they were . this is a picture of the site at mohenjo-daro in modern-day sindh pakistan , and you can see how tight this brick work is , even by modern standards this is quite good . you 'd need to think of how many things we would build would last 5,000 years in this good , being exposed to the environments . they think this was a public bath . you see a citadel in the background . we 've discovered defensive structures . perhaps most impressively , there is , or most impressive , there 's sewage systems . they think houses had wells , water . so this was a technologically advanced civilization especially for that time . in many ways , more advanced than the other civilizations , the contemporary civilizations that we had talked about . here are some examples of their sculpture or of their art . this is , this one right over here is a picture , it 's called dancing girl , but she 's not dancing , but they think that might be her profession . it 's all speculation by archaeologists today . this they believe is called priest-king , once again , it 's all speculation . this is an example of the types of seals they made . this is their jewelry , once again , this is quite intricate jewelry , and this jewelry was not just discovered in archaeological digs in these various sites . there 's evidence of their jewelry as far as mesopotamia in digs there . and they believe that there was actually a very active maritime trade network between these areas . there 's jewelry discovered in these indus valley civilizations that were based on shells from the arabian peninsula . they have materials from china , so there 's materials from other parts of india , so once again , a very very extensive trade network . these civilizations would have known about them . but as we said , they were extremely , they seemed somewhat organized . even though we ca n't read their writing , in fact i have some examples of their writing here . and you might notice , so this is examples of their writing and you might notice there , this is turned into a somewhat infamous symbol now , because of the nazis , this is a swastika . but the swastika was one of the symbols they used , it 's a symbol in hinduism , it 's considered a symbol of good luck . it 's something that the nazis kind of usurped and turned it into a very negative thing , but it does show this connection between that indus valley or that harappan civilization and modern cultures that are in india and things like the hindu religion . although once again , we do not know a ton about their religion because their language has n't survived and we can not decipher their actual writing . but because of their organization and the consistency , or relative consistency amongst these different sites that are so far flung , this is a large distance even on modern day terms , but especially if we 're talking about four or five thousand years ago . because of that , we think that , okay , there must have been at least decent government administration or organization at a city-state level , although we 're unsure whether there was a connected empire , whether you had an organization beyond that or they all just decided to take each other 's standards and symbols and brick sizes and things like that . now , one of the key mysteries of the indus valley civilization is why did it end ? it seemed to be this thriving civilization , perhaps the most extensive one . in other videos , i talk about right now , the oldest wheel was discovered in mesopotamia , but some people think that the wheel might have been used even earlier in the indus valley civilization . i talk about this period , as early as 3300 bce , but there 's evidence that the civilization started much earlier . in the site right over here in mehrgarh , right over here in pakistan . they think that humans were having simple villages and agriculture as early , there 's evidence as early as 7000 bce and that site was discovered just in 1974 . we might discover things that take us even further into the past , and when you have a civilization that was around for so long , if there were people there as early as 7000 bce , we 're talking about it was there for thousands of years , but all of a sudden , it starts to decline . there 's evidence of less and less trade going on , less and less sophistication , and then it ends . and it 's one of the mysteries of history , of archaeology today . why did this indus valley civilization end ? some of the older theories were it was maybe it was a foreign invasion , maybe some of the ancestors of the modern indians invaded , or maybe they assimilated it somehow . more current theories do n't think that was the case . they think it might be some form of climate change , that some of the important rivers dried up , made the agriculture much harder . some people think it might have been a natural disaster , it might have been a flood of some kind . but we just do n't know . or the people , for some reason , decided to leave , die , migrate to maybe other parts of the region . but needless to say , it was a significant civilization , and we 're just scratching the surface of what we know about it . we know a lot and we know it was impressive , even though we ca n't read their script and we do n't know as much about it as we know about ancient mesopotamia and the ancient egyptians , but signs are that as more time passes , we 'll realize that it was more and more sophisticated and impressive than maybe we even appreciate today .
|
the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization .
|
how do you define when a civilization ended ?
|
as we 've talked about in multiple videos , some of the earliest civilizations we have found have been around river valleys , and that is no coincidence because some of the first agriculture emerged around river valleys and the agriculture supported higher population densities and more sedentary populations , and allowed for more specialization . and we have talked about several of these , the ancient egyptians around the nile river , the ancient mesopotamians around the tigris and euphrates . and now we 're gon na talk about the ancient civilization around the indus river . the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization . now to get ourselves acquainted in time , this shows when archaeologists , historians consider to be the main part of the harappan civilization . there 's evidence that people had basic villages , civilizations , agriculture here , as far back as 7,000 bce , and that 's just based on the evidence we have today , but when people refer to the indus valley civilization in particular , they 're usually staring around 3300 bce and in orange right over here , this is the early period , or you could say the early indus valley civilization . now some of the biggest structures and pieces of technology that have been discovered have been right over here , which is often referred to as the mature period for the indus valley civilization , and then it goes into decline . we 'll talk about why it might have gone into decline , although we 're not really sure , and this is called the late . now to put it in context relative to these other civilizations , remember the ancient sumerians were starting to be quite , i guess you could say civilized , by about this period . you start having a lot of intermingling between the acadians and the sumerians as you get into the late third millennium . that 's when you have the empire of sargon the great , the acadian empire . as you get to the end of this mature period right over here , this is close to or around the time of hammurabi , the babylonian empire , and in egypt , if you go back to around 2500 , around this time , that 's when the pyramids were built and you have the egyptian kings , these god-kings that were ruling for most of this period right over here and as we 'll see , there was actually , we believe , a good bit of cultural interchange between the significant civilizations . now just to appreciate how extensive this indus valley civilization was , i will show you this map . and this map , it 's zoomed in of that region around the indus valley that i just showed you . this is a map of most of pakistan here , and these red squares are places where they have found evidence of the civilization . the first place was harappa , right over here , the punjab region of pakistan . and that 's why it 's called the harappan civilization . but as you can see , it 's much more than just around harappa . the largest site is at mohenjo-daro , right over here in the sindh region of pakistan and it 's believed that as many as 40,000 people lived in that city that we now , or that site , that we now call mohenjo-daro . and so far , we have discovered over 1,000 sites in this area and we believe that as many as five million people might have been part of the civilization . now the reason why we think it is a civilization and now , and let me actually keep scrolling around so you appreciate the extent of it . there 's sites in mainly , many in pakistan that you see here . there 's also quite a few in modern-day india right over here , so it 's an extensive network of these sites and the reason why we think it 's one civilization , or at least a connected culture , is that you find a lot of standardization . you find standardization in their weights and measures . in fact , they have a unit of measurement that 's as small as 1.6 millimeters , and the reason why that 's important is you would n't create a unit of measurement of 1.6 millimeters unless you knew how to use something , unless you know how to make things that precise . and one of the things that they made that precise are things like their structures . they had these standard bricks and this brick size and many of these symbols that they used were found throughout these sites . which said we do n't know whether they were controlled by one ruler or one emperor , but there was definitely a lot of cultural interchange to the point that they were using the same size bricks , they were using the same symbols , they were using the same units of measurement . and also , as you can imagine , having a unit of measurement that precise , that small implies that they were great builders . and the evidence we find today says yes , they were . this is a picture of the site at mohenjo-daro in modern-day sindh pakistan , and you can see how tight this brick work is , even by modern standards this is quite good . you 'd need to think of how many things we would build would last 5,000 years in this good , being exposed to the environments . they think this was a public bath . you see a citadel in the background . we 've discovered defensive structures . perhaps most impressively , there is , or most impressive , there 's sewage systems . they think houses had wells , water . so this was a technologically advanced civilization especially for that time . in many ways , more advanced than the other civilizations , the contemporary civilizations that we had talked about . here are some examples of their sculpture or of their art . this is , this one right over here is a picture , it 's called dancing girl , but she 's not dancing , but they think that might be her profession . it 's all speculation by archaeologists today . this they believe is called priest-king , once again , it 's all speculation . this is an example of the types of seals they made . this is their jewelry , once again , this is quite intricate jewelry , and this jewelry was not just discovered in archaeological digs in these various sites . there 's evidence of their jewelry as far as mesopotamia in digs there . and they believe that there was actually a very active maritime trade network between these areas . there 's jewelry discovered in these indus valley civilizations that were based on shells from the arabian peninsula . they have materials from china , so there 's materials from other parts of india , so once again , a very very extensive trade network . these civilizations would have known about them . but as we said , they were extremely , they seemed somewhat organized . even though we ca n't read their writing , in fact i have some examples of their writing here . and you might notice , so this is examples of their writing and you might notice there , this is turned into a somewhat infamous symbol now , because of the nazis , this is a swastika . but the swastika was one of the symbols they used , it 's a symbol in hinduism , it 's considered a symbol of good luck . it 's something that the nazis kind of usurped and turned it into a very negative thing , but it does show this connection between that indus valley or that harappan civilization and modern cultures that are in india and things like the hindu religion . although once again , we do not know a ton about their religion because their language has n't survived and we can not decipher their actual writing . but because of their organization and the consistency , or relative consistency amongst these different sites that are so far flung , this is a large distance even on modern day terms , but especially if we 're talking about four or five thousand years ago . because of that , we think that , okay , there must have been at least decent government administration or organization at a city-state level , although we 're unsure whether there was a connected empire , whether you had an organization beyond that or they all just decided to take each other 's standards and symbols and brick sizes and things like that . now , one of the key mysteries of the indus valley civilization is why did it end ? it seemed to be this thriving civilization , perhaps the most extensive one . in other videos , i talk about right now , the oldest wheel was discovered in mesopotamia , but some people think that the wheel might have been used even earlier in the indus valley civilization . i talk about this period , as early as 3300 bce , but there 's evidence that the civilization started much earlier . in the site right over here in mehrgarh , right over here in pakistan . they think that humans were having simple villages and agriculture as early , there 's evidence as early as 7000 bce and that site was discovered just in 1974 . we might discover things that take us even further into the past , and when you have a civilization that was around for so long , if there were people there as early as 7000 bce , we 're talking about it was there for thousands of years , but all of a sudden , it starts to decline . there 's evidence of less and less trade going on , less and less sophistication , and then it ends . and it 's one of the mysteries of history , of archaeology today . why did this indus valley civilization end ? some of the older theories were it was maybe it was a foreign invasion , maybe some of the ancestors of the modern indians invaded , or maybe they assimilated it somehow . more current theories do n't think that was the case . they think it might be some form of climate change , that some of the important rivers dried up , made the agriculture much harder . some people think it might have been a natural disaster , it might have been a flood of some kind . but we just do n't know . or the people , for some reason , decided to leave , die , migrate to maybe other parts of the region . but needless to say , it was a significant civilization , and we 're just scratching the surface of what we know about it . we know a lot and we know it was impressive , even though we ca n't read their script and we do n't know as much about it as we know about ancient mesopotamia and the ancient egyptians , but signs are that as more time passes , we 'll realize that it was more and more sophisticated and impressive than maybe we even appreciate today .
|
the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization .
|
do we know of any wars between the harappan civilization and any other groups ?
|
as we 've talked about in multiple videos , some of the earliest civilizations we have found have been around river valleys , and that is no coincidence because some of the first agriculture emerged around river valleys and the agriculture supported higher population densities and more sedentary populations , and allowed for more specialization . and we have talked about several of these , the ancient egyptians around the nile river , the ancient mesopotamians around the tigris and euphrates . and now we 're gon na talk about the ancient civilization around the indus river . the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization . now to get ourselves acquainted in time , this shows when archaeologists , historians consider to be the main part of the harappan civilization . there 's evidence that people had basic villages , civilizations , agriculture here , as far back as 7,000 bce , and that 's just based on the evidence we have today , but when people refer to the indus valley civilization in particular , they 're usually staring around 3300 bce and in orange right over here , this is the early period , or you could say the early indus valley civilization . now some of the biggest structures and pieces of technology that have been discovered have been right over here , which is often referred to as the mature period for the indus valley civilization , and then it goes into decline . we 'll talk about why it might have gone into decline , although we 're not really sure , and this is called the late . now to put it in context relative to these other civilizations , remember the ancient sumerians were starting to be quite , i guess you could say civilized , by about this period . you start having a lot of intermingling between the acadians and the sumerians as you get into the late third millennium . that 's when you have the empire of sargon the great , the acadian empire . as you get to the end of this mature period right over here , this is close to or around the time of hammurabi , the babylonian empire , and in egypt , if you go back to around 2500 , around this time , that 's when the pyramids were built and you have the egyptian kings , these god-kings that were ruling for most of this period right over here and as we 'll see , there was actually , we believe , a good bit of cultural interchange between the significant civilizations . now just to appreciate how extensive this indus valley civilization was , i will show you this map . and this map , it 's zoomed in of that region around the indus valley that i just showed you . this is a map of most of pakistan here , and these red squares are places where they have found evidence of the civilization . the first place was harappa , right over here , the punjab region of pakistan . and that 's why it 's called the harappan civilization . but as you can see , it 's much more than just around harappa . the largest site is at mohenjo-daro , right over here in the sindh region of pakistan and it 's believed that as many as 40,000 people lived in that city that we now , or that site , that we now call mohenjo-daro . and so far , we have discovered over 1,000 sites in this area and we believe that as many as five million people might have been part of the civilization . now the reason why we think it is a civilization and now , and let me actually keep scrolling around so you appreciate the extent of it . there 's sites in mainly , many in pakistan that you see here . there 's also quite a few in modern-day india right over here , so it 's an extensive network of these sites and the reason why we think it 's one civilization , or at least a connected culture , is that you find a lot of standardization . you find standardization in their weights and measures . in fact , they have a unit of measurement that 's as small as 1.6 millimeters , and the reason why that 's important is you would n't create a unit of measurement of 1.6 millimeters unless you knew how to use something , unless you know how to make things that precise . and one of the things that they made that precise are things like their structures . they had these standard bricks and this brick size and many of these symbols that they used were found throughout these sites . which said we do n't know whether they were controlled by one ruler or one emperor , but there was definitely a lot of cultural interchange to the point that they were using the same size bricks , they were using the same symbols , they were using the same units of measurement . and also , as you can imagine , having a unit of measurement that precise , that small implies that they were great builders . and the evidence we find today says yes , they were . this is a picture of the site at mohenjo-daro in modern-day sindh pakistan , and you can see how tight this brick work is , even by modern standards this is quite good . you 'd need to think of how many things we would build would last 5,000 years in this good , being exposed to the environments . they think this was a public bath . you see a citadel in the background . we 've discovered defensive structures . perhaps most impressively , there is , or most impressive , there 's sewage systems . they think houses had wells , water . so this was a technologically advanced civilization especially for that time . in many ways , more advanced than the other civilizations , the contemporary civilizations that we had talked about . here are some examples of their sculpture or of their art . this is , this one right over here is a picture , it 's called dancing girl , but she 's not dancing , but they think that might be her profession . it 's all speculation by archaeologists today . this they believe is called priest-king , once again , it 's all speculation . this is an example of the types of seals they made . this is their jewelry , once again , this is quite intricate jewelry , and this jewelry was not just discovered in archaeological digs in these various sites . there 's evidence of their jewelry as far as mesopotamia in digs there . and they believe that there was actually a very active maritime trade network between these areas . there 's jewelry discovered in these indus valley civilizations that were based on shells from the arabian peninsula . they have materials from china , so there 's materials from other parts of india , so once again , a very very extensive trade network . these civilizations would have known about them . but as we said , they were extremely , they seemed somewhat organized . even though we ca n't read their writing , in fact i have some examples of their writing here . and you might notice , so this is examples of their writing and you might notice there , this is turned into a somewhat infamous symbol now , because of the nazis , this is a swastika . but the swastika was one of the symbols they used , it 's a symbol in hinduism , it 's considered a symbol of good luck . it 's something that the nazis kind of usurped and turned it into a very negative thing , but it does show this connection between that indus valley or that harappan civilization and modern cultures that are in india and things like the hindu religion . although once again , we do not know a ton about their religion because their language has n't survived and we can not decipher their actual writing . but because of their organization and the consistency , or relative consistency amongst these different sites that are so far flung , this is a large distance even on modern day terms , but especially if we 're talking about four or five thousand years ago . because of that , we think that , okay , there must have been at least decent government administration or organization at a city-state level , although we 're unsure whether there was a connected empire , whether you had an organization beyond that or they all just decided to take each other 's standards and symbols and brick sizes and things like that . now , one of the key mysteries of the indus valley civilization is why did it end ? it seemed to be this thriving civilization , perhaps the most extensive one . in other videos , i talk about right now , the oldest wheel was discovered in mesopotamia , but some people think that the wheel might have been used even earlier in the indus valley civilization . i talk about this period , as early as 3300 bce , but there 's evidence that the civilization started much earlier . in the site right over here in mehrgarh , right over here in pakistan . they think that humans were having simple villages and agriculture as early , there 's evidence as early as 7000 bce and that site was discovered just in 1974 . we might discover things that take us even further into the past , and when you have a civilization that was around for so long , if there were people there as early as 7000 bce , we 're talking about it was there for thousands of years , but all of a sudden , it starts to decline . there 's evidence of less and less trade going on , less and less sophistication , and then it ends . and it 's one of the mysteries of history , of archaeology today . why did this indus valley civilization end ? some of the older theories were it was maybe it was a foreign invasion , maybe some of the ancestors of the modern indians invaded , or maybe they assimilated it somehow . more current theories do n't think that was the case . they think it might be some form of climate change , that some of the important rivers dried up , made the agriculture much harder . some people think it might have been a natural disaster , it might have been a flood of some kind . but we just do n't know . or the people , for some reason , decided to leave , die , migrate to maybe other parts of the region . but needless to say , it was a significant civilization , and we 're just scratching the surface of what we know about it . we know a lot and we know it was impressive , even though we ca n't read their script and we do n't know as much about it as we know about ancient mesopotamia and the ancient egyptians , but signs are that as more time passes , we 'll realize that it was more and more sophisticated and impressive than maybe we even appreciate today .
|
the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization .
|
there 's the trade theory indicated , but is that all of the interaction between the indus river valley and anywhere else that is known ?
|
as we 've talked about in multiple videos , some of the earliest civilizations we have found have been around river valleys , and that is no coincidence because some of the first agriculture emerged around river valleys and the agriculture supported higher population densities and more sedentary populations , and allowed for more specialization . and we have talked about several of these , the ancient egyptians around the nile river , the ancient mesopotamians around the tigris and euphrates . and now we 're gon na talk about the ancient civilization around the indus river . the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization . now to get ourselves acquainted in time , this shows when archaeologists , historians consider to be the main part of the harappan civilization . there 's evidence that people had basic villages , civilizations , agriculture here , as far back as 7,000 bce , and that 's just based on the evidence we have today , but when people refer to the indus valley civilization in particular , they 're usually staring around 3300 bce and in orange right over here , this is the early period , or you could say the early indus valley civilization . now some of the biggest structures and pieces of technology that have been discovered have been right over here , which is often referred to as the mature period for the indus valley civilization , and then it goes into decline . we 'll talk about why it might have gone into decline , although we 're not really sure , and this is called the late . now to put it in context relative to these other civilizations , remember the ancient sumerians were starting to be quite , i guess you could say civilized , by about this period . you start having a lot of intermingling between the acadians and the sumerians as you get into the late third millennium . that 's when you have the empire of sargon the great , the acadian empire . as you get to the end of this mature period right over here , this is close to or around the time of hammurabi , the babylonian empire , and in egypt , if you go back to around 2500 , around this time , that 's when the pyramids were built and you have the egyptian kings , these god-kings that were ruling for most of this period right over here and as we 'll see , there was actually , we believe , a good bit of cultural interchange between the significant civilizations . now just to appreciate how extensive this indus valley civilization was , i will show you this map . and this map , it 's zoomed in of that region around the indus valley that i just showed you . this is a map of most of pakistan here , and these red squares are places where they have found evidence of the civilization . the first place was harappa , right over here , the punjab region of pakistan . and that 's why it 's called the harappan civilization . but as you can see , it 's much more than just around harappa . the largest site is at mohenjo-daro , right over here in the sindh region of pakistan and it 's believed that as many as 40,000 people lived in that city that we now , or that site , that we now call mohenjo-daro . and so far , we have discovered over 1,000 sites in this area and we believe that as many as five million people might have been part of the civilization . now the reason why we think it is a civilization and now , and let me actually keep scrolling around so you appreciate the extent of it . there 's sites in mainly , many in pakistan that you see here . there 's also quite a few in modern-day india right over here , so it 's an extensive network of these sites and the reason why we think it 's one civilization , or at least a connected culture , is that you find a lot of standardization . you find standardization in their weights and measures . in fact , they have a unit of measurement that 's as small as 1.6 millimeters , and the reason why that 's important is you would n't create a unit of measurement of 1.6 millimeters unless you knew how to use something , unless you know how to make things that precise . and one of the things that they made that precise are things like their structures . they had these standard bricks and this brick size and many of these symbols that they used were found throughout these sites . which said we do n't know whether they were controlled by one ruler or one emperor , but there was definitely a lot of cultural interchange to the point that they were using the same size bricks , they were using the same symbols , they were using the same units of measurement . and also , as you can imagine , having a unit of measurement that precise , that small implies that they were great builders . and the evidence we find today says yes , they were . this is a picture of the site at mohenjo-daro in modern-day sindh pakistan , and you can see how tight this brick work is , even by modern standards this is quite good . you 'd need to think of how many things we would build would last 5,000 years in this good , being exposed to the environments . they think this was a public bath . you see a citadel in the background . we 've discovered defensive structures . perhaps most impressively , there is , or most impressive , there 's sewage systems . they think houses had wells , water . so this was a technologically advanced civilization especially for that time . in many ways , more advanced than the other civilizations , the contemporary civilizations that we had talked about . here are some examples of their sculpture or of their art . this is , this one right over here is a picture , it 's called dancing girl , but she 's not dancing , but they think that might be her profession . it 's all speculation by archaeologists today . this they believe is called priest-king , once again , it 's all speculation . this is an example of the types of seals they made . this is their jewelry , once again , this is quite intricate jewelry , and this jewelry was not just discovered in archaeological digs in these various sites . there 's evidence of their jewelry as far as mesopotamia in digs there . and they believe that there was actually a very active maritime trade network between these areas . there 's jewelry discovered in these indus valley civilizations that were based on shells from the arabian peninsula . they have materials from china , so there 's materials from other parts of india , so once again , a very very extensive trade network . these civilizations would have known about them . but as we said , they were extremely , they seemed somewhat organized . even though we ca n't read their writing , in fact i have some examples of their writing here . and you might notice , so this is examples of their writing and you might notice there , this is turned into a somewhat infamous symbol now , because of the nazis , this is a swastika . but the swastika was one of the symbols they used , it 's a symbol in hinduism , it 's considered a symbol of good luck . it 's something that the nazis kind of usurped and turned it into a very negative thing , but it does show this connection between that indus valley or that harappan civilization and modern cultures that are in india and things like the hindu religion . although once again , we do not know a ton about their religion because their language has n't survived and we can not decipher their actual writing . but because of their organization and the consistency , or relative consistency amongst these different sites that are so far flung , this is a large distance even on modern day terms , but especially if we 're talking about four or five thousand years ago . because of that , we think that , okay , there must have been at least decent government administration or organization at a city-state level , although we 're unsure whether there was a connected empire , whether you had an organization beyond that or they all just decided to take each other 's standards and symbols and brick sizes and things like that . now , one of the key mysteries of the indus valley civilization is why did it end ? it seemed to be this thriving civilization , perhaps the most extensive one . in other videos , i talk about right now , the oldest wheel was discovered in mesopotamia , but some people think that the wheel might have been used even earlier in the indus valley civilization . i talk about this period , as early as 3300 bce , but there 's evidence that the civilization started much earlier . in the site right over here in mehrgarh , right over here in pakistan . they think that humans were having simple villages and agriculture as early , there 's evidence as early as 7000 bce and that site was discovered just in 1974 . we might discover things that take us even further into the past , and when you have a civilization that was around for so long , if there were people there as early as 7000 bce , we 're talking about it was there for thousands of years , but all of a sudden , it starts to decline . there 's evidence of less and less trade going on , less and less sophistication , and then it ends . and it 's one of the mysteries of history , of archaeology today . why did this indus valley civilization end ? some of the older theories were it was maybe it was a foreign invasion , maybe some of the ancestors of the modern indians invaded , or maybe they assimilated it somehow . more current theories do n't think that was the case . they think it might be some form of climate change , that some of the important rivers dried up , made the agriculture much harder . some people think it might have been a natural disaster , it might have been a flood of some kind . but we just do n't know . or the people , for some reason , decided to leave , die , migrate to maybe other parts of the region . but needless to say , it was a significant civilization , and we 're just scratching the surface of what we know about it . we know a lot and we know it was impressive , even though we ca n't read their script and we do n't know as much about it as we know about ancient mesopotamia and the ancient egyptians , but signs are that as more time passes , we 'll realize that it was more and more sophisticated and impressive than maybe we even appreciate today .
|
this is , this one right over here is a picture , it 's called dancing girl , but she 's not dancing , but they think that might be her profession . it 's all speculation by archaeologists today . this they believe is called priest-king , once again , it 's all speculation .
|
is anyone today trying to decipher the old language ?
|
as we 've talked about in multiple videos , some of the earliest civilizations we have found have been around river valleys , and that is no coincidence because some of the first agriculture emerged around river valleys and the agriculture supported higher population densities and more sedentary populations , and allowed for more specialization . and we have talked about several of these , the ancient egyptians around the nile river , the ancient mesopotamians around the tigris and euphrates . and now we 're gon na talk about the ancient civilization around the indus river . the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization . now to get ourselves acquainted in time , this shows when archaeologists , historians consider to be the main part of the harappan civilization . there 's evidence that people had basic villages , civilizations , agriculture here , as far back as 7,000 bce , and that 's just based on the evidence we have today , but when people refer to the indus valley civilization in particular , they 're usually staring around 3300 bce and in orange right over here , this is the early period , or you could say the early indus valley civilization . now some of the biggest structures and pieces of technology that have been discovered have been right over here , which is often referred to as the mature period for the indus valley civilization , and then it goes into decline . we 'll talk about why it might have gone into decline , although we 're not really sure , and this is called the late . now to put it in context relative to these other civilizations , remember the ancient sumerians were starting to be quite , i guess you could say civilized , by about this period . you start having a lot of intermingling between the acadians and the sumerians as you get into the late third millennium . that 's when you have the empire of sargon the great , the acadian empire . as you get to the end of this mature period right over here , this is close to or around the time of hammurabi , the babylonian empire , and in egypt , if you go back to around 2500 , around this time , that 's when the pyramids were built and you have the egyptian kings , these god-kings that were ruling for most of this period right over here and as we 'll see , there was actually , we believe , a good bit of cultural interchange between the significant civilizations . now just to appreciate how extensive this indus valley civilization was , i will show you this map . and this map , it 's zoomed in of that region around the indus valley that i just showed you . this is a map of most of pakistan here , and these red squares are places where they have found evidence of the civilization . the first place was harappa , right over here , the punjab region of pakistan . and that 's why it 's called the harappan civilization . but as you can see , it 's much more than just around harappa . the largest site is at mohenjo-daro , right over here in the sindh region of pakistan and it 's believed that as many as 40,000 people lived in that city that we now , or that site , that we now call mohenjo-daro . and so far , we have discovered over 1,000 sites in this area and we believe that as many as five million people might have been part of the civilization . now the reason why we think it is a civilization and now , and let me actually keep scrolling around so you appreciate the extent of it . there 's sites in mainly , many in pakistan that you see here . there 's also quite a few in modern-day india right over here , so it 's an extensive network of these sites and the reason why we think it 's one civilization , or at least a connected culture , is that you find a lot of standardization . you find standardization in their weights and measures . in fact , they have a unit of measurement that 's as small as 1.6 millimeters , and the reason why that 's important is you would n't create a unit of measurement of 1.6 millimeters unless you knew how to use something , unless you know how to make things that precise . and one of the things that they made that precise are things like their structures . they had these standard bricks and this brick size and many of these symbols that they used were found throughout these sites . which said we do n't know whether they were controlled by one ruler or one emperor , but there was definitely a lot of cultural interchange to the point that they were using the same size bricks , they were using the same symbols , they were using the same units of measurement . and also , as you can imagine , having a unit of measurement that precise , that small implies that they were great builders . and the evidence we find today says yes , they were . this is a picture of the site at mohenjo-daro in modern-day sindh pakistan , and you can see how tight this brick work is , even by modern standards this is quite good . you 'd need to think of how many things we would build would last 5,000 years in this good , being exposed to the environments . they think this was a public bath . you see a citadel in the background . we 've discovered defensive structures . perhaps most impressively , there is , or most impressive , there 's sewage systems . they think houses had wells , water . so this was a technologically advanced civilization especially for that time . in many ways , more advanced than the other civilizations , the contemporary civilizations that we had talked about . here are some examples of their sculpture or of their art . this is , this one right over here is a picture , it 's called dancing girl , but she 's not dancing , but they think that might be her profession . it 's all speculation by archaeologists today . this they believe is called priest-king , once again , it 's all speculation . this is an example of the types of seals they made . this is their jewelry , once again , this is quite intricate jewelry , and this jewelry was not just discovered in archaeological digs in these various sites . there 's evidence of their jewelry as far as mesopotamia in digs there . and they believe that there was actually a very active maritime trade network between these areas . there 's jewelry discovered in these indus valley civilizations that were based on shells from the arabian peninsula . they have materials from china , so there 's materials from other parts of india , so once again , a very very extensive trade network . these civilizations would have known about them . but as we said , they were extremely , they seemed somewhat organized . even though we ca n't read their writing , in fact i have some examples of their writing here . and you might notice , so this is examples of their writing and you might notice there , this is turned into a somewhat infamous symbol now , because of the nazis , this is a swastika . but the swastika was one of the symbols they used , it 's a symbol in hinduism , it 's considered a symbol of good luck . it 's something that the nazis kind of usurped and turned it into a very negative thing , but it does show this connection between that indus valley or that harappan civilization and modern cultures that are in india and things like the hindu religion . although once again , we do not know a ton about their religion because their language has n't survived and we can not decipher their actual writing . but because of their organization and the consistency , or relative consistency amongst these different sites that are so far flung , this is a large distance even on modern day terms , but especially if we 're talking about four or five thousand years ago . because of that , we think that , okay , there must have been at least decent government administration or organization at a city-state level , although we 're unsure whether there was a connected empire , whether you had an organization beyond that or they all just decided to take each other 's standards and symbols and brick sizes and things like that . now , one of the key mysteries of the indus valley civilization is why did it end ? it seemed to be this thriving civilization , perhaps the most extensive one . in other videos , i talk about right now , the oldest wheel was discovered in mesopotamia , but some people think that the wheel might have been used even earlier in the indus valley civilization . i talk about this period , as early as 3300 bce , but there 's evidence that the civilization started much earlier . in the site right over here in mehrgarh , right over here in pakistan . they think that humans were having simple villages and agriculture as early , there 's evidence as early as 7000 bce and that site was discovered just in 1974 . we might discover things that take us even further into the past , and when you have a civilization that was around for so long , if there were people there as early as 7000 bce , we 're talking about it was there for thousands of years , but all of a sudden , it starts to decline . there 's evidence of less and less trade going on , less and less sophistication , and then it ends . and it 's one of the mysteries of history , of archaeology today . why did this indus valley civilization end ? some of the older theories were it was maybe it was a foreign invasion , maybe some of the ancestors of the modern indians invaded , or maybe they assimilated it somehow . more current theories do n't think that was the case . they think it might be some form of climate change , that some of the important rivers dried up , made the agriculture much harder . some people think it might have been a natural disaster , it might have been a flood of some kind . but we just do n't know . or the people , for some reason , decided to leave , die , migrate to maybe other parts of the region . but needless to say , it was a significant civilization , and we 're just scratching the surface of what we know about it . we know a lot and we know it was impressive , even though we ca n't read their script and we do n't know as much about it as we know about ancient mesopotamia and the ancient egyptians , but signs are that as more time passes , we 'll realize that it was more and more sophisticated and impressive than maybe we even appreciate today .
|
the largest site is at mohenjo-daro , right over here in the sindh region of pakistan and it 's believed that as many as 40,000 people lived in that city that we now , or that site , that we now call mohenjo-daro . and so far , we have discovered over 1,000 sites in this area and we believe that as many as five million people might have been part of the civilization . now the reason why we think it is a civilization and now , and let me actually keep scrolling around so you appreciate the extent of it .
|
how is the size of the population determined ... in one area you say there were 40,000 and in another you say 4 million ?
|
as we 've talked about in multiple videos , some of the earliest civilizations we have found have been around river valleys , and that is no coincidence because some of the first agriculture emerged around river valleys and the agriculture supported higher population densities and more sedentary populations , and allowed for more specialization . and we have talked about several of these , the ancient egyptians around the nile river , the ancient mesopotamians around the tigris and euphrates . and now we 're gon na talk about the ancient civilization around the indus river . the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization . now to get ourselves acquainted in time , this shows when archaeologists , historians consider to be the main part of the harappan civilization . there 's evidence that people had basic villages , civilizations , agriculture here , as far back as 7,000 bce , and that 's just based on the evidence we have today , but when people refer to the indus valley civilization in particular , they 're usually staring around 3300 bce and in orange right over here , this is the early period , or you could say the early indus valley civilization . now some of the biggest structures and pieces of technology that have been discovered have been right over here , which is often referred to as the mature period for the indus valley civilization , and then it goes into decline . we 'll talk about why it might have gone into decline , although we 're not really sure , and this is called the late . now to put it in context relative to these other civilizations , remember the ancient sumerians were starting to be quite , i guess you could say civilized , by about this period . you start having a lot of intermingling between the acadians and the sumerians as you get into the late third millennium . that 's when you have the empire of sargon the great , the acadian empire . as you get to the end of this mature period right over here , this is close to or around the time of hammurabi , the babylonian empire , and in egypt , if you go back to around 2500 , around this time , that 's when the pyramids were built and you have the egyptian kings , these god-kings that were ruling for most of this period right over here and as we 'll see , there was actually , we believe , a good bit of cultural interchange between the significant civilizations . now just to appreciate how extensive this indus valley civilization was , i will show you this map . and this map , it 's zoomed in of that region around the indus valley that i just showed you . this is a map of most of pakistan here , and these red squares are places where they have found evidence of the civilization . the first place was harappa , right over here , the punjab region of pakistan . and that 's why it 's called the harappan civilization . but as you can see , it 's much more than just around harappa . the largest site is at mohenjo-daro , right over here in the sindh region of pakistan and it 's believed that as many as 40,000 people lived in that city that we now , or that site , that we now call mohenjo-daro . and so far , we have discovered over 1,000 sites in this area and we believe that as many as five million people might have been part of the civilization . now the reason why we think it is a civilization and now , and let me actually keep scrolling around so you appreciate the extent of it . there 's sites in mainly , many in pakistan that you see here . there 's also quite a few in modern-day india right over here , so it 's an extensive network of these sites and the reason why we think it 's one civilization , or at least a connected culture , is that you find a lot of standardization . you find standardization in their weights and measures . in fact , they have a unit of measurement that 's as small as 1.6 millimeters , and the reason why that 's important is you would n't create a unit of measurement of 1.6 millimeters unless you knew how to use something , unless you know how to make things that precise . and one of the things that they made that precise are things like their structures . they had these standard bricks and this brick size and many of these symbols that they used were found throughout these sites . which said we do n't know whether they were controlled by one ruler or one emperor , but there was definitely a lot of cultural interchange to the point that they were using the same size bricks , they were using the same symbols , they were using the same units of measurement . and also , as you can imagine , having a unit of measurement that precise , that small implies that they were great builders . and the evidence we find today says yes , they were . this is a picture of the site at mohenjo-daro in modern-day sindh pakistan , and you can see how tight this brick work is , even by modern standards this is quite good . you 'd need to think of how many things we would build would last 5,000 years in this good , being exposed to the environments . they think this was a public bath . you see a citadel in the background . we 've discovered defensive structures . perhaps most impressively , there is , or most impressive , there 's sewage systems . they think houses had wells , water . so this was a technologically advanced civilization especially for that time . in many ways , more advanced than the other civilizations , the contemporary civilizations that we had talked about . here are some examples of their sculpture or of their art . this is , this one right over here is a picture , it 's called dancing girl , but she 's not dancing , but they think that might be her profession . it 's all speculation by archaeologists today . this they believe is called priest-king , once again , it 's all speculation . this is an example of the types of seals they made . this is their jewelry , once again , this is quite intricate jewelry , and this jewelry was not just discovered in archaeological digs in these various sites . there 's evidence of their jewelry as far as mesopotamia in digs there . and they believe that there was actually a very active maritime trade network between these areas . there 's jewelry discovered in these indus valley civilizations that were based on shells from the arabian peninsula . they have materials from china , so there 's materials from other parts of india , so once again , a very very extensive trade network . these civilizations would have known about them . but as we said , they were extremely , they seemed somewhat organized . even though we ca n't read their writing , in fact i have some examples of their writing here . and you might notice , so this is examples of their writing and you might notice there , this is turned into a somewhat infamous symbol now , because of the nazis , this is a swastika . but the swastika was one of the symbols they used , it 's a symbol in hinduism , it 's considered a symbol of good luck . it 's something that the nazis kind of usurped and turned it into a very negative thing , but it does show this connection between that indus valley or that harappan civilization and modern cultures that are in india and things like the hindu religion . although once again , we do not know a ton about their religion because their language has n't survived and we can not decipher their actual writing . but because of their organization and the consistency , or relative consistency amongst these different sites that are so far flung , this is a large distance even on modern day terms , but especially if we 're talking about four or five thousand years ago . because of that , we think that , okay , there must have been at least decent government administration or organization at a city-state level , although we 're unsure whether there was a connected empire , whether you had an organization beyond that or they all just decided to take each other 's standards and symbols and brick sizes and things like that . now , one of the key mysteries of the indus valley civilization is why did it end ? it seemed to be this thriving civilization , perhaps the most extensive one . in other videos , i talk about right now , the oldest wheel was discovered in mesopotamia , but some people think that the wheel might have been used even earlier in the indus valley civilization . i talk about this period , as early as 3300 bce , but there 's evidence that the civilization started much earlier . in the site right over here in mehrgarh , right over here in pakistan . they think that humans were having simple villages and agriculture as early , there 's evidence as early as 7000 bce and that site was discovered just in 1974 . we might discover things that take us even further into the past , and when you have a civilization that was around for so long , if there were people there as early as 7000 bce , we 're talking about it was there for thousands of years , but all of a sudden , it starts to decline . there 's evidence of less and less trade going on , less and less sophistication , and then it ends . and it 's one of the mysteries of history , of archaeology today . why did this indus valley civilization end ? some of the older theories were it was maybe it was a foreign invasion , maybe some of the ancestors of the modern indians invaded , or maybe they assimilated it somehow . more current theories do n't think that was the case . they think it might be some form of climate change , that some of the important rivers dried up , made the agriculture much harder . some people think it might have been a natural disaster , it might have been a flood of some kind . but we just do n't know . or the people , for some reason , decided to leave , die , migrate to maybe other parts of the region . but needless to say , it was a significant civilization , and we 're just scratching the surface of what we know about it . we know a lot and we know it was impressive , even though we ca n't read their script and we do n't know as much about it as we know about ancient mesopotamia and the ancient egyptians , but signs are that as more time passes , we 'll realize that it was more and more sophisticated and impressive than maybe we even appreciate today .
|
the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization .
|
is it possible that the rise of the babylonian empire caused the indus valley civilization to collapse ?
|
as we 've talked about in multiple videos , some of the earliest civilizations we have found have been around river valleys , and that is no coincidence because some of the first agriculture emerged around river valleys and the agriculture supported higher population densities and more sedentary populations , and allowed for more specialization . and we have talked about several of these , the ancient egyptians around the nile river , the ancient mesopotamians around the tigris and euphrates . and now we 're gon na talk about the ancient civilization around the indus river . the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization . now to get ourselves acquainted in time , this shows when archaeologists , historians consider to be the main part of the harappan civilization . there 's evidence that people had basic villages , civilizations , agriculture here , as far back as 7,000 bce , and that 's just based on the evidence we have today , but when people refer to the indus valley civilization in particular , they 're usually staring around 3300 bce and in orange right over here , this is the early period , or you could say the early indus valley civilization . now some of the biggest structures and pieces of technology that have been discovered have been right over here , which is often referred to as the mature period for the indus valley civilization , and then it goes into decline . we 'll talk about why it might have gone into decline , although we 're not really sure , and this is called the late . now to put it in context relative to these other civilizations , remember the ancient sumerians were starting to be quite , i guess you could say civilized , by about this period . you start having a lot of intermingling between the acadians and the sumerians as you get into the late third millennium . that 's when you have the empire of sargon the great , the acadian empire . as you get to the end of this mature period right over here , this is close to or around the time of hammurabi , the babylonian empire , and in egypt , if you go back to around 2500 , around this time , that 's when the pyramids were built and you have the egyptian kings , these god-kings that were ruling for most of this period right over here and as we 'll see , there was actually , we believe , a good bit of cultural interchange between the significant civilizations . now just to appreciate how extensive this indus valley civilization was , i will show you this map . and this map , it 's zoomed in of that region around the indus valley that i just showed you . this is a map of most of pakistan here , and these red squares are places where they have found evidence of the civilization . the first place was harappa , right over here , the punjab region of pakistan . and that 's why it 's called the harappan civilization . but as you can see , it 's much more than just around harappa . the largest site is at mohenjo-daro , right over here in the sindh region of pakistan and it 's believed that as many as 40,000 people lived in that city that we now , or that site , that we now call mohenjo-daro . and so far , we have discovered over 1,000 sites in this area and we believe that as many as five million people might have been part of the civilization . now the reason why we think it is a civilization and now , and let me actually keep scrolling around so you appreciate the extent of it . there 's sites in mainly , many in pakistan that you see here . there 's also quite a few in modern-day india right over here , so it 's an extensive network of these sites and the reason why we think it 's one civilization , or at least a connected culture , is that you find a lot of standardization . you find standardization in their weights and measures . in fact , they have a unit of measurement that 's as small as 1.6 millimeters , and the reason why that 's important is you would n't create a unit of measurement of 1.6 millimeters unless you knew how to use something , unless you know how to make things that precise . and one of the things that they made that precise are things like their structures . they had these standard bricks and this brick size and many of these symbols that they used were found throughout these sites . which said we do n't know whether they were controlled by one ruler or one emperor , but there was definitely a lot of cultural interchange to the point that they were using the same size bricks , they were using the same symbols , they were using the same units of measurement . and also , as you can imagine , having a unit of measurement that precise , that small implies that they were great builders . and the evidence we find today says yes , they were . this is a picture of the site at mohenjo-daro in modern-day sindh pakistan , and you can see how tight this brick work is , even by modern standards this is quite good . you 'd need to think of how many things we would build would last 5,000 years in this good , being exposed to the environments . they think this was a public bath . you see a citadel in the background . we 've discovered defensive structures . perhaps most impressively , there is , or most impressive , there 's sewage systems . they think houses had wells , water . so this was a technologically advanced civilization especially for that time . in many ways , more advanced than the other civilizations , the contemporary civilizations that we had talked about . here are some examples of their sculpture or of their art . this is , this one right over here is a picture , it 's called dancing girl , but she 's not dancing , but they think that might be her profession . it 's all speculation by archaeologists today . this they believe is called priest-king , once again , it 's all speculation . this is an example of the types of seals they made . this is their jewelry , once again , this is quite intricate jewelry , and this jewelry was not just discovered in archaeological digs in these various sites . there 's evidence of their jewelry as far as mesopotamia in digs there . and they believe that there was actually a very active maritime trade network between these areas . there 's jewelry discovered in these indus valley civilizations that were based on shells from the arabian peninsula . they have materials from china , so there 's materials from other parts of india , so once again , a very very extensive trade network . these civilizations would have known about them . but as we said , they were extremely , they seemed somewhat organized . even though we ca n't read their writing , in fact i have some examples of their writing here . and you might notice , so this is examples of their writing and you might notice there , this is turned into a somewhat infamous symbol now , because of the nazis , this is a swastika . but the swastika was one of the symbols they used , it 's a symbol in hinduism , it 's considered a symbol of good luck . it 's something that the nazis kind of usurped and turned it into a very negative thing , but it does show this connection between that indus valley or that harappan civilization and modern cultures that are in india and things like the hindu religion . although once again , we do not know a ton about their religion because their language has n't survived and we can not decipher their actual writing . but because of their organization and the consistency , or relative consistency amongst these different sites that are so far flung , this is a large distance even on modern day terms , but especially if we 're talking about four or five thousand years ago . because of that , we think that , okay , there must have been at least decent government administration or organization at a city-state level , although we 're unsure whether there was a connected empire , whether you had an organization beyond that or they all just decided to take each other 's standards and symbols and brick sizes and things like that . now , one of the key mysteries of the indus valley civilization is why did it end ? it seemed to be this thriving civilization , perhaps the most extensive one . in other videos , i talk about right now , the oldest wheel was discovered in mesopotamia , but some people think that the wheel might have been used even earlier in the indus valley civilization . i talk about this period , as early as 3300 bce , but there 's evidence that the civilization started much earlier . in the site right over here in mehrgarh , right over here in pakistan . they think that humans were having simple villages and agriculture as early , there 's evidence as early as 7000 bce and that site was discovered just in 1974 . we might discover things that take us even further into the past , and when you have a civilization that was around for so long , if there were people there as early as 7000 bce , we 're talking about it was there for thousands of years , but all of a sudden , it starts to decline . there 's evidence of less and less trade going on , less and less sophistication , and then it ends . and it 's one of the mysteries of history , of archaeology today . why did this indus valley civilization end ? some of the older theories were it was maybe it was a foreign invasion , maybe some of the ancestors of the modern indians invaded , or maybe they assimilated it somehow . more current theories do n't think that was the case . they think it might be some form of climate change , that some of the important rivers dried up , made the agriculture much harder . some people think it might have been a natural disaster , it might have been a flood of some kind . but we just do n't know . or the people , for some reason , decided to leave , die , migrate to maybe other parts of the region . but needless to say , it was a significant civilization , and we 're just scratching the surface of what we know about it . we know a lot and we know it was impressive , even though we ca n't read their script and we do n't know as much about it as we know about ancient mesopotamia and the ancient egyptians , but signs are that as more time passes , we 'll realize that it was more and more sophisticated and impressive than maybe we even appreciate today .
|
this is an example of the types of seals they made . this is their jewelry , once again , this is quite intricate jewelry , and this jewelry was not just discovered in archaeological digs in these various sites . there 's evidence of their jewelry as far as mesopotamia in digs there .
|
is n't it possible that the exportation of jewelry was not from ancient india ?
|
as we 've talked about in multiple videos , some of the earliest civilizations we have found have been around river valleys , and that is no coincidence because some of the first agriculture emerged around river valleys and the agriculture supported higher population densities and more sedentary populations , and allowed for more specialization . and we have talked about several of these , the ancient egyptians around the nile river , the ancient mesopotamians around the tigris and euphrates . and now we 're gon na talk about the ancient civilization around the indus river . the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization . now to get ourselves acquainted in time , this shows when archaeologists , historians consider to be the main part of the harappan civilization . there 's evidence that people had basic villages , civilizations , agriculture here , as far back as 7,000 bce , and that 's just based on the evidence we have today , but when people refer to the indus valley civilization in particular , they 're usually staring around 3300 bce and in orange right over here , this is the early period , or you could say the early indus valley civilization . now some of the biggest structures and pieces of technology that have been discovered have been right over here , which is often referred to as the mature period for the indus valley civilization , and then it goes into decline . we 'll talk about why it might have gone into decline , although we 're not really sure , and this is called the late . now to put it in context relative to these other civilizations , remember the ancient sumerians were starting to be quite , i guess you could say civilized , by about this period . you start having a lot of intermingling between the acadians and the sumerians as you get into the late third millennium . that 's when you have the empire of sargon the great , the acadian empire . as you get to the end of this mature period right over here , this is close to or around the time of hammurabi , the babylonian empire , and in egypt , if you go back to around 2500 , around this time , that 's when the pyramids were built and you have the egyptian kings , these god-kings that were ruling for most of this period right over here and as we 'll see , there was actually , we believe , a good bit of cultural interchange between the significant civilizations . now just to appreciate how extensive this indus valley civilization was , i will show you this map . and this map , it 's zoomed in of that region around the indus valley that i just showed you . this is a map of most of pakistan here , and these red squares are places where they have found evidence of the civilization . the first place was harappa , right over here , the punjab region of pakistan . and that 's why it 's called the harappan civilization . but as you can see , it 's much more than just around harappa . the largest site is at mohenjo-daro , right over here in the sindh region of pakistan and it 's believed that as many as 40,000 people lived in that city that we now , or that site , that we now call mohenjo-daro . and so far , we have discovered over 1,000 sites in this area and we believe that as many as five million people might have been part of the civilization . now the reason why we think it is a civilization and now , and let me actually keep scrolling around so you appreciate the extent of it . there 's sites in mainly , many in pakistan that you see here . there 's also quite a few in modern-day india right over here , so it 's an extensive network of these sites and the reason why we think it 's one civilization , or at least a connected culture , is that you find a lot of standardization . you find standardization in their weights and measures . in fact , they have a unit of measurement that 's as small as 1.6 millimeters , and the reason why that 's important is you would n't create a unit of measurement of 1.6 millimeters unless you knew how to use something , unless you know how to make things that precise . and one of the things that they made that precise are things like their structures . they had these standard bricks and this brick size and many of these symbols that they used were found throughout these sites . which said we do n't know whether they were controlled by one ruler or one emperor , but there was definitely a lot of cultural interchange to the point that they were using the same size bricks , they were using the same symbols , they were using the same units of measurement . and also , as you can imagine , having a unit of measurement that precise , that small implies that they were great builders . and the evidence we find today says yes , they were . this is a picture of the site at mohenjo-daro in modern-day sindh pakistan , and you can see how tight this brick work is , even by modern standards this is quite good . you 'd need to think of how many things we would build would last 5,000 years in this good , being exposed to the environments . they think this was a public bath . you see a citadel in the background . we 've discovered defensive structures . perhaps most impressively , there is , or most impressive , there 's sewage systems . they think houses had wells , water . so this was a technologically advanced civilization especially for that time . in many ways , more advanced than the other civilizations , the contemporary civilizations that we had talked about . here are some examples of their sculpture or of their art . this is , this one right over here is a picture , it 's called dancing girl , but she 's not dancing , but they think that might be her profession . it 's all speculation by archaeologists today . this they believe is called priest-king , once again , it 's all speculation . this is an example of the types of seals they made . this is their jewelry , once again , this is quite intricate jewelry , and this jewelry was not just discovered in archaeological digs in these various sites . there 's evidence of their jewelry as far as mesopotamia in digs there . and they believe that there was actually a very active maritime trade network between these areas . there 's jewelry discovered in these indus valley civilizations that were based on shells from the arabian peninsula . they have materials from china , so there 's materials from other parts of india , so once again , a very very extensive trade network . these civilizations would have known about them . but as we said , they were extremely , they seemed somewhat organized . even though we ca n't read their writing , in fact i have some examples of their writing here . and you might notice , so this is examples of their writing and you might notice there , this is turned into a somewhat infamous symbol now , because of the nazis , this is a swastika . but the swastika was one of the symbols they used , it 's a symbol in hinduism , it 's considered a symbol of good luck . it 's something that the nazis kind of usurped and turned it into a very negative thing , but it does show this connection between that indus valley or that harappan civilization and modern cultures that are in india and things like the hindu religion . although once again , we do not know a ton about their religion because their language has n't survived and we can not decipher their actual writing . but because of their organization and the consistency , or relative consistency amongst these different sites that are so far flung , this is a large distance even on modern day terms , but especially if we 're talking about four or five thousand years ago . because of that , we think that , okay , there must have been at least decent government administration or organization at a city-state level , although we 're unsure whether there was a connected empire , whether you had an organization beyond that or they all just decided to take each other 's standards and symbols and brick sizes and things like that . now , one of the key mysteries of the indus valley civilization is why did it end ? it seemed to be this thriving civilization , perhaps the most extensive one . in other videos , i talk about right now , the oldest wheel was discovered in mesopotamia , but some people think that the wheel might have been used even earlier in the indus valley civilization . i talk about this period , as early as 3300 bce , but there 's evidence that the civilization started much earlier . in the site right over here in mehrgarh , right over here in pakistan . they think that humans were having simple villages and agriculture as early , there 's evidence as early as 7000 bce and that site was discovered just in 1974 . we might discover things that take us even further into the past , and when you have a civilization that was around for so long , if there were people there as early as 7000 bce , we 're talking about it was there for thousands of years , but all of a sudden , it starts to decline . there 's evidence of less and less trade going on , less and less sophistication , and then it ends . and it 's one of the mysteries of history , of archaeology today . why did this indus valley civilization end ? some of the older theories were it was maybe it was a foreign invasion , maybe some of the ancestors of the modern indians invaded , or maybe they assimilated it somehow . more current theories do n't think that was the case . they think it might be some form of climate change , that some of the important rivers dried up , made the agriculture much harder . some people think it might have been a natural disaster , it might have been a flood of some kind . but we just do n't know . or the people , for some reason , decided to leave , die , migrate to maybe other parts of the region . but needless to say , it was a significant civilization , and we 're just scratching the surface of what we know about it . we know a lot and we know it was impressive , even though we ca n't read their script and we do n't know as much about it as we know about ancient mesopotamia and the ancient egyptians , but signs are that as more time passes , we 'll realize that it was more and more sophisticated and impressive than maybe we even appreciate today .
|
indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization . now to get ourselves acquainted in time , this shows when archaeologists , historians consider to be the main part of the harappan civilization .
|
how can we have predictions of the times of the evidences found in there ?
|
as we 've talked about in multiple videos , some of the earliest civilizations we have found have been around river valleys , and that is no coincidence because some of the first agriculture emerged around river valleys and the agriculture supported higher population densities and more sedentary populations , and allowed for more specialization . and we have talked about several of these , the ancient egyptians around the nile river , the ancient mesopotamians around the tigris and euphrates . and now we 're gon na talk about the ancient civilization around the indus river . the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization . now to get ourselves acquainted in time , this shows when archaeologists , historians consider to be the main part of the harappan civilization . there 's evidence that people had basic villages , civilizations , agriculture here , as far back as 7,000 bce , and that 's just based on the evidence we have today , but when people refer to the indus valley civilization in particular , they 're usually staring around 3300 bce and in orange right over here , this is the early period , or you could say the early indus valley civilization . now some of the biggest structures and pieces of technology that have been discovered have been right over here , which is often referred to as the mature period for the indus valley civilization , and then it goes into decline . we 'll talk about why it might have gone into decline , although we 're not really sure , and this is called the late . now to put it in context relative to these other civilizations , remember the ancient sumerians were starting to be quite , i guess you could say civilized , by about this period . you start having a lot of intermingling between the acadians and the sumerians as you get into the late third millennium . that 's when you have the empire of sargon the great , the acadian empire . as you get to the end of this mature period right over here , this is close to or around the time of hammurabi , the babylonian empire , and in egypt , if you go back to around 2500 , around this time , that 's when the pyramids were built and you have the egyptian kings , these god-kings that were ruling for most of this period right over here and as we 'll see , there was actually , we believe , a good bit of cultural interchange between the significant civilizations . now just to appreciate how extensive this indus valley civilization was , i will show you this map . and this map , it 's zoomed in of that region around the indus valley that i just showed you . this is a map of most of pakistan here , and these red squares are places where they have found evidence of the civilization . the first place was harappa , right over here , the punjab region of pakistan . and that 's why it 's called the harappan civilization . but as you can see , it 's much more than just around harappa . the largest site is at mohenjo-daro , right over here in the sindh region of pakistan and it 's believed that as many as 40,000 people lived in that city that we now , or that site , that we now call mohenjo-daro . and so far , we have discovered over 1,000 sites in this area and we believe that as many as five million people might have been part of the civilization . now the reason why we think it is a civilization and now , and let me actually keep scrolling around so you appreciate the extent of it . there 's sites in mainly , many in pakistan that you see here . there 's also quite a few in modern-day india right over here , so it 's an extensive network of these sites and the reason why we think it 's one civilization , or at least a connected culture , is that you find a lot of standardization . you find standardization in their weights and measures . in fact , they have a unit of measurement that 's as small as 1.6 millimeters , and the reason why that 's important is you would n't create a unit of measurement of 1.6 millimeters unless you knew how to use something , unless you know how to make things that precise . and one of the things that they made that precise are things like their structures . they had these standard bricks and this brick size and many of these symbols that they used were found throughout these sites . which said we do n't know whether they were controlled by one ruler or one emperor , but there was definitely a lot of cultural interchange to the point that they were using the same size bricks , they were using the same symbols , they were using the same units of measurement . and also , as you can imagine , having a unit of measurement that precise , that small implies that they were great builders . and the evidence we find today says yes , they were . this is a picture of the site at mohenjo-daro in modern-day sindh pakistan , and you can see how tight this brick work is , even by modern standards this is quite good . you 'd need to think of how many things we would build would last 5,000 years in this good , being exposed to the environments . they think this was a public bath . you see a citadel in the background . we 've discovered defensive structures . perhaps most impressively , there is , or most impressive , there 's sewage systems . they think houses had wells , water . so this was a technologically advanced civilization especially for that time . in many ways , more advanced than the other civilizations , the contemporary civilizations that we had talked about . here are some examples of their sculpture or of their art . this is , this one right over here is a picture , it 's called dancing girl , but she 's not dancing , but they think that might be her profession . it 's all speculation by archaeologists today . this they believe is called priest-king , once again , it 's all speculation . this is an example of the types of seals they made . this is their jewelry , once again , this is quite intricate jewelry , and this jewelry was not just discovered in archaeological digs in these various sites . there 's evidence of their jewelry as far as mesopotamia in digs there . and they believe that there was actually a very active maritime trade network between these areas . there 's jewelry discovered in these indus valley civilizations that were based on shells from the arabian peninsula . they have materials from china , so there 's materials from other parts of india , so once again , a very very extensive trade network . these civilizations would have known about them . but as we said , they were extremely , they seemed somewhat organized . even though we ca n't read their writing , in fact i have some examples of their writing here . and you might notice , so this is examples of their writing and you might notice there , this is turned into a somewhat infamous symbol now , because of the nazis , this is a swastika . but the swastika was one of the symbols they used , it 's a symbol in hinduism , it 's considered a symbol of good luck . it 's something that the nazis kind of usurped and turned it into a very negative thing , but it does show this connection between that indus valley or that harappan civilization and modern cultures that are in india and things like the hindu religion . although once again , we do not know a ton about their religion because their language has n't survived and we can not decipher their actual writing . but because of their organization and the consistency , or relative consistency amongst these different sites that are so far flung , this is a large distance even on modern day terms , but especially if we 're talking about four or five thousand years ago . because of that , we think that , okay , there must have been at least decent government administration or organization at a city-state level , although we 're unsure whether there was a connected empire , whether you had an organization beyond that or they all just decided to take each other 's standards and symbols and brick sizes and things like that . now , one of the key mysteries of the indus valley civilization is why did it end ? it seemed to be this thriving civilization , perhaps the most extensive one . in other videos , i talk about right now , the oldest wheel was discovered in mesopotamia , but some people think that the wheel might have been used even earlier in the indus valley civilization . i talk about this period , as early as 3300 bce , but there 's evidence that the civilization started much earlier . in the site right over here in mehrgarh , right over here in pakistan . they think that humans were having simple villages and agriculture as early , there 's evidence as early as 7000 bce and that site was discovered just in 1974 . we might discover things that take us even further into the past , and when you have a civilization that was around for so long , if there were people there as early as 7000 bce , we 're talking about it was there for thousands of years , but all of a sudden , it starts to decline . there 's evidence of less and less trade going on , less and less sophistication , and then it ends . and it 's one of the mysteries of history , of archaeology today . why did this indus valley civilization end ? some of the older theories were it was maybe it was a foreign invasion , maybe some of the ancestors of the modern indians invaded , or maybe they assimilated it somehow . more current theories do n't think that was the case . they think it might be some form of climate change , that some of the important rivers dried up , made the agriculture much harder . some people think it might have been a natural disaster , it might have been a flood of some kind . but we just do n't know . or the people , for some reason , decided to leave , die , migrate to maybe other parts of the region . but needless to say , it was a significant civilization , and we 're just scratching the surface of what we know about it . we know a lot and we know it was impressive , even though we ca n't read their script and we do n't know as much about it as we know about ancient mesopotamia and the ancient egyptians , but signs are that as more time passes , we 'll realize that it was more and more sophisticated and impressive than maybe we even appreciate today .
|
as we 've talked about in multiple videos , some of the earliest civilizations we have found have been around river valleys , and that is no coincidence because some of the first agriculture emerged around river valleys and the agriculture supported higher population densities and more sedentary populations , and allowed for more specialization . and we have talked about several of these , the ancient egyptians around the nile river , the ancient mesopotamians around the tigris and euphrates . and now we 're gon na talk about the ancient civilization around the indus river .
|
where were the ancient egyptians found ?
|
as we 've talked about in multiple videos , some of the earliest civilizations we have found have been around river valleys , and that is no coincidence because some of the first agriculture emerged around river valleys and the agriculture supported higher population densities and more sedentary populations , and allowed for more specialization . and we have talked about several of these , the ancient egyptians around the nile river , the ancient mesopotamians around the tigris and euphrates . and now we 're gon na talk about the ancient civilization around the indus river . the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization . now to get ourselves acquainted in time , this shows when archaeologists , historians consider to be the main part of the harappan civilization . there 's evidence that people had basic villages , civilizations , agriculture here , as far back as 7,000 bce , and that 's just based on the evidence we have today , but when people refer to the indus valley civilization in particular , they 're usually staring around 3300 bce and in orange right over here , this is the early period , or you could say the early indus valley civilization . now some of the biggest structures and pieces of technology that have been discovered have been right over here , which is often referred to as the mature period for the indus valley civilization , and then it goes into decline . we 'll talk about why it might have gone into decline , although we 're not really sure , and this is called the late . now to put it in context relative to these other civilizations , remember the ancient sumerians were starting to be quite , i guess you could say civilized , by about this period . you start having a lot of intermingling between the acadians and the sumerians as you get into the late third millennium . that 's when you have the empire of sargon the great , the acadian empire . as you get to the end of this mature period right over here , this is close to or around the time of hammurabi , the babylonian empire , and in egypt , if you go back to around 2500 , around this time , that 's when the pyramids were built and you have the egyptian kings , these god-kings that were ruling for most of this period right over here and as we 'll see , there was actually , we believe , a good bit of cultural interchange between the significant civilizations . now just to appreciate how extensive this indus valley civilization was , i will show you this map . and this map , it 's zoomed in of that region around the indus valley that i just showed you . this is a map of most of pakistan here , and these red squares are places where they have found evidence of the civilization . the first place was harappa , right over here , the punjab region of pakistan . and that 's why it 's called the harappan civilization . but as you can see , it 's much more than just around harappa . the largest site is at mohenjo-daro , right over here in the sindh region of pakistan and it 's believed that as many as 40,000 people lived in that city that we now , or that site , that we now call mohenjo-daro . and so far , we have discovered over 1,000 sites in this area and we believe that as many as five million people might have been part of the civilization . now the reason why we think it is a civilization and now , and let me actually keep scrolling around so you appreciate the extent of it . there 's sites in mainly , many in pakistan that you see here . there 's also quite a few in modern-day india right over here , so it 's an extensive network of these sites and the reason why we think it 's one civilization , or at least a connected culture , is that you find a lot of standardization . you find standardization in their weights and measures . in fact , they have a unit of measurement that 's as small as 1.6 millimeters , and the reason why that 's important is you would n't create a unit of measurement of 1.6 millimeters unless you knew how to use something , unless you know how to make things that precise . and one of the things that they made that precise are things like their structures . they had these standard bricks and this brick size and many of these symbols that they used were found throughout these sites . which said we do n't know whether they were controlled by one ruler or one emperor , but there was definitely a lot of cultural interchange to the point that they were using the same size bricks , they were using the same symbols , they were using the same units of measurement . and also , as you can imagine , having a unit of measurement that precise , that small implies that they were great builders . and the evidence we find today says yes , they were . this is a picture of the site at mohenjo-daro in modern-day sindh pakistan , and you can see how tight this brick work is , even by modern standards this is quite good . you 'd need to think of how many things we would build would last 5,000 years in this good , being exposed to the environments . they think this was a public bath . you see a citadel in the background . we 've discovered defensive structures . perhaps most impressively , there is , or most impressive , there 's sewage systems . they think houses had wells , water . so this was a technologically advanced civilization especially for that time . in many ways , more advanced than the other civilizations , the contemporary civilizations that we had talked about . here are some examples of their sculpture or of their art . this is , this one right over here is a picture , it 's called dancing girl , but she 's not dancing , but they think that might be her profession . it 's all speculation by archaeologists today . this they believe is called priest-king , once again , it 's all speculation . this is an example of the types of seals they made . this is their jewelry , once again , this is quite intricate jewelry , and this jewelry was not just discovered in archaeological digs in these various sites . there 's evidence of their jewelry as far as mesopotamia in digs there . and they believe that there was actually a very active maritime trade network between these areas . there 's jewelry discovered in these indus valley civilizations that were based on shells from the arabian peninsula . they have materials from china , so there 's materials from other parts of india , so once again , a very very extensive trade network . these civilizations would have known about them . but as we said , they were extremely , they seemed somewhat organized . even though we ca n't read their writing , in fact i have some examples of their writing here . and you might notice , so this is examples of their writing and you might notice there , this is turned into a somewhat infamous symbol now , because of the nazis , this is a swastika . but the swastika was one of the symbols they used , it 's a symbol in hinduism , it 's considered a symbol of good luck . it 's something that the nazis kind of usurped and turned it into a very negative thing , but it does show this connection between that indus valley or that harappan civilization and modern cultures that are in india and things like the hindu religion . although once again , we do not know a ton about their religion because their language has n't survived and we can not decipher their actual writing . but because of their organization and the consistency , or relative consistency amongst these different sites that are so far flung , this is a large distance even on modern day terms , but especially if we 're talking about four or five thousand years ago . because of that , we think that , okay , there must have been at least decent government administration or organization at a city-state level , although we 're unsure whether there was a connected empire , whether you had an organization beyond that or they all just decided to take each other 's standards and symbols and brick sizes and things like that . now , one of the key mysteries of the indus valley civilization is why did it end ? it seemed to be this thriving civilization , perhaps the most extensive one . in other videos , i talk about right now , the oldest wheel was discovered in mesopotamia , but some people think that the wheel might have been used even earlier in the indus valley civilization . i talk about this period , as early as 3300 bce , but there 's evidence that the civilization started much earlier . in the site right over here in mehrgarh , right over here in pakistan . they think that humans were having simple villages and agriculture as early , there 's evidence as early as 7000 bce and that site was discovered just in 1974 . we might discover things that take us even further into the past , and when you have a civilization that was around for so long , if there were people there as early as 7000 bce , we 're talking about it was there for thousands of years , but all of a sudden , it starts to decline . there 's evidence of less and less trade going on , less and less sophistication , and then it ends . and it 's one of the mysteries of history , of archaeology today . why did this indus valley civilization end ? some of the older theories were it was maybe it was a foreign invasion , maybe some of the ancestors of the modern indians invaded , or maybe they assimilated it somehow . more current theories do n't think that was the case . they think it might be some form of climate change , that some of the important rivers dried up , made the agriculture much harder . some people think it might have been a natural disaster , it might have been a flood of some kind . but we just do n't know . or the people , for some reason , decided to leave , die , migrate to maybe other parts of the region . but needless to say , it was a significant civilization , and we 're just scratching the surface of what we know about it . we know a lot and we know it was impressive , even though we ca n't read their script and we do n't know as much about it as we know about ancient mesopotamia and the ancient egyptians , but signs are that as more time passes , we 'll realize that it was more and more sophisticated and impressive than maybe we even appreciate today .
|
the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization .
|
why urbanization in indus valley civilization happened faster than egyptian and mesopotamian civilizations ?
|
as we 've talked about in multiple videos , some of the earliest civilizations we have found have been around river valleys , and that is no coincidence because some of the first agriculture emerged around river valleys and the agriculture supported higher population densities and more sedentary populations , and allowed for more specialization . and we have talked about several of these , the ancient egyptians around the nile river , the ancient mesopotamians around the tigris and euphrates . and now we 're gon na talk about the ancient civilization around the indus river . the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization . now to get ourselves acquainted in time , this shows when archaeologists , historians consider to be the main part of the harappan civilization . there 's evidence that people had basic villages , civilizations , agriculture here , as far back as 7,000 bce , and that 's just based on the evidence we have today , but when people refer to the indus valley civilization in particular , they 're usually staring around 3300 bce and in orange right over here , this is the early period , or you could say the early indus valley civilization . now some of the biggest structures and pieces of technology that have been discovered have been right over here , which is often referred to as the mature period for the indus valley civilization , and then it goes into decline . we 'll talk about why it might have gone into decline , although we 're not really sure , and this is called the late . now to put it in context relative to these other civilizations , remember the ancient sumerians were starting to be quite , i guess you could say civilized , by about this period . you start having a lot of intermingling between the acadians and the sumerians as you get into the late third millennium . that 's when you have the empire of sargon the great , the acadian empire . as you get to the end of this mature period right over here , this is close to or around the time of hammurabi , the babylonian empire , and in egypt , if you go back to around 2500 , around this time , that 's when the pyramids were built and you have the egyptian kings , these god-kings that were ruling for most of this period right over here and as we 'll see , there was actually , we believe , a good bit of cultural interchange between the significant civilizations . now just to appreciate how extensive this indus valley civilization was , i will show you this map . and this map , it 's zoomed in of that region around the indus valley that i just showed you . this is a map of most of pakistan here , and these red squares are places where they have found evidence of the civilization . the first place was harappa , right over here , the punjab region of pakistan . and that 's why it 's called the harappan civilization . but as you can see , it 's much more than just around harappa . the largest site is at mohenjo-daro , right over here in the sindh region of pakistan and it 's believed that as many as 40,000 people lived in that city that we now , or that site , that we now call mohenjo-daro . and so far , we have discovered over 1,000 sites in this area and we believe that as many as five million people might have been part of the civilization . now the reason why we think it is a civilization and now , and let me actually keep scrolling around so you appreciate the extent of it . there 's sites in mainly , many in pakistan that you see here . there 's also quite a few in modern-day india right over here , so it 's an extensive network of these sites and the reason why we think it 's one civilization , or at least a connected culture , is that you find a lot of standardization . you find standardization in their weights and measures . in fact , they have a unit of measurement that 's as small as 1.6 millimeters , and the reason why that 's important is you would n't create a unit of measurement of 1.6 millimeters unless you knew how to use something , unless you know how to make things that precise . and one of the things that they made that precise are things like their structures . they had these standard bricks and this brick size and many of these symbols that they used were found throughout these sites . which said we do n't know whether they were controlled by one ruler or one emperor , but there was definitely a lot of cultural interchange to the point that they were using the same size bricks , they were using the same symbols , they were using the same units of measurement . and also , as you can imagine , having a unit of measurement that precise , that small implies that they were great builders . and the evidence we find today says yes , they were . this is a picture of the site at mohenjo-daro in modern-day sindh pakistan , and you can see how tight this brick work is , even by modern standards this is quite good . you 'd need to think of how many things we would build would last 5,000 years in this good , being exposed to the environments . they think this was a public bath . you see a citadel in the background . we 've discovered defensive structures . perhaps most impressively , there is , or most impressive , there 's sewage systems . they think houses had wells , water . so this was a technologically advanced civilization especially for that time . in many ways , more advanced than the other civilizations , the contemporary civilizations that we had talked about . here are some examples of their sculpture or of their art . this is , this one right over here is a picture , it 's called dancing girl , but she 's not dancing , but they think that might be her profession . it 's all speculation by archaeologists today . this they believe is called priest-king , once again , it 's all speculation . this is an example of the types of seals they made . this is their jewelry , once again , this is quite intricate jewelry , and this jewelry was not just discovered in archaeological digs in these various sites . there 's evidence of their jewelry as far as mesopotamia in digs there . and they believe that there was actually a very active maritime trade network between these areas . there 's jewelry discovered in these indus valley civilizations that were based on shells from the arabian peninsula . they have materials from china , so there 's materials from other parts of india , so once again , a very very extensive trade network . these civilizations would have known about them . but as we said , they were extremely , they seemed somewhat organized . even though we ca n't read their writing , in fact i have some examples of their writing here . and you might notice , so this is examples of their writing and you might notice there , this is turned into a somewhat infamous symbol now , because of the nazis , this is a swastika . but the swastika was one of the symbols they used , it 's a symbol in hinduism , it 's considered a symbol of good luck . it 's something that the nazis kind of usurped and turned it into a very negative thing , but it does show this connection between that indus valley or that harappan civilization and modern cultures that are in india and things like the hindu religion . although once again , we do not know a ton about their religion because their language has n't survived and we can not decipher their actual writing . but because of their organization and the consistency , or relative consistency amongst these different sites that are so far flung , this is a large distance even on modern day terms , but especially if we 're talking about four or five thousand years ago . because of that , we think that , okay , there must have been at least decent government administration or organization at a city-state level , although we 're unsure whether there was a connected empire , whether you had an organization beyond that or they all just decided to take each other 's standards and symbols and brick sizes and things like that . now , one of the key mysteries of the indus valley civilization is why did it end ? it seemed to be this thriving civilization , perhaps the most extensive one . in other videos , i talk about right now , the oldest wheel was discovered in mesopotamia , but some people think that the wheel might have been used even earlier in the indus valley civilization . i talk about this period , as early as 3300 bce , but there 's evidence that the civilization started much earlier . in the site right over here in mehrgarh , right over here in pakistan . they think that humans were having simple villages and agriculture as early , there 's evidence as early as 7000 bce and that site was discovered just in 1974 . we might discover things that take us even further into the past , and when you have a civilization that was around for so long , if there were people there as early as 7000 bce , we 're talking about it was there for thousands of years , but all of a sudden , it starts to decline . there 's evidence of less and less trade going on , less and less sophistication , and then it ends . and it 's one of the mysteries of history , of archaeology today . why did this indus valley civilization end ? some of the older theories were it was maybe it was a foreign invasion , maybe some of the ancestors of the modern indians invaded , or maybe they assimilated it somehow . more current theories do n't think that was the case . they think it might be some form of climate change , that some of the important rivers dried up , made the agriculture much harder . some people think it might have been a natural disaster , it might have been a flood of some kind . but we just do n't know . or the people , for some reason , decided to leave , die , migrate to maybe other parts of the region . but needless to say , it was a significant civilization , and we 're just scratching the surface of what we know about it . we know a lot and we know it was impressive , even though we ca n't read their script and we do n't know as much about it as we know about ancient mesopotamia and the ancient egyptians , but signs are that as more time passes , we 'll realize that it was more and more sophisticated and impressive than maybe we even appreciate today .
|
the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization .
|
i might just have this question bcuz i did n't watch the full video but why is n't the basic civilization that started around 7000 bce not considered the indus valley civilization ?
|
as we 've talked about in multiple videos , some of the earliest civilizations we have found have been around river valleys , and that is no coincidence because some of the first agriculture emerged around river valleys and the agriculture supported higher population densities and more sedentary populations , and allowed for more specialization . and we have talked about several of these , the ancient egyptians around the nile river , the ancient mesopotamians around the tigris and euphrates . and now we 're gon na talk about the ancient civilization around the indus river . the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization . now to get ourselves acquainted in time , this shows when archaeologists , historians consider to be the main part of the harappan civilization . there 's evidence that people had basic villages , civilizations , agriculture here , as far back as 7,000 bce , and that 's just based on the evidence we have today , but when people refer to the indus valley civilization in particular , they 're usually staring around 3300 bce and in orange right over here , this is the early period , or you could say the early indus valley civilization . now some of the biggest structures and pieces of technology that have been discovered have been right over here , which is often referred to as the mature period for the indus valley civilization , and then it goes into decline . we 'll talk about why it might have gone into decline , although we 're not really sure , and this is called the late . now to put it in context relative to these other civilizations , remember the ancient sumerians were starting to be quite , i guess you could say civilized , by about this period . you start having a lot of intermingling between the acadians and the sumerians as you get into the late third millennium . that 's when you have the empire of sargon the great , the acadian empire . as you get to the end of this mature period right over here , this is close to or around the time of hammurabi , the babylonian empire , and in egypt , if you go back to around 2500 , around this time , that 's when the pyramids were built and you have the egyptian kings , these god-kings that were ruling for most of this period right over here and as we 'll see , there was actually , we believe , a good bit of cultural interchange between the significant civilizations . now just to appreciate how extensive this indus valley civilization was , i will show you this map . and this map , it 's zoomed in of that region around the indus valley that i just showed you . this is a map of most of pakistan here , and these red squares are places where they have found evidence of the civilization . the first place was harappa , right over here , the punjab region of pakistan . and that 's why it 's called the harappan civilization . but as you can see , it 's much more than just around harappa . the largest site is at mohenjo-daro , right over here in the sindh region of pakistan and it 's believed that as many as 40,000 people lived in that city that we now , or that site , that we now call mohenjo-daro . and so far , we have discovered over 1,000 sites in this area and we believe that as many as five million people might have been part of the civilization . now the reason why we think it is a civilization and now , and let me actually keep scrolling around so you appreciate the extent of it . there 's sites in mainly , many in pakistan that you see here . there 's also quite a few in modern-day india right over here , so it 's an extensive network of these sites and the reason why we think it 's one civilization , or at least a connected culture , is that you find a lot of standardization . you find standardization in their weights and measures . in fact , they have a unit of measurement that 's as small as 1.6 millimeters , and the reason why that 's important is you would n't create a unit of measurement of 1.6 millimeters unless you knew how to use something , unless you know how to make things that precise . and one of the things that they made that precise are things like their structures . they had these standard bricks and this brick size and many of these symbols that they used were found throughout these sites . which said we do n't know whether they were controlled by one ruler or one emperor , but there was definitely a lot of cultural interchange to the point that they were using the same size bricks , they were using the same symbols , they were using the same units of measurement . and also , as you can imagine , having a unit of measurement that precise , that small implies that they were great builders . and the evidence we find today says yes , they were . this is a picture of the site at mohenjo-daro in modern-day sindh pakistan , and you can see how tight this brick work is , even by modern standards this is quite good . you 'd need to think of how many things we would build would last 5,000 years in this good , being exposed to the environments . they think this was a public bath . you see a citadel in the background . we 've discovered defensive structures . perhaps most impressively , there is , or most impressive , there 's sewage systems . they think houses had wells , water . so this was a technologically advanced civilization especially for that time . in many ways , more advanced than the other civilizations , the contemporary civilizations that we had talked about . here are some examples of their sculpture or of their art . this is , this one right over here is a picture , it 's called dancing girl , but she 's not dancing , but they think that might be her profession . it 's all speculation by archaeologists today . this they believe is called priest-king , once again , it 's all speculation . this is an example of the types of seals they made . this is their jewelry , once again , this is quite intricate jewelry , and this jewelry was not just discovered in archaeological digs in these various sites . there 's evidence of their jewelry as far as mesopotamia in digs there . and they believe that there was actually a very active maritime trade network between these areas . there 's jewelry discovered in these indus valley civilizations that were based on shells from the arabian peninsula . they have materials from china , so there 's materials from other parts of india , so once again , a very very extensive trade network . these civilizations would have known about them . but as we said , they were extremely , they seemed somewhat organized . even though we ca n't read their writing , in fact i have some examples of their writing here . and you might notice , so this is examples of their writing and you might notice there , this is turned into a somewhat infamous symbol now , because of the nazis , this is a swastika . but the swastika was one of the symbols they used , it 's a symbol in hinduism , it 's considered a symbol of good luck . it 's something that the nazis kind of usurped and turned it into a very negative thing , but it does show this connection between that indus valley or that harappan civilization and modern cultures that are in india and things like the hindu religion . although once again , we do not know a ton about their religion because their language has n't survived and we can not decipher their actual writing . but because of their organization and the consistency , or relative consistency amongst these different sites that are so far flung , this is a large distance even on modern day terms , but especially if we 're talking about four or five thousand years ago . because of that , we think that , okay , there must have been at least decent government administration or organization at a city-state level , although we 're unsure whether there was a connected empire , whether you had an organization beyond that or they all just decided to take each other 's standards and symbols and brick sizes and things like that . now , one of the key mysteries of the indus valley civilization is why did it end ? it seemed to be this thriving civilization , perhaps the most extensive one . in other videos , i talk about right now , the oldest wheel was discovered in mesopotamia , but some people think that the wheel might have been used even earlier in the indus valley civilization . i talk about this period , as early as 3300 bce , but there 's evidence that the civilization started much earlier . in the site right over here in mehrgarh , right over here in pakistan . they think that humans were having simple villages and agriculture as early , there 's evidence as early as 7000 bce and that site was discovered just in 1974 . we might discover things that take us even further into the past , and when you have a civilization that was around for so long , if there were people there as early as 7000 bce , we 're talking about it was there for thousands of years , but all of a sudden , it starts to decline . there 's evidence of less and less trade going on , less and less sophistication , and then it ends . and it 's one of the mysteries of history , of archaeology today . why did this indus valley civilization end ? some of the older theories were it was maybe it was a foreign invasion , maybe some of the ancestors of the modern indians invaded , or maybe they assimilated it somehow . more current theories do n't think that was the case . they think it might be some form of climate change , that some of the important rivers dried up , made the agriculture much harder . some people think it might have been a natural disaster , it might have been a flood of some kind . but we just do n't know . or the people , for some reason , decided to leave , die , migrate to maybe other parts of the region . but needless to say , it was a significant civilization , and we 're just scratching the surface of what we know about it . we know a lot and we know it was impressive , even though we ca n't read their script and we do n't know as much about it as we know about ancient mesopotamia and the ancient egyptians , but signs are that as more time passes , we 'll realize that it was more and more sophisticated and impressive than maybe we even appreciate today .
|
you 'd need to think of how many things we would build would last 5,000 years in this good , being exposed to the environments . they think this was a public bath . you see a citadel in the background .
|
was n't the great bath ( the structure sal mentioned ) used for ritual practices ?
|
as we 've talked about in multiple videos , some of the earliest civilizations we have found have been around river valleys , and that is no coincidence because some of the first agriculture emerged around river valleys and the agriculture supported higher population densities and more sedentary populations , and allowed for more specialization . and we have talked about several of these , the ancient egyptians around the nile river , the ancient mesopotamians around the tigris and euphrates . and now we 're gon na talk about the ancient civilization around the indus river . the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization . now to get ourselves acquainted in time , this shows when archaeologists , historians consider to be the main part of the harappan civilization . there 's evidence that people had basic villages , civilizations , agriculture here , as far back as 7,000 bce , and that 's just based on the evidence we have today , but when people refer to the indus valley civilization in particular , they 're usually staring around 3300 bce and in orange right over here , this is the early period , or you could say the early indus valley civilization . now some of the biggest structures and pieces of technology that have been discovered have been right over here , which is often referred to as the mature period for the indus valley civilization , and then it goes into decline . we 'll talk about why it might have gone into decline , although we 're not really sure , and this is called the late . now to put it in context relative to these other civilizations , remember the ancient sumerians were starting to be quite , i guess you could say civilized , by about this period . you start having a lot of intermingling between the acadians and the sumerians as you get into the late third millennium . that 's when you have the empire of sargon the great , the acadian empire . as you get to the end of this mature period right over here , this is close to or around the time of hammurabi , the babylonian empire , and in egypt , if you go back to around 2500 , around this time , that 's when the pyramids were built and you have the egyptian kings , these god-kings that were ruling for most of this period right over here and as we 'll see , there was actually , we believe , a good bit of cultural interchange between the significant civilizations . now just to appreciate how extensive this indus valley civilization was , i will show you this map . and this map , it 's zoomed in of that region around the indus valley that i just showed you . this is a map of most of pakistan here , and these red squares are places where they have found evidence of the civilization . the first place was harappa , right over here , the punjab region of pakistan . and that 's why it 's called the harappan civilization . but as you can see , it 's much more than just around harappa . the largest site is at mohenjo-daro , right over here in the sindh region of pakistan and it 's believed that as many as 40,000 people lived in that city that we now , or that site , that we now call mohenjo-daro . and so far , we have discovered over 1,000 sites in this area and we believe that as many as five million people might have been part of the civilization . now the reason why we think it is a civilization and now , and let me actually keep scrolling around so you appreciate the extent of it . there 's sites in mainly , many in pakistan that you see here . there 's also quite a few in modern-day india right over here , so it 's an extensive network of these sites and the reason why we think it 's one civilization , or at least a connected culture , is that you find a lot of standardization . you find standardization in their weights and measures . in fact , they have a unit of measurement that 's as small as 1.6 millimeters , and the reason why that 's important is you would n't create a unit of measurement of 1.6 millimeters unless you knew how to use something , unless you know how to make things that precise . and one of the things that they made that precise are things like their structures . they had these standard bricks and this brick size and many of these symbols that they used were found throughout these sites . which said we do n't know whether they were controlled by one ruler or one emperor , but there was definitely a lot of cultural interchange to the point that they were using the same size bricks , they were using the same symbols , they were using the same units of measurement . and also , as you can imagine , having a unit of measurement that precise , that small implies that they were great builders . and the evidence we find today says yes , they were . this is a picture of the site at mohenjo-daro in modern-day sindh pakistan , and you can see how tight this brick work is , even by modern standards this is quite good . you 'd need to think of how many things we would build would last 5,000 years in this good , being exposed to the environments . they think this was a public bath . you see a citadel in the background . we 've discovered defensive structures . perhaps most impressively , there is , or most impressive , there 's sewage systems . they think houses had wells , water . so this was a technologically advanced civilization especially for that time . in many ways , more advanced than the other civilizations , the contemporary civilizations that we had talked about . here are some examples of their sculpture or of their art . this is , this one right over here is a picture , it 's called dancing girl , but she 's not dancing , but they think that might be her profession . it 's all speculation by archaeologists today . this they believe is called priest-king , once again , it 's all speculation . this is an example of the types of seals they made . this is their jewelry , once again , this is quite intricate jewelry , and this jewelry was not just discovered in archaeological digs in these various sites . there 's evidence of their jewelry as far as mesopotamia in digs there . and they believe that there was actually a very active maritime trade network between these areas . there 's jewelry discovered in these indus valley civilizations that were based on shells from the arabian peninsula . they have materials from china , so there 's materials from other parts of india , so once again , a very very extensive trade network . these civilizations would have known about them . but as we said , they were extremely , they seemed somewhat organized . even though we ca n't read their writing , in fact i have some examples of their writing here . and you might notice , so this is examples of their writing and you might notice there , this is turned into a somewhat infamous symbol now , because of the nazis , this is a swastika . but the swastika was one of the symbols they used , it 's a symbol in hinduism , it 's considered a symbol of good luck . it 's something that the nazis kind of usurped and turned it into a very negative thing , but it does show this connection between that indus valley or that harappan civilization and modern cultures that are in india and things like the hindu religion . although once again , we do not know a ton about their religion because their language has n't survived and we can not decipher their actual writing . but because of their organization and the consistency , or relative consistency amongst these different sites that are so far flung , this is a large distance even on modern day terms , but especially if we 're talking about four or five thousand years ago . because of that , we think that , okay , there must have been at least decent government administration or organization at a city-state level , although we 're unsure whether there was a connected empire , whether you had an organization beyond that or they all just decided to take each other 's standards and symbols and brick sizes and things like that . now , one of the key mysteries of the indus valley civilization is why did it end ? it seemed to be this thriving civilization , perhaps the most extensive one . in other videos , i talk about right now , the oldest wheel was discovered in mesopotamia , but some people think that the wheel might have been used even earlier in the indus valley civilization . i talk about this period , as early as 3300 bce , but there 's evidence that the civilization started much earlier . in the site right over here in mehrgarh , right over here in pakistan . they think that humans were having simple villages and agriculture as early , there 's evidence as early as 7000 bce and that site was discovered just in 1974 . we might discover things that take us even further into the past , and when you have a civilization that was around for so long , if there were people there as early as 7000 bce , we 're talking about it was there for thousands of years , but all of a sudden , it starts to decline . there 's evidence of less and less trade going on , less and less sophistication , and then it ends . and it 's one of the mysteries of history , of archaeology today . why did this indus valley civilization end ? some of the older theories were it was maybe it was a foreign invasion , maybe some of the ancestors of the modern indians invaded , or maybe they assimilated it somehow . more current theories do n't think that was the case . they think it might be some form of climate change , that some of the important rivers dried up , made the agriculture much harder . some people think it might have been a natural disaster , it might have been a flood of some kind . but we just do n't know . or the people , for some reason , decided to leave , die , migrate to maybe other parts of the region . but needless to say , it was a significant civilization , and we 're just scratching the surface of what we know about it . we know a lot and we know it was impressive , even though we ca n't read their script and we do n't know as much about it as we know about ancient mesopotamia and the ancient egyptians , but signs are that as more time passes , we 'll realize that it was more and more sophisticated and impressive than maybe we even appreciate today .
|
the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization .
|
if the indus river valley civilization was probably earlier , had ( probably ) more people and were technologically more advanced then all the other contemporary civilizations , why is n't it know as 'the craddle of civilization ' ?
|
as we 've talked about in multiple videos , some of the earliest civilizations we have found have been around river valleys , and that is no coincidence because some of the first agriculture emerged around river valleys and the agriculture supported higher population densities and more sedentary populations , and allowed for more specialization . and we have talked about several of these , the ancient egyptians around the nile river , the ancient mesopotamians around the tigris and euphrates . and now we 're gon na talk about the ancient civilization around the indus river . the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization . now to get ourselves acquainted in time , this shows when archaeologists , historians consider to be the main part of the harappan civilization . there 's evidence that people had basic villages , civilizations , agriculture here , as far back as 7,000 bce , and that 's just based on the evidence we have today , but when people refer to the indus valley civilization in particular , they 're usually staring around 3300 bce and in orange right over here , this is the early period , or you could say the early indus valley civilization . now some of the biggest structures and pieces of technology that have been discovered have been right over here , which is often referred to as the mature period for the indus valley civilization , and then it goes into decline . we 'll talk about why it might have gone into decline , although we 're not really sure , and this is called the late . now to put it in context relative to these other civilizations , remember the ancient sumerians were starting to be quite , i guess you could say civilized , by about this period . you start having a lot of intermingling between the acadians and the sumerians as you get into the late third millennium . that 's when you have the empire of sargon the great , the acadian empire . as you get to the end of this mature period right over here , this is close to or around the time of hammurabi , the babylonian empire , and in egypt , if you go back to around 2500 , around this time , that 's when the pyramids were built and you have the egyptian kings , these god-kings that were ruling for most of this period right over here and as we 'll see , there was actually , we believe , a good bit of cultural interchange between the significant civilizations . now just to appreciate how extensive this indus valley civilization was , i will show you this map . and this map , it 's zoomed in of that region around the indus valley that i just showed you . this is a map of most of pakistan here , and these red squares are places where they have found evidence of the civilization . the first place was harappa , right over here , the punjab region of pakistan . and that 's why it 's called the harappan civilization . but as you can see , it 's much more than just around harappa . the largest site is at mohenjo-daro , right over here in the sindh region of pakistan and it 's believed that as many as 40,000 people lived in that city that we now , or that site , that we now call mohenjo-daro . and so far , we have discovered over 1,000 sites in this area and we believe that as many as five million people might have been part of the civilization . now the reason why we think it is a civilization and now , and let me actually keep scrolling around so you appreciate the extent of it . there 's sites in mainly , many in pakistan that you see here . there 's also quite a few in modern-day india right over here , so it 's an extensive network of these sites and the reason why we think it 's one civilization , or at least a connected culture , is that you find a lot of standardization . you find standardization in their weights and measures . in fact , they have a unit of measurement that 's as small as 1.6 millimeters , and the reason why that 's important is you would n't create a unit of measurement of 1.6 millimeters unless you knew how to use something , unless you know how to make things that precise . and one of the things that they made that precise are things like their structures . they had these standard bricks and this brick size and many of these symbols that they used were found throughout these sites . which said we do n't know whether they were controlled by one ruler or one emperor , but there was definitely a lot of cultural interchange to the point that they were using the same size bricks , they were using the same symbols , they were using the same units of measurement . and also , as you can imagine , having a unit of measurement that precise , that small implies that they were great builders . and the evidence we find today says yes , they were . this is a picture of the site at mohenjo-daro in modern-day sindh pakistan , and you can see how tight this brick work is , even by modern standards this is quite good . you 'd need to think of how many things we would build would last 5,000 years in this good , being exposed to the environments . they think this was a public bath . you see a citadel in the background . we 've discovered defensive structures . perhaps most impressively , there is , or most impressive , there 's sewage systems . they think houses had wells , water . so this was a technologically advanced civilization especially for that time . in many ways , more advanced than the other civilizations , the contemporary civilizations that we had talked about . here are some examples of their sculpture or of their art . this is , this one right over here is a picture , it 's called dancing girl , but she 's not dancing , but they think that might be her profession . it 's all speculation by archaeologists today . this they believe is called priest-king , once again , it 's all speculation . this is an example of the types of seals they made . this is their jewelry , once again , this is quite intricate jewelry , and this jewelry was not just discovered in archaeological digs in these various sites . there 's evidence of their jewelry as far as mesopotamia in digs there . and they believe that there was actually a very active maritime trade network between these areas . there 's jewelry discovered in these indus valley civilizations that were based on shells from the arabian peninsula . they have materials from china , so there 's materials from other parts of india , so once again , a very very extensive trade network . these civilizations would have known about them . but as we said , they were extremely , they seemed somewhat organized . even though we ca n't read their writing , in fact i have some examples of their writing here . and you might notice , so this is examples of their writing and you might notice there , this is turned into a somewhat infamous symbol now , because of the nazis , this is a swastika . but the swastika was one of the symbols they used , it 's a symbol in hinduism , it 's considered a symbol of good luck . it 's something that the nazis kind of usurped and turned it into a very negative thing , but it does show this connection between that indus valley or that harappan civilization and modern cultures that are in india and things like the hindu religion . although once again , we do not know a ton about their religion because their language has n't survived and we can not decipher their actual writing . but because of their organization and the consistency , or relative consistency amongst these different sites that are so far flung , this is a large distance even on modern day terms , but especially if we 're talking about four or five thousand years ago . because of that , we think that , okay , there must have been at least decent government administration or organization at a city-state level , although we 're unsure whether there was a connected empire , whether you had an organization beyond that or they all just decided to take each other 's standards and symbols and brick sizes and things like that . now , one of the key mysteries of the indus valley civilization is why did it end ? it seemed to be this thriving civilization , perhaps the most extensive one . in other videos , i talk about right now , the oldest wheel was discovered in mesopotamia , but some people think that the wheel might have been used even earlier in the indus valley civilization . i talk about this period , as early as 3300 bce , but there 's evidence that the civilization started much earlier . in the site right over here in mehrgarh , right over here in pakistan . they think that humans were having simple villages and agriculture as early , there 's evidence as early as 7000 bce and that site was discovered just in 1974 . we might discover things that take us even further into the past , and when you have a civilization that was around for so long , if there were people there as early as 7000 bce , we 're talking about it was there for thousands of years , but all of a sudden , it starts to decline . there 's evidence of less and less trade going on , less and less sophistication , and then it ends . and it 's one of the mysteries of history , of archaeology today . why did this indus valley civilization end ? some of the older theories were it was maybe it was a foreign invasion , maybe some of the ancestors of the modern indians invaded , or maybe they assimilated it somehow . more current theories do n't think that was the case . they think it might be some form of climate change , that some of the important rivers dried up , made the agriculture much harder . some people think it might have been a natural disaster , it might have been a flood of some kind . but we just do n't know . or the people , for some reason , decided to leave , die , migrate to maybe other parts of the region . but needless to say , it was a significant civilization , and we 're just scratching the surface of what we know about it . we know a lot and we know it was impressive , even though we ca n't read their script and we do n't know as much about it as we know about ancient mesopotamia and the ancient egyptians , but signs are that as more time passes , we 'll realize that it was more and more sophisticated and impressive than maybe we even appreciate today .
|
the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization .
|
why is it that mesopotamia has this title and not the indus river valley civilization ?
|
as we 've talked about in multiple videos , some of the earliest civilizations we have found have been around river valleys , and that is no coincidence because some of the first agriculture emerged around river valleys and the agriculture supported higher population densities and more sedentary populations , and allowed for more specialization . and we have talked about several of these , the ancient egyptians around the nile river , the ancient mesopotamians around the tigris and euphrates . and now we 're gon na talk about the ancient civilization around the indus river . the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization . now to get ourselves acquainted in time , this shows when archaeologists , historians consider to be the main part of the harappan civilization . there 's evidence that people had basic villages , civilizations , agriculture here , as far back as 7,000 bce , and that 's just based on the evidence we have today , but when people refer to the indus valley civilization in particular , they 're usually staring around 3300 bce and in orange right over here , this is the early period , or you could say the early indus valley civilization . now some of the biggest structures and pieces of technology that have been discovered have been right over here , which is often referred to as the mature period for the indus valley civilization , and then it goes into decline . we 'll talk about why it might have gone into decline , although we 're not really sure , and this is called the late . now to put it in context relative to these other civilizations , remember the ancient sumerians were starting to be quite , i guess you could say civilized , by about this period . you start having a lot of intermingling between the acadians and the sumerians as you get into the late third millennium . that 's when you have the empire of sargon the great , the acadian empire . as you get to the end of this mature period right over here , this is close to or around the time of hammurabi , the babylonian empire , and in egypt , if you go back to around 2500 , around this time , that 's when the pyramids were built and you have the egyptian kings , these god-kings that were ruling for most of this period right over here and as we 'll see , there was actually , we believe , a good bit of cultural interchange between the significant civilizations . now just to appreciate how extensive this indus valley civilization was , i will show you this map . and this map , it 's zoomed in of that region around the indus valley that i just showed you . this is a map of most of pakistan here , and these red squares are places where they have found evidence of the civilization . the first place was harappa , right over here , the punjab region of pakistan . and that 's why it 's called the harappan civilization . but as you can see , it 's much more than just around harappa . the largest site is at mohenjo-daro , right over here in the sindh region of pakistan and it 's believed that as many as 40,000 people lived in that city that we now , or that site , that we now call mohenjo-daro . and so far , we have discovered over 1,000 sites in this area and we believe that as many as five million people might have been part of the civilization . now the reason why we think it is a civilization and now , and let me actually keep scrolling around so you appreciate the extent of it . there 's sites in mainly , many in pakistan that you see here . there 's also quite a few in modern-day india right over here , so it 's an extensive network of these sites and the reason why we think it 's one civilization , or at least a connected culture , is that you find a lot of standardization . you find standardization in their weights and measures . in fact , they have a unit of measurement that 's as small as 1.6 millimeters , and the reason why that 's important is you would n't create a unit of measurement of 1.6 millimeters unless you knew how to use something , unless you know how to make things that precise . and one of the things that they made that precise are things like their structures . they had these standard bricks and this brick size and many of these symbols that they used were found throughout these sites . which said we do n't know whether they were controlled by one ruler or one emperor , but there was definitely a lot of cultural interchange to the point that they were using the same size bricks , they were using the same symbols , they were using the same units of measurement . and also , as you can imagine , having a unit of measurement that precise , that small implies that they were great builders . and the evidence we find today says yes , they were . this is a picture of the site at mohenjo-daro in modern-day sindh pakistan , and you can see how tight this brick work is , even by modern standards this is quite good . you 'd need to think of how many things we would build would last 5,000 years in this good , being exposed to the environments . they think this was a public bath . you see a citadel in the background . we 've discovered defensive structures . perhaps most impressively , there is , or most impressive , there 's sewage systems . they think houses had wells , water . so this was a technologically advanced civilization especially for that time . in many ways , more advanced than the other civilizations , the contemporary civilizations that we had talked about . here are some examples of their sculpture or of their art . this is , this one right over here is a picture , it 's called dancing girl , but she 's not dancing , but they think that might be her profession . it 's all speculation by archaeologists today . this they believe is called priest-king , once again , it 's all speculation . this is an example of the types of seals they made . this is their jewelry , once again , this is quite intricate jewelry , and this jewelry was not just discovered in archaeological digs in these various sites . there 's evidence of their jewelry as far as mesopotamia in digs there . and they believe that there was actually a very active maritime trade network between these areas . there 's jewelry discovered in these indus valley civilizations that were based on shells from the arabian peninsula . they have materials from china , so there 's materials from other parts of india , so once again , a very very extensive trade network . these civilizations would have known about them . but as we said , they were extremely , they seemed somewhat organized . even though we ca n't read their writing , in fact i have some examples of their writing here . and you might notice , so this is examples of their writing and you might notice there , this is turned into a somewhat infamous symbol now , because of the nazis , this is a swastika . but the swastika was one of the symbols they used , it 's a symbol in hinduism , it 's considered a symbol of good luck . it 's something that the nazis kind of usurped and turned it into a very negative thing , but it does show this connection between that indus valley or that harappan civilization and modern cultures that are in india and things like the hindu religion . although once again , we do not know a ton about their religion because their language has n't survived and we can not decipher their actual writing . but because of their organization and the consistency , or relative consistency amongst these different sites that are so far flung , this is a large distance even on modern day terms , but especially if we 're talking about four or five thousand years ago . because of that , we think that , okay , there must have been at least decent government administration or organization at a city-state level , although we 're unsure whether there was a connected empire , whether you had an organization beyond that or they all just decided to take each other 's standards and symbols and brick sizes and things like that . now , one of the key mysteries of the indus valley civilization is why did it end ? it seemed to be this thriving civilization , perhaps the most extensive one . in other videos , i talk about right now , the oldest wheel was discovered in mesopotamia , but some people think that the wheel might have been used even earlier in the indus valley civilization . i talk about this period , as early as 3300 bce , but there 's evidence that the civilization started much earlier . in the site right over here in mehrgarh , right over here in pakistan . they think that humans were having simple villages and agriculture as early , there 's evidence as early as 7000 bce and that site was discovered just in 1974 . we might discover things that take us even further into the past , and when you have a civilization that was around for so long , if there were people there as early as 7000 bce , we 're talking about it was there for thousands of years , but all of a sudden , it starts to decline . there 's evidence of less and less trade going on , less and less sophistication , and then it ends . and it 's one of the mysteries of history , of archaeology today . why did this indus valley civilization end ? some of the older theories were it was maybe it was a foreign invasion , maybe some of the ancestors of the modern indians invaded , or maybe they assimilated it somehow . more current theories do n't think that was the case . they think it might be some form of climate change , that some of the important rivers dried up , made the agriculture much harder . some people think it might have been a natural disaster , it might have been a flood of some kind . but we just do n't know . or the people , for some reason , decided to leave , die , migrate to maybe other parts of the region . but needless to say , it was a significant civilization , and we 're just scratching the surface of what we know about it . we know a lot and we know it was impressive , even though we ca n't read their script and we do n't know as much about it as we know about ancient mesopotamia and the ancient egyptians , but signs are that as more time passes , we 'll realize that it was more and more sophisticated and impressive than maybe we even appreciate today .
|
the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization .
|
was there any treaties or diplomacy made during that period of time in the indus river civilization with others ?
|
as we 've talked about in multiple videos , some of the earliest civilizations we have found have been around river valleys , and that is no coincidence because some of the first agriculture emerged around river valleys and the agriculture supported higher population densities and more sedentary populations , and allowed for more specialization . and we have talked about several of these , the ancient egyptians around the nile river , the ancient mesopotamians around the tigris and euphrates . and now we 're gon na talk about the ancient civilization around the indus river . the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization . now to get ourselves acquainted in time , this shows when archaeologists , historians consider to be the main part of the harappan civilization . there 's evidence that people had basic villages , civilizations , agriculture here , as far back as 7,000 bce , and that 's just based on the evidence we have today , but when people refer to the indus valley civilization in particular , they 're usually staring around 3300 bce and in orange right over here , this is the early period , or you could say the early indus valley civilization . now some of the biggest structures and pieces of technology that have been discovered have been right over here , which is often referred to as the mature period for the indus valley civilization , and then it goes into decline . we 'll talk about why it might have gone into decline , although we 're not really sure , and this is called the late . now to put it in context relative to these other civilizations , remember the ancient sumerians were starting to be quite , i guess you could say civilized , by about this period . you start having a lot of intermingling between the acadians and the sumerians as you get into the late third millennium . that 's when you have the empire of sargon the great , the acadian empire . as you get to the end of this mature period right over here , this is close to or around the time of hammurabi , the babylonian empire , and in egypt , if you go back to around 2500 , around this time , that 's when the pyramids were built and you have the egyptian kings , these god-kings that were ruling for most of this period right over here and as we 'll see , there was actually , we believe , a good bit of cultural interchange between the significant civilizations . now just to appreciate how extensive this indus valley civilization was , i will show you this map . and this map , it 's zoomed in of that region around the indus valley that i just showed you . this is a map of most of pakistan here , and these red squares are places where they have found evidence of the civilization . the first place was harappa , right over here , the punjab region of pakistan . and that 's why it 's called the harappan civilization . but as you can see , it 's much more than just around harappa . the largest site is at mohenjo-daro , right over here in the sindh region of pakistan and it 's believed that as many as 40,000 people lived in that city that we now , or that site , that we now call mohenjo-daro . and so far , we have discovered over 1,000 sites in this area and we believe that as many as five million people might have been part of the civilization . now the reason why we think it is a civilization and now , and let me actually keep scrolling around so you appreciate the extent of it . there 's sites in mainly , many in pakistan that you see here . there 's also quite a few in modern-day india right over here , so it 's an extensive network of these sites and the reason why we think it 's one civilization , or at least a connected culture , is that you find a lot of standardization . you find standardization in their weights and measures . in fact , they have a unit of measurement that 's as small as 1.6 millimeters , and the reason why that 's important is you would n't create a unit of measurement of 1.6 millimeters unless you knew how to use something , unless you know how to make things that precise . and one of the things that they made that precise are things like their structures . they had these standard bricks and this brick size and many of these symbols that they used were found throughout these sites . which said we do n't know whether they were controlled by one ruler or one emperor , but there was definitely a lot of cultural interchange to the point that they were using the same size bricks , they were using the same symbols , they were using the same units of measurement . and also , as you can imagine , having a unit of measurement that precise , that small implies that they were great builders . and the evidence we find today says yes , they were . this is a picture of the site at mohenjo-daro in modern-day sindh pakistan , and you can see how tight this brick work is , even by modern standards this is quite good . you 'd need to think of how many things we would build would last 5,000 years in this good , being exposed to the environments . they think this was a public bath . you see a citadel in the background . we 've discovered defensive structures . perhaps most impressively , there is , or most impressive , there 's sewage systems . they think houses had wells , water . so this was a technologically advanced civilization especially for that time . in many ways , more advanced than the other civilizations , the contemporary civilizations that we had talked about . here are some examples of their sculpture or of their art . this is , this one right over here is a picture , it 's called dancing girl , but she 's not dancing , but they think that might be her profession . it 's all speculation by archaeologists today . this they believe is called priest-king , once again , it 's all speculation . this is an example of the types of seals they made . this is their jewelry , once again , this is quite intricate jewelry , and this jewelry was not just discovered in archaeological digs in these various sites . there 's evidence of their jewelry as far as mesopotamia in digs there . and they believe that there was actually a very active maritime trade network between these areas . there 's jewelry discovered in these indus valley civilizations that were based on shells from the arabian peninsula . they have materials from china , so there 's materials from other parts of india , so once again , a very very extensive trade network . these civilizations would have known about them . but as we said , they were extremely , they seemed somewhat organized . even though we ca n't read their writing , in fact i have some examples of their writing here . and you might notice , so this is examples of their writing and you might notice there , this is turned into a somewhat infamous symbol now , because of the nazis , this is a swastika . but the swastika was one of the symbols they used , it 's a symbol in hinduism , it 's considered a symbol of good luck . it 's something that the nazis kind of usurped and turned it into a very negative thing , but it does show this connection between that indus valley or that harappan civilization and modern cultures that are in india and things like the hindu religion . although once again , we do not know a ton about their religion because their language has n't survived and we can not decipher their actual writing . but because of their organization and the consistency , or relative consistency amongst these different sites that are so far flung , this is a large distance even on modern day terms , but especially if we 're talking about four or five thousand years ago . because of that , we think that , okay , there must have been at least decent government administration or organization at a city-state level , although we 're unsure whether there was a connected empire , whether you had an organization beyond that or they all just decided to take each other 's standards and symbols and brick sizes and things like that . now , one of the key mysteries of the indus valley civilization is why did it end ? it seemed to be this thriving civilization , perhaps the most extensive one . in other videos , i talk about right now , the oldest wheel was discovered in mesopotamia , but some people think that the wheel might have been used even earlier in the indus valley civilization . i talk about this period , as early as 3300 bce , but there 's evidence that the civilization started much earlier . in the site right over here in mehrgarh , right over here in pakistan . they think that humans were having simple villages and agriculture as early , there 's evidence as early as 7000 bce and that site was discovered just in 1974 . we might discover things that take us even further into the past , and when you have a civilization that was around for so long , if there were people there as early as 7000 bce , we 're talking about it was there for thousands of years , but all of a sudden , it starts to decline . there 's evidence of less and less trade going on , less and less sophistication , and then it ends . and it 's one of the mysteries of history , of archaeology today . why did this indus valley civilization end ? some of the older theories were it was maybe it was a foreign invasion , maybe some of the ancestors of the modern indians invaded , or maybe they assimilated it somehow . more current theories do n't think that was the case . they think it might be some form of climate change , that some of the important rivers dried up , made the agriculture much harder . some people think it might have been a natural disaster , it might have been a flood of some kind . but we just do n't know . or the people , for some reason , decided to leave , die , migrate to maybe other parts of the region . but needless to say , it was a significant civilization , and we 're just scratching the surface of what we know about it . we know a lot and we know it was impressive , even though we ca n't read their script and we do n't know as much about it as we know about ancient mesopotamia and the ancient egyptians , but signs are that as more time passes , we 'll realize that it was more and more sophisticated and impressive than maybe we even appreciate today .
|
the indus river runs mostly in modern-day pakistan , and that 's why it 's called the indus valley civilization . indus valley civilization . it 's also sometimes referred to as the harappan civilization , which was the first site where they found evidence of this fairly extensive civilization .
|
how do we know when something happened if i 'm retaining two different dates for the start of indus valley civilizations and two separate dates for the end of it ?
|
( cheerful music ) dr. steven zucker : according to legend , st. luke had a vision of the virgin mary and child , and painted that vision . as a result , he is the patron saint of painters . dr. beth harris : you 'll notice that st. luke 's eyes are half-closed , so we know that he is not actually seeing the virgin and child in front of him , but having a vision . dr. zucker : it is not his painting , in a sense . he is literally the hand of this angel . st. luke 's image , then , of the virgin mary and child has a kind of authority because it is god 's , actually , and not his . dr. harris : what 's interesting then is that the artist , gossaert , is painting his virgin mary and child not from the same authority as the painter st. luke , in his painting . one wonders about what it was like for artists to paint heavenly figures . how does one imagine the virgin mary ? how does one paint jesus christ ? these are , i think , difficult questions always for artists . dr. zucker : right ; we have absolutely no historical references to their likenesses , and so where is the authority of any painter who is transcribing their images ? and that issue of even the legitimacy of transcribing an image is called into question in the top right corner , where the artist has rendered [ in grise ] , in greys , a sculpture of moses . you can tell it 's moses because he 's holding the two tablets with the 10 laws . dr. harris : the 10 commandments . dr. zucker : in the christian tradition , he 's shown with horns on his head , and so we know it 's moses . moses seems to actually be pointing at something , and one of the laws is to not render people , not to render the fish below the sea , not to render the birds in the sky . the idea that the artist tries to take on the role of god , perhaps , by trying to create . dr. harris : `` thou shalt not create graven images , '' might be how most people know that commandment . gossaert is living right at the time that the protestant reformation begins , and one of the things that luther 's followers talked about is the danger of images , of people worshipping images instead of using them only as an aid in prayer . this is certainly reflecting on the role of the artist and whether images have a legitimacy or not . dr. zucker : well , that 's right . this is absolutely supporting the legitimacy of the artist creating religious imagery . dr. harris : because one of the writers of the gospel , st. luke himself , painted mary . dr. zucker : and the artist has blown out all the stops . he is rendering every detail with a precision that comes out of the northern tradition . dr. harris : we know that gossaert copied van eyck . he 's fully steeped in the northern rennaisance tradition of painting everything with a clarity and exactitude and attention to different textures . dr. zucker : well , look at the angel 's wings . look at the detail of the relief carving in the architecture . this is an arist who is just enjoying the ability to magically render form . now , look for just a second back at moses and those two tablets . notice the way that the shape of those two tablets rhyme with the architectural space . i think when most art historians look at this painting , they look back to this tradition of dividing the earthly space from the spiritual space . certainly , that central column does that ; but it also makes the entire painting two tablets . there is this way in which the tablets that moses holds is actually embodied in the architectural space itself . dr. harris : that 's true . although we think about the space as being very classical-looking , looking like ancient roman architecture , with those round arches and pilasters , it 's still to me a very mysterious space , much more like northern rennaisance spaces , where , as we look back toward moses , we have those repeated round arches , moving back into a space that we ca n't quite determine there . although the foreground of the painting seems to be carefully mapped out according to the rules of linear perscpective , which obviously gossaert has learned as a northern rennaisance artist from traveling to italy , but we see so much of the north here . if we look at the drapery that st. luke wears , it 's typical northern rennaisance , angular folds of drapery that we see in the art of campin or rogier van der weyden . dr. zucker : and so is the color . dr. harris : the green that that angel wears against the complementary red color worn by st. luke . there 's a real thoughtfulness about color here . dr. zucker : this is an artist who was working in antwerp , which was one of the great merchantile cities of the 15th and early 16th centuries . that was a culture and an economy that was based on importation , that was based on trade , and , in some ways , this is a painting that is also trading . dr. harris : that idea of the north and the south coming together that we see in the work of [ dore ] and beginning with michael pacher in the late 15th century . ( lively music )
|
you can tell it 's moses because he 's holding the two tablets with the 10 laws . dr. harris : the 10 commandments . dr. zucker : in the christian tradition , he 's shown with horns on his head , and so we know it 's moses .
|
do you think the artist was consciously trying to imitate the presentation of the ten commandments ?
|
( cheerful music ) dr. steven zucker : according to legend , st. luke had a vision of the virgin mary and child , and painted that vision . as a result , he is the patron saint of painters . dr. beth harris : you 'll notice that st. luke 's eyes are half-closed , so we know that he is not actually seeing the virgin and child in front of him , but having a vision . dr. zucker : it is not his painting , in a sense . he is literally the hand of this angel . st. luke 's image , then , of the virgin mary and child has a kind of authority because it is god 's , actually , and not his . dr. harris : what 's interesting then is that the artist , gossaert , is painting his virgin mary and child not from the same authority as the painter st. luke , in his painting . one wonders about what it was like for artists to paint heavenly figures . how does one imagine the virgin mary ? how does one paint jesus christ ? these are , i think , difficult questions always for artists . dr. zucker : right ; we have absolutely no historical references to their likenesses , and so where is the authority of any painter who is transcribing their images ? and that issue of even the legitimacy of transcribing an image is called into question in the top right corner , where the artist has rendered [ in grise ] , in greys , a sculpture of moses . you can tell it 's moses because he 's holding the two tablets with the 10 laws . dr. harris : the 10 commandments . dr. zucker : in the christian tradition , he 's shown with horns on his head , and so we know it 's moses . moses seems to actually be pointing at something , and one of the laws is to not render people , not to render the fish below the sea , not to render the birds in the sky . the idea that the artist tries to take on the role of god , perhaps , by trying to create . dr. harris : `` thou shalt not create graven images , '' might be how most people know that commandment . gossaert is living right at the time that the protestant reformation begins , and one of the things that luther 's followers talked about is the danger of images , of people worshipping images instead of using them only as an aid in prayer . this is certainly reflecting on the role of the artist and whether images have a legitimacy or not . dr. zucker : well , that 's right . this is absolutely supporting the legitimacy of the artist creating religious imagery . dr. harris : because one of the writers of the gospel , st. luke himself , painted mary . dr. zucker : and the artist has blown out all the stops . he is rendering every detail with a precision that comes out of the northern tradition . dr. harris : we know that gossaert copied van eyck . he 's fully steeped in the northern rennaisance tradition of painting everything with a clarity and exactitude and attention to different textures . dr. zucker : well , look at the angel 's wings . look at the detail of the relief carving in the architecture . this is an arist who is just enjoying the ability to magically render form . now , look for just a second back at moses and those two tablets . notice the way that the shape of those two tablets rhyme with the architectural space . i think when most art historians look at this painting , they look back to this tradition of dividing the earthly space from the spiritual space . certainly , that central column does that ; but it also makes the entire painting two tablets . there is this way in which the tablets that moses holds is actually embodied in the architectural space itself . dr. harris : that 's true . although we think about the space as being very classical-looking , looking like ancient roman architecture , with those round arches and pilasters , it 's still to me a very mysterious space , much more like northern rennaisance spaces , where , as we look back toward moses , we have those repeated round arches , moving back into a space that we ca n't quite determine there . although the foreground of the painting seems to be carefully mapped out according to the rules of linear perscpective , which obviously gossaert has learned as a northern rennaisance artist from traveling to italy , but we see so much of the north here . if we look at the drapery that st. luke wears , it 's typical northern rennaisance , angular folds of drapery that we see in the art of campin or rogier van der weyden . dr. zucker : and so is the color . dr. harris : the green that that angel wears against the complementary red color worn by st. luke . there 's a real thoughtfulness about color here . dr. zucker : this is an artist who was working in antwerp , which was one of the great merchantile cities of the 15th and early 16th centuries . that was a culture and an economy that was based on importation , that was based on trade , and , in some ways , this is a painting that is also trading . dr. harris : that idea of the north and the south coming together that we see in the work of [ dore ] and beginning with michael pacher in the late 15th century . ( lively music )
|
dr. zucker : right ; we have absolutely no historical references to their likenesses , and so where is the authority of any painter who is transcribing their images ? and that issue of even the legitimacy of transcribing an image is called into question in the top right corner , where the artist has rendered [ in grise ] , in greys , a sculpture of moses . you can tell it 's moses because he 's holding the two tablets with the 10 laws .
|
is n't this more a reference to the famous sculpture of moses ?
|
( cheerful music ) dr. steven zucker : according to legend , st. luke had a vision of the virgin mary and child , and painted that vision . as a result , he is the patron saint of painters . dr. beth harris : you 'll notice that st. luke 's eyes are half-closed , so we know that he is not actually seeing the virgin and child in front of him , but having a vision . dr. zucker : it is not his painting , in a sense . he is literally the hand of this angel . st. luke 's image , then , of the virgin mary and child has a kind of authority because it is god 's , actually , and not his . dr. harris : what 's interesting then is that the artist , gossaert , is painting his virgin mary and child not from the same authority as the painter st. luke , in his painting . one wonders about what it was like for artists to paint heavenly figures . how does one imagine the virgin mary ? how does one paint jesus christ ? these are , i think , difficult questions always for artists . dr. zucker : right ; we have absolutely no historical references to their likenesses , and so where is the authority of any painter who is transcribing their images ? and that issue of even the legitimacy of transcribing an image is called into question in the top right corner , where the artist has rendered [ in grise ] , in greys , a sculpture of moses . you can tell it 's moses because he 's holding the two tablets with the 10 laws . dr. harris : the 10 commandments . dr. zucker : in the christian tradition , he 's shown with horns on his head , and so we know it 's moses . moses seems to actually be pointing at something , and one of the laws is to not render people , not to render the fish below the sea , not to render the birds in the sky . the idea that the artist tries to take on the role of god , perhaps , by trying to create . dr. harris : `` thou shalt not create graven images , '' might be how most people know that commandment . gossaert is living right at the time that the protestant reformation begins , and one of the things that luther 's followers talked about is the danger of images , of people worshipping images instead of using them only as an aid in prayer . this is certainly reflecting on the role of the artist and whether images have a legitimacy or not . dr. zucker : well , that 's right . this is absolutely supporting the legitimacy of the artist creating religious imagery . dr. harris : because one of the writers of the gospel , st. luke himself , painted mary . dr. zucker : and the artist has blown out all the stops . he is rendering every detail with a precision that comes out of the northern tradition . dr. harris : we know that gossaert copied van eyck . he 's fully steeped in the northern rennaisance tradition of painting everything with a clarity and exactitude and attention to different textures . dr. zucker : well , look at the angel 's wings . look at the detail of the relief carving in the architecture . this is an arist who is just enjoying the ability to magically render form . now , look for just a second back at moses and those two tablets . notice the way that the shape of those two tablets rhyme with the architectural space . i think when most art historians look at this painting , they look back to this tradition of dividing the earthly space from the spiritual space . certainly , that central column does that ; but it also makes the entire painting two tablets . there is this way in which the tablets that moses holds is actually embodied in the architectural space itself . dr. harris : that 's true . although we think about the space as being very classical-looking , looking like ancient roman architecture , with those round arches and pilasters , it 's still to me a very mysterious space , much more like northern rennaisance spaces , where , as we look back toward moses , we have those repeated round arches , moving back into a space that we ca n't quite determine there . although the foreground of the painting seems to be carefully mapped out according to the rules of linear perscpective , which obviously gossaert has learned as a northern rennaisance artist from traveling to italy , but we see so much of the north here . if we look at the drapery that st. luke wears , it 's typical northern rennaisance , angular folds of drapery that we see in the art of campin or rogier van der weyden . dr. zucker : and so is the color . dr. harris : the green that that angel wears against the complementary red color worn by st. luke . there 's a real thoughtfulness about color here . dr. zucker : this is an artist who was working in antwerp , which was one of the great merchantile cities of the 15th and early 16th centuries . that was a culture and an economy that was based on importation , that was based on trade , and , in some ways , this is a painting that is also trading . dr. harris : that idea of the north and the south coming together that we see in the work of [ dore ] and beginning with michael pacher in the late 15th century . ( lively music )
|
these are , i think , difficult questions always for artists . dr. zucker : right ; we have absolutely no historical references to their likenesses , and so where is the authority of any painter who is transcribing their images ? and that issue of even the legitimacy of transcribing an image is called into question in the top right corner , where the artist has rendered [ in grise ] , in greys , a sculpture of moses .
|
then what references have survived ?
|
( cheerful music ) dr. steven zucker : according to legend , st. luke had a vision of the virgin mary and child , and painted that vision . as a result , he is the patron saint of painters . dr. beth harris : you 'll notice that st. luke 's eyes are half-closed , so we know that he is not actually seeing the virgin and child in front of him , but having a vision . dr. zucker : it is not his painting , in a sense . he is literally the hand of this angel . st. luke 's image , then , of the virgin mary and child has a kind of authority because it is god 's , actually , and not his . dr. harris : what 's interesting then is that the artist , gossaert , is painting his virgin mary and child not from the same authority as the painter st. luke , in his painting . one wonders about what it was like for artists to paint heavenly figures . how does one imagine the virgin mary ? how does one paint jesus christ ? these are , i think , difficult questions always for artists . dr. zucker : right ; we have absolutely no historical references to their likenesses , and so where is the authority of any painter who is transcribing their images ? and that issue of even the legitimacy of transcribing an image is called into question in the top right corner , where the artist has rendered [ in grise ] , in greys , a sculpture of moses . you can tell it 's moses because he 's holding the two tablets with the 10 laws . dr. harris : the 10 commandments . dr. zucker : in the christian tradition , he 's shown with horns on his head , and so we know it 's moses . moses seems to actually be pointing at something , and one of the laws is to not render people , not to render the fish below the sea , not to render the birds in the sky . the idea that the artist tries to take on the role of god , perhaps , by trying to create . dr. harris : `` thou shalt not create graven images , '' might be how most people know that commandment . gossaert is living right at the time that the protestant reformation begins , and one of the things that luther 's followers talked about is the danger of images , of people worshipping images instead of using them only as an aid in prayer . this is certainly reflecting on the role of the artist and whether images have a legitimacy or not . dr. zucker : well , that 's right . this is absolutely supporting the legitimacy of the artist creating religious imagery . dr. harris : because one of the writers of the gospel , st. luke himself , painted mary . dr. zucker : and the artist has blown out all the stops . he is rendering every detail with a precision that comes out of the northern tradition . dr. harris : we know that gossaert copied van eyck . he 's fully steeped in the northern rennaisance tradition of painting everything with a clarity and exactitude and attention to different textures . dr. zucker : well , look at the angel 's wings . look at the detail of the relief carving in the architecture . this is an arist who is just enjoying the ability to magically render form . now , look for just a second back at moses and those two tablets . notice the way that the shape of those two tablets rhyme with the architectural space . i think when most art historians look at this painting , they look back to this tradition of dividing the earthly space from the spiritual space . certainly , that central column does that ; but it also makes the entire painting two tablets . there is this way in which the tablets that moses holds is actually embodied in the architectural space itself . dr. harris : that 's true . although we think about the space as being very classical-looking , looking like ancient roman architecture , with those round arches and pilasters , it 's still to me a very mysterious space , much more like northern rennaisance spaces , where , as we look back toward moses , we have those repeated round arches , moving back into a space that we ca n't quite determine there . although the foreground of the painting seems to be carefully mapped out according to the rules of linear perscpective , which obviously gossaert has learned as a northern rennaisance artist from traveling to italy , but we see so much of the north here . if we look at the drapery that st. luke wears , it 's typical northern rennaisance , angular folds of drapery that we see in the art of campin or rogier van der weyden . dr. zucker : and so is the color . dr. harris : the green that that angel wears against the complementary red color worn by st. luke . there 's a real thoughtfulness about color here . dr. zucker : this is an artist who was working in antwerp , which was one of the great merchantile cities of the 15th and early 16th centuries . that was a culture and an economy that was based on importation , that was based on trade , and , in some ways , this is a painting that is also trading . dr. harris : that idea of the north and the south coming together that we see in the work of [ dore ] and beginning with michael pacher in the late 15th century . ( lively music )
|
dr. zucker : right ; we have absolutely no historical references to their likenesses , and so where is the authority of any painter who is transcribing their images ? and that issue of even the legitimacy of transcribing an image is called into question in the top right corner , where the artist has rendered [ in grise ] , in greys , a sculpture of moses . you can tell it 's moses because he 's holding the two tablets with the 10 laws .
|
what does steven say about how the sculpture of moses is rendered ?
|
( cheerful music ) dr. steven zucker : according to legend , st. luke had a vision of the virgin mary and child , and painted that vision . as a result , he is the patron saint of painters . dr. beth harris : you 'll notice that st. luke 's eyes are half-closed , so we know that he is not actually seeing the virgin and child in front of him , but having a vision . dr. zucker : it is not his painting , in a sense . he is literally the hand of this angel . st. luke 's image , then , of the virgin mary and child has a kind of authority because it is god 's , actually , and not his . dr. harris : what 's interesting then is that the artist , gossaert , is painting his virgin mary and child not from the same authority as the painter st. luke , in his painting . one wonders about what it was like for artists to paint heavenly figures . how does one imagine the virgin mary ? how does one paint jesus christ ? these are , i think , difficult questions always for artists . dr. zucker : right ; we have absolutely no historical references to their likenesses , and so where is the authority of any painter who is transcribing their images ? and that issue of even the legitimacy of transcribing an image is called into question in the top right corner , where the artist has rendered [ in grise ] , in greys , a sculpture of moses . you can tell it 's moses because he 's holding the two tablets with the 10 laws . dr. harris : the 10 commandments . dr. zucker : in the christian tradition , he 's shown with horns on his head , and so we know it 's moses . moses seems to actually be pointing at something , and one of the laws is to not render people , not to render the fish below the sea , not to render the birds in the sky . the idea that the artist tries to take on the role of god , perhaps , by trying to create . dr. harris : `` thou shalt not create graven images , '' might be how most people know that commandment . gossaert is living right at the time that the protestant reformation begins , and one of the things that luther 's followers talked about is the danger of images , of people worshipping images instead of using them only as an aid in prayer . this is certainly reflecting on the role of the artist and whether images have a legitimacy or not . dr. zucker : well , that 's right . this is absolutely supporting the legitimacy of the artist creating religious imagery . dr. harris : because one of the writers of the gospel , st. luke himself , painted mary . dr. zucker : and the artist has blown out all the stops . he is rendering every detail with a precision that comes out of the northern tradition . dr. harris : we know that gossaert copied van eyck . he 's fully steeped in the northern rennaisance tradition of painting everything with a clarity and exactitude and attention to different textures . dr. zucker : well , look at the angel 's wings . look at the detail of the relief carving in the architecture . this is an arist who is just enjoying the ability to magically render form . now , look for just a second back at moses and those two tablets . notice the way that the shape of those two tablets rhyme with the architectural space . i think when most art historians look at this painting , they look back to this tradition of dividing the earthly space from the spiritual space . certainly , that central column does that ; but it also makes the entire painting two tablets . there is this way in which the tablets that moses holds is actually embodied in the architectural space itself . dr. harris : that 's true . although we think about the space as being very classical-looking , looking like ancient roman architecture , with those round arches and pilasters , it 's still to me a very mysterious space , much more like northern rennaisance spaces , where , as we look back toward moses , we have those repeated round arches , moving back into a space that we ca n't quite determine there . although the foreground of the painting seems to be carefully mapped out according to the rules of linear perscpective , which obviously gossaert has learned as a northern rennaisance artist from traveling to italy , but we see so much of the north here . if we look at the drapery that st. luke wears , it 's typical northern rennaisance , angular folds of drapery that we see in the art of campin or rogier van der weyden . dr. zucker : and so is the color . dr. harris : the green that that angel wears against the complementary red color worn by st. luke . there 's a real thoughtfulness about color here . dr. zucker : this is an artist who was working in antwerp , which was one of the great merchantile cities of the 15th and early 16th centuries . that was a culture and an economy that was based on importation , that was based on trade , and , in some ways , this is a painting that is also trading . dr. harris : that idea of the north and the south coming together that we see in the work of [ dore ] and beginning with michael pacher in the late 15th century . ( lively music )
|
how does one imagine the virgin mary ? how does one paint jesus christ ? these are , i think , difficult questions always for artists .
|
if luke was a disciple of christ how was he able to draw the madonna with the child ?
|
in the last video where we generalized the linear consumption function . i said that the tax , the total amount of taxes , the aggregate taxes are constant , all of these were constants right here . you can merge them into a constant that ended up being our independent variable intercept right over here . youtube user nilsor1337 asks a very interesting and good question . `` are n't taxes in some way a function of aggregate income ? `` in most modern economies `` people pay a percentage of their income . `` in general , the tax base grows as aggregate income `` or as gdp grows . `` is it appropriate to make this constant ? '' the simple answer is it depends on how carefully you want to model it . in some cases you might just say , `` well , let 's just assume that this is a bulk tax . `` we 're just trying to understand one aspect of it . '' you will see that in some economics courses or some economics textbooks . the other way is you could actually model it a little bit more realistic . you could say , `` hey , taxes really are `` a function of aggregate income . '' we could say that t really is going to be equal to some tax rate . i 'll write that as a lower case t times aggregate income . in a place like the u.s. , this might be close to the 30 % of aggregate income or 20 % . whatever it might be or aggregate income is what is going to go for taxes . if you do it this way , and you substitute back to this you could actually get an expression for consumption in terms of aggregate income that takes into consideration the idea that taxes are function of aggregate income . just to do that algebraically , we can rewrite this expression up here . you have aggregate consumption = my marginal propensity to consume times aggregate income + autonomous consumption , the amount that would be consumed no matter what . minus the marginal propensity to consume , shows up again . instead of writing t right over here , i 'm going to write lower case t x y , tax rate times aggregate income . times the tax rate times aggregate income . i just took this , instead of writing upper case t , i wrote lower case t times aggregate income and they should be the same thing . but now we 've expressed t as a function of aggregate income . now we can merge both of these , these are something times aggregate income . we can combine those 2 terms . this one and this one write over here . if we factor our a common factor of c1 x y , we get , let me write it this way . actually , let me just combine them first so that the algebra does n't confuse you . we get c = c1 x y . marginal propensity to consume times aggregate income and i 'm going to write this one . minus the marginal propensity to consume times ... i 'll switch the order here . well , let me not switch the order , times the tax rate , not just the aggregate total tax value but the actual tax rate times aggregate income . that 's those 2 terms there and then we 're just left with the autonomous consumption . so , plus the autonomous consumption . over here , we have a common factor . we can factor out the c1 and the y , or essentially the marginal propensity to consume and the aggregate income . this is just algebraic manipulation right over here . we get aggregate consumption is equal to , let 's see , we could write this c1 ( 1 - t ) y . you can multiply this out to verify . if you multiply it all out then the 1st term is c1 ( 1 ) y is this right over here and c1 ( -t ) y is this term right over here . then you 're left with your autonomous consumption . this actually makes a lot of sense because when you write it like this , when you write it like this you could look at this term right over here . what is this term right over here ? well , ( 1 - t ) y , if the tax rate is 30 % then this 1 - 30 % is going to be 70 % . 70 % x aggregate income , that 's essentially what people get in their pockets . this whole term right over here is essentially disposable income . disposable income right over here . we could actually , if we wanted to write this as some other variable we could just put that variable right over there and say it 's disposable income and then it actually becomes a very simple thing to graph . we could graph this 2 different ways . if we wanted to write a function of aggregate income we would graph it like this . now , when we express it this way , taxes as a function of aggregate income now our vertical intercept . this is aggregate consumption . our vertical intercept is this term right over here . that is c [ not ] and our slope is all of this business . the slope of our line is going to be c1 ( 1 - t ) and this right over here , the independent variable is aggregate income . another option , we could set some other variable to what we could say disposable income . let me call it y disposable = ( 1 - t ) y then we could write this . it 's essentially equal to this business right over there . then we could rewrite the consumption function as aggregate consumption = marginal propensity to consume times disposable income + sum level of autonomous consumption . plus sum level of autonomous consumption . this actually takes us back to the basics . this takes us back to our very original situation here where we had some autonomous consumption plus our marginal propensity to consume times disposable income . if we wanted to plot it this way as a function of disposable income , not aggregate income then it would look like this . this is consumption , and now this is an aggregate income , this is disposable income which is the same thing as ( 1 - t ) y . now , still our vertical intercept is c [ not ] and our line slope is the marginal propensity to consume . this is c1 just like that . all of these are completely valid consumption functions and i thank nilsor1337 for bringing up a topic that actually was a cause of confusion for me because it really does depend . because i thought the way , he or she , originally thought about the problem . well , taxes are a function and a lot of econ books tend to treat this as a constant . that is actually just an assumption they make to often simplify the calculations . if they do n't want to make that assumption you can still show that it is a linear function , that aggregate consumption is still a linear function of aggregate income .
|
just to do that algebraically , we can rewrite this expression up here . you have aggregate consumption = my marginal propensity to consume times aggregate income + autonomous consumption , the amount that would be consumed no matter what . minus the marginal propensity to consume , shows up again .
|
would n't the base consumption ( csub0 ) has come out of the total income ( y ) ?
|
in the last video where we generalized the linear consumption function . i said that the tax , the total amount of taxes , the aggregate taxes are constant , all of these were constants right here . you can merge them into a constant that ended up being our independent variable intercept right over here . youtube user nilsor1337 asks a very interesting and good question . `` are n't taxes in some way a function of aggregate income ? `` in most modern economies `` people pay a percentage of their income . `` in general , the tax base grows as aggregate income `` or as gdp grows . `` is it appropriate to make this constant ? '' the simple answer is it depends on how carefully you want to model it . in some cases you might just say , `` well , let 's just assume that this is a bulk tax . `` we 're just trying to understand one aspect of it . '' you will see that in some economics courses or some economics textbooks . the other way is you could actually model it a little bit more realistic . you could say , `` hey , taxes really are `` a function of aggregate income . '' we could say that t really is going to be equal to some tax rate . i 'll write that as a lower case t times aggregate income . in a place like the u.s. , this might be close to the 30 % of aggregate income or 20 % . whatever it might be or aggregate income is what is going to go for taxes . if you do it this way , and you substitute back to this you could actually get an expression for consumption in terms of aggregate income that takes into consideration the idea that taxes are function of aggregate income . just to do that algebraically , we can rewrite this expression up here . you have aggregate consumption = my marginal propensity to consume times aggregate income + autonomous consumption , the amount that would be consumed no matter what . minus the marginal propensity to consume , shows up again . instead of writing t right over here , i 'm going to write lower case t x y , tax rate times aggregate income . times the tax rate times aggregate income . i just took this , instead of writing upper case t , i wrote lower case t times aggregate income and they should be the same thing . but now we 've expressed t as a function of aggregate income . now we can merge both of these , these are something times aggregate income . we can combine those 2 terms . this one and this one write over here . if we factor our a common factor of c1 x y , we get , let me write it this way . actually , let me just combine them first so that the algebra does n't confuse you . we get c = c1 x y . marginal propensity to consume times aggregate income and i 'm going to write this one . minus the marginal propensity to consume times ... i 'll switch the order here . well , let me not switch the order , times the tax rate , not just the aggregate total tax value but the actual tax rate times aggregate income . that 's those 2 terms there and then we 're just left with the autonomous consumption . so , plus the autonomous consumption . over here , we have a common factor . we can factor out the c1 and the y , or essentially the marginal propensity to consume and the aggregate income . this is just algebraic manipulation right over here . we get aggregate consumption is equal to , let 's see , we could write this c1 ( 1 - t ) y . you can multiply this out to verify . if you multiply it all out then the 1st term is c1 ( 1 ) y is this right over here and c1 ( -t ) y is this term right over here . then you 're left with your autonomous consumption . this actually makes a lot of sense because when you write it like this , when you write it like this you could look at this term right over here . what is this term right over here ? well , ( 1 - t ) y , if the tax rate is 30 % then this 1 - 30 % is going to be 70 % . 70 % x aggregate income , that 's essentially what people get in their pockets . this whole term right over here is essentially disposable income . disposable income right over here . we could actually , if we wanted to write this as some other variable we could just put that variable right over there and say it 's disposable income and then it actually becomes a very simple thing to graph . we could graph this 2 different ways . if we wanted to write a function of aggregate income we would graph it like this . now , when we express it this way , taxes as a function of aggregate income now our vertical intercept . this is aggregate consumption . our vertical intercept is this term right over here . that is c [ not ] and our slope is all of this business . the slope of our line is going to be c1 ( 1 - t ) and this right over here , the independent variable is aggregate income . another option , we could set some other variable to what we could say disposable income . let me call it y disposable = ( 1 - t ) y then we could write this . it 's essentially equal to this business right over there . then we could rewrite the consumption function as aggregate consumption = marginal propensity to consume times disposable income + sum level of autonomous consumption . plus sum level of autonomous consumption . this actually takes us back to the basics . this takes us back to our very original situation here where we had some autonomous consumption plus our marginal propensity to consume times disposable income . if we wanted to plot it this way as a function of disposable income , not aggregate income then it would look like this . this is consumption , and now this is an aggregate income , this is disposable income which is the same thing as ( 1 - t ) y . now , still our vertical intercept is c [ not ] and our line slope is the marginal propensity to consume . this is c1 just like that . all of these are completely valid consumption functions and i thank nilsor1337 for bringing up a topic that actually was a cause of confusion for me because it really does depend . because i thought the way , he or she , originally thought about the problem . well , taxes are a function and a lot of econ books tend to treat this as a constant . that is actually just an assumption they make to often simplify the calculations . if they do n't want to make that assumption you can still show that it is a linear function , that aggregate consumption is still a linear function of aggregate income .
|
this whole term right over here is essentially disposable income . disposable income right over here . we could actually , if we wanted to write this as some other variable we could just put that variable right over there and say it 's disposable income and then it actually becomes a very simple thing to graph .
|
if consumtion= base + disposable income , would n't we have to also substract , taxes and the base consumption to get to disposable income ?
|
in the last video where we generalized the linear consumption function . i said that the tax , the total amount of taxes , the aggregate taxes are constant , all of these were constants right here . you can merge them into a constant that ended up being our independent variable intercept right over here . youtube user nilsor1337 asks a very interesting and good question . `` are n't taxes in some way a function of aggregate income ? `` in most modern economies `` people pay a percentage of their income . `` in general , the tax base grows as aggregate income `` or as gdp grows . `` is it appropriate to make this constant ? '' the simple answer is it depends on how carefully you want to model it . in some cases you might just say , `` well , let 's just assume that this is a bulk tax . `` we 're just trying to understand one aspect of it . '' you will see that in some economics courses or some economics textbooks . the other way is you could actually model it a little bit more realistic . you could say , `` hey , taxes really are `` a function of aggregate income . '' we could say that t really is going to be equal to some tax rate . i 'll write that as a lower case t times aggregate income . in a place like the u.s. , this might be close to the 30 % of aggregate income or 20 % . whatever it might be or aggregate income is what is going to go for taxes . if you do it this way , and you substitute back to this you could actually get an expression for consumption in terms of aggregate income that takes into consideration the idea that taxes are function of aggregate income . just to do that algebraically , we can rewrite this expression up here . you have aggregate consumption = my marginal propensity to consume times aggregate income + autonomous consumption , the amount that would be consumed no matter what . minus the marginal propensity to consume , shows up again . instead of writing t right over here , i 'm going to write lower case t x y , tax rate times aggregate income . times the tax rate times aggregate income . i just took this , instead of writing upper case t , i wrote lower case t times aggregate income and they should be the same thing . but now we 've expressed t as a function of aggregate income . now we can merge both of these , these are something times aggregate income . we can combine those 2 terms . this one and this one write over here . if we factor our a common factor of c1 x y , we get , let me write it this way . actually , let me just combine them first so that the algebra does n't confuse you . we get c = c1 x y . marginal propensity to consume times aggregate income and i 'm going to write this one . minus the marginal propensity to consume times ... i 'll switch the order here . well , let me not switch the order , times the tax rate , not just the aggregate total tax value but the actual tax rate times aggregate income . that 's those 2 terms there and then we 're just left with the autonomous consumption . so , plus the autonomous consumption . over here , we have a common factor . we can factor out the c1 and the y , or essentially the marginal propensity to consume and the aggregate income . this is just algebraic manipulation right over here . we get aggregate consumption is equal to , let 's see , we could write this c1 ( 1 - t ) y . you can multiply this out to verify . if you multiply it all out then the 1st term is c1 ( 1 ) y is this right over here and c1 ( -t ) y is this term right over here . then you 're left with your autonomous consumption . this actually makes a lot of sense because when you write it like this , when you write it like this you could look at this term right over here . what is this term right over here ? well , ( 1 - t ) y , if the tax rate is 30 % then this 1 - 30 % is going to be 70 % . 70 % x aggregate income , that 's essentially what people get in their pockets . this whole term right over here is essentially disposable income . disposable income right over here . we could actually , if we wanted to write this as some other variable we could just put that variable right over there and say it 's disposable income and then it actually becomes a very simple thing to graph . we could graph this 2 different ways . if we wanted to write a function of aggregate income we would graph it like this . now , when we express it this way , taxes as a function of aggregate income now our vertical intercept . this is aggregate consumption . our vertical intercept is this term right over here . that is c [ not ] and our slope is all of this business . the slope of our line is going to be c1 ( 1 - t ) and this right over here , the independent variable is aggregate income . another option , we could set some other variable to what we could say disposable income . let me call it y disposable = ( 1 - t ) y then we could write this . it 's essentially equal to this business right over there . then we could rewrite the consumption function as aggregate consumption = marginal propensity to consume times disposable income + sum level of autonomous consumption . plus sum level of autonomous consumption . this actually takes us back to the basics . this takes us back to our very original situation here where we had some autonomous consumption plus our marginal propensity to consume times disposable income . if we wanted to plot it this way as a function of disposable income , not aggregate income then it would look like this . this is consumption , and now this is an aggregate income , this is disposable income which is the same thing as ( 1 - t ) y . now , still our vertical intercept is c [ not ] and our line slope is the marginal propensity to consume . this is c1 just like that . all of these are completely valid consumption functions and i thank nilsor1337 for bringing up a topic that actually was a cause of confusion for me because it really does depend . because i thought the way , he or she , originally thought about the problem . well , taxes are a function and a lot of econ books tend to treat this as a constant . that is actually just an assumption they make to often simplify the calculations . if they do n't want to make that assumption you can still show that it is a linear function , that aggregate consumption is still a linear function of aggregate income .
|
what is this term right over here ? well , ( 1 - t ) y , if the tax rate is 30 % then this 1 - 30 % is going to be 70 % . 70 % x aggregate income , that 's essentially what people get in their pockets .
|
is there any mathematical relationship between mpc and tax rates that the government makes use of to increase aggregate consumption : c1x ( 1 - t1 ) < c2x ( 1 - t2 ) ?
|
in the last video where we generalized the linear consumption function . i said that the tax , the total amount of taxes , the aggregate taxes are constant , all of these were constants right here . you can merge them into a constant that ended up being our independent variable intercept right over here . youtube user nilsor1337 asks a very interesting and good question . `` are n't taxes in some way a function of aggregate income ? `` in most modern economies `` people pay a percentage of their income . `` in general , the tax base grows as aggregate income `` or as gdp grows . `` is it appropriate to make this constant ? '' the simple answer is it depends on how carefully you want to model it . in some cases you might just say , `` well , let 's just assume that this is a bulk tax . `` we 're just trying to understand one aspect of it . '' you will see that in some economics courses or some economics textbooks . the other way is you could actually model it a little bit more realistic . you could say , `` hey , taxes really are `` a function of aggregate income . '' we could say that t really is going to be equal to some tax rate . i 'll write that as a lower case t times aggregate income . in a place like the u.s. , this might be close to the 30 % of aggregate income or 20 % . whatever it might be or aggregate income is what is going to go for taxes . if you do it this way , and you substitute back to this you could actually get an expression for consumption in terms of aggregate income that takes into consideration the idea that taxes are function of aggregate income . just to do that algebraically , we can rewrite this expression up here . you have aggregate consumption = my marginal propensity to consume times aggregate income + autonomous consumption , the amount that would be consumed no matter what . minus the marginal propensity to consume , shows up again . instead of writing t right over here , i 'm going to write lower case t x y , tax rate times aggregate income . times the tax rate times aggregate income . i just took this , instead of writing upper case t , i wrote lower case t times aggregate income and they should be the same thing . but now we 've expressed t as a function of aggregate income . now we can merge both of these , these are something times aggregate income . we can combine those 2 terms . this one and this one write over here . if we factor our a common factor of c1 x y , we get , let me write it this way . actually , let me just combine them first so that the algebra does n't confuse you . we get c = c1 x y . marginal propensity to consume times aggregate income and i 'm going to write this one . minus the marginal propensity to consume times ... i 'll switch the order here . well , let me not switch the order , times the tax rate , not just the aggregate total tax value but the actual tax rate times aggregate income . that 's those 2 terms there and then we 're just left with the autonomous consumption . so , plus the autonomous consumption . over here , we have a common factor . we can factor out the c1 and the y , or essentially the marginal propensity to consume and the aggregate income . this is just algebraic manipulation right over here . we get aggregate consumption is equal to , let 's see , we could write this c1 ( 1 - t ) y . you can multiply this out to verify . if you multiply it all out then the 1st term is c1 ( 1 ) y is this right over here and c1 ( -t ) y is this term right over here . then you 're left with your autonomous consumption . this actually makes a lot of sense because when you write it like this , when you write it like this you could look at this term right over here . what is this term right over here ? well , ( 1 - t ) y , if the tax rate is 30 % then this 1 - 30 % is going to be 70 % . 70 % x aggregate income , that 's essentially what people get in their pockets . this whole term right over here is essentially disposable income . disposable income right over here . we could actually , if we wanted to write this as some other variable we could just put that variable right over there and say it 's disposable income and then it actually becomes a very simple thing to graph . we could graph this 2 different ways . if we wanted to write a function of aggregate income we would graph it like this . now , when we express it this way , taxes as a function of aggregate income now our vertical intercept . this is aggregate consumption . our vertical intercept is this term right over here . that is c [ not ] and our slope is all of this business . the slope of our line is going to be c1 ( 1 - t ) and this right over here , the independent variable is aggregate income . another option , we could set some other variable to what we could say disposable income . let me call it y disposable = ( 1 - t ) y then we could write this . it 's essentially equal to this business right over there . then we could rewrite the consumption function as aggregate consumption = marginal propensity to consume times disposable income + sum level of autonomous consumption . plus sum level of autonomous consumption . this actually takes us back to the basics . this takes us back to our very original situation here where we had some autonomous consumption plus our marginal propensity to consume times disposable income . if we wanted to plot it this way as a function of disposable income , not aggregate income then it would look like this . this is consumption , and now this is an aggregate income , this is disposable income which is the same thing as ( 1 - t ) y . now , still our vertical intercept is c [ not ] and our line slope is the marginal propensity to consume . this is c1 just like that . all of these are completely valid consumption functions and i thank nilsor1337 for bringing up a topic that actually was a cause of confusion for me because it really does depend . because i thought the way , he or she , originally thought about the problem . well , taxes are a function and a lot of econ books tend to treat this as a constant . that is actually just an assumption they make to often simplify the calculations . if they do n't want to make that assumption you can still show that it is a linear function , that aggregate consumption is still a linear function of aggregate income .
|
i 'll switch the order here . well , let me not switch the order , times the tax rate , not just the aggregate total tax value but the actual tax rate times aggregate income . that 's those 2 terms there and then we 're just left with the autonomous consumption .
|
are n't tax rates not constant anyway ?
|
in the last video where we generalized the linear consumption function . i said that the tax , the total amount of taxes , the aggregate taxes are constant , all of these were constants right here . you can merge them into a constant that ended up being our independent variable intercept right over here . youtube user nilsor1337 asks a very interesting and good question . `` are n't taxes in some way a function of aggregate income ? `` in most modern economies `` people pay a percentage of their income . `` in general , the tax base grows as aggregate income `` or as gdp grows . `` is it appropriate to make this constant ? '' the simple answer is it depends on how carefully you want to model it . in some cases you might just say , `` well , let 's just assume that this is a bulk tax . `` we 're just trying to understand one aspect of it . '' you will see that in some economics courses or some economics textbooks . the other way is you could actually model it a little bit more realistic . you could say , `` hey , taxes really are `` a function of aggregate income . '' we could say that t really is going to be equal to some tax rate . i 'll write that as a lower case t times aggregate income . in a place like the u.s. , this might be close to the 30 % of aggregate income or 20 % . whatever it might be or aggregate income is what is going to go for taxes . if you do it this way , and you substitute back to this you could actually get an expression for consumption in terms of aggregate income that takes into consideration the idea that taxes are function of aggregate income . just to do that algebraically , we can rewrite this expression up here . you have aggregate consumption = my marginal propensity to consume times aggregate income + autonomous consumption , the amount that would be consumed no matter what . minus the marginal propensity to consume , shows up again . instead of writing t right over here , i 'm going to write lower case t x y , tax rate times aggregate income . times the tax rate times aggregate income . i just took this , instead of writing upper case t , i wrote lower case t times aggregate income and they should be the same thing . but now we 've expressed t as a function of aggregate income . now we can merge both of these , these are something times aggregate income . we can combine those 2 terms . this one and this one write over here . if we factor our a common factor of c1 x y , we get , let me write it this way . actually , let me just combine them first so that the algebra does n't confuse you . we get c = c1 x y . marginal propensity to consume times aggregate income and i 'm going to write this one . minus the marginal propensity to consume times ... i 'll switch the order here . well , let me not switch the order , times the tax rate , not just the aggregate total tax value but the actual tax rate times aggregate income . that 's those 2 terms there and then we 're just left with the autonomous consumption . so , plus the autonomous consumption . over here , we have a common factor . we can factor out the c1 and the y , or essentially the marginal propensity to consume and the aggregate income . this is just algebraic manipulation right over here . we get aggregate consumption is equal to , let 's see , we could write this c1 ( 1 - t ) y . you can multiply this out to verify . if you multiply it all out then the 1st term is c1 ( 1 ) y is this right over here and c1 ( -t ) y is this term right over here . then you 're left with your autonomous consumption . this actually makes a lot of sense because when you write it like this , when you write it like this you could look at this term right over here . what is this term right over here ? well , ( 1 - t ) y , if the tax rate is 30 % then this 1 - 30 % is going to be 70 % . 70 % x aggregate income , that 's essentially what people get in their pockets . this whole term right over here is essentially disposable income . disposable income right over here . we could actually , if we wanted to write this as some other variable we could just put that variable right over there and say it 's disposable income and then it actually becomes a very simple thing to graph . we could graph this 2 different ways . if we wanted to write a function of aggregate income we would graph it like this . now , when we express it this way , taxes as a function of aggregate income now our vertical intercept . this is aggregate consumption . our vertical intercept is this term right over here . that is c [ not ] and our slope is all of this business . the slope of our line is going to be c1 ( 1 - t ) and this right over here , the independent variable is aggregate income . another option , we could set some other variable to what we could say disposable income . let me call it y disposable = ( 1 - t ) y then we could write this . it 's essentially equal to this business right over there . then we could rewrite the consumption function as aggregate consumption = marginal propensity to consume times disposable income + sum level of autonomous consumption . plus sum level of autonomous consumption . this actually takes us back to the basics . this takes us back to our very original situation here where we had some autonomous consumption plus our marginal propensity to consume times disposable income . if we wanted to plot it this way as a function of disposable income , not aggregate income then it would look like this . this is consumption , and now this is an aggregate income , this is disposable income which is the same thing as ( 1 - t ) y . now , still our vertical intercept is c [ not ] and our line slope is the marginal propensity to consume . this is c1 just like that . all of these are completely valid consumption functions and i thank nilsor1337 for bringing up a topic that actually was a cause of confusion for me because it really does depend . because i thought the way , he or she , originally thought about the problem . well , taxes are a function and a lot of econ books tend to treat this as a constant . that is actually just an assumption they make to often simplify the calculations . if they do n't want to make that assumption you can still show that it is a linear function , that aggregate consumption is still a linear function of aggregate income .
|
in the last video where we generalized the linear consumption function . i said that the tax , the total amount of taxes , the aggregate taxes are constant , all of these were constants right here . you can merge them into a constant that ended up being our independent variable intercept right over here .
|
given that total demand is the same what should we expect that the next step for squeezy oranges be ?
|
in the last video where we generalized the linear consumption function . i said that the tax , the total amount of taxes , the aggregate taxes are constant , all of these were constants right here . you can merge them into a constant that ended up being our independent variable intercept right over here . youtube user nilsor1337 asks a very interesting and good question . `` are n't taxes in some way a function of aggregate income ? `` in most modern economies `` people pay a percentage of their income . `` in general , the tax base grows as aggregate income `` or as gdp grows . `` is it appropriate to make this constant ? '' the simple answer is it depends on how carefully you want to model it . in some cases you might just say , `` well , let 's just assume that this is a bulk tax . `` we 're just trying to understand one aspect of it . '' you will see that in some economics courses or some economics textbooks . the other way is you could actually model it a little bit more realistic . you could say , `` hey , taxes really are `` a function of aggregate income . '' we could say that t really is going to be equal to some tax rate . i 'll write that as a lower case t times aggregate income . in a place like the u.s. , this might be close to the 30 % of aggregate income or 20 % . whatever it might be or aggregate income is what is going to go for taxes . if you do it this way , and you substitute back to this you could actually get an expression for consumption in terms of aggregate income that takes into consideration the idea that taxes are function of aggregate income . just to do that algebraically , we can rewrite this expression up here . you have aggregate consumption = my marginal propensity to consume times aggregate income + autonomous consumption , the amount that would be consumed no matter what . minus the marginal propensity to consume , shows up again . instead of writing t right over here , i 'm going to write lower case t x y , tax rate times aggregate income . times the tax rate times aggregate income . i just took this , instead of writing upper case t , i wrote lower case t times aggregate income and they should be the same thing . but now we 've expressed t as a function of aggregate income . now we can merge both of these , these are something times aggregate income . we can combine those 2 terms . this one and this one write over here . if we factor our a common factor of c1 x y , we get , let me write it this way . actually , let me just combine them first so that the algebra does n't confuse you . we get c = c1 x y . marginal propensity to consume times aggregate income and i 'm going to write this one . minus the marginal propensity to consume times ... i 'll switch the order here . well , let me not switch the order , times the tax rate , not just the aggregate total tax value but the actual tax rate times aggregate income . that 's those 2 terms there and then we 're just left with the autonomous consumption . so , plus the autonomous consumption . over here , we have a common factor . we can factor out the c1 and the y , or essentially the marginal propensity to consume and the aggregate income . this is just algebraic manipulation right over here . we get aggregate consumption is equal to , let 's see , we could write this c1 ( 1 - t ) y . you can multiply this out to verify . if you multiply it all out then the 1st term is c1 ( 1 ) y is this right over here and c1 ( -t ) y is this term right over here . then you 're left with your autonomous consumption . this actually makes a lot of sense because when you write it like this , when you write it like this you could look at this term right over here . what is this term right over here ? well , ( 1 - t ) y , if the tax rate is 30 % then this 1 - 30 % is going to be 70 % . 70 % x aggregate income , that 's essentially what people get in their pockets . this whole term right over here is essentially disposable income . disposable income right over here . we could actually , if we wanted to write this as some other variable we could just put that variable right over there and say it 's disposable income and then it actually becomes a very simple thing to graph . we could graph this 2 different ways . if we wanted to write a function of aggregate income we would graph it like this . now , when we express it this way , taxes as a function of aggregate income now our vertical intercept . this is aggregate consumption . our vertical intercept is this term right over here . that is c [ not ] and our slope is all of this business . the slope of our line is going to be c1 ( 1 - t ) and this right over here , the independent variable is aggregate income . another option , we could set some other variable to what we could say disposable income . let me call it y disposable = ( 1 - t ) y then we could write this . it 's essentially equal to this business right over there . then we could rewrite the consumption function as aggregate consumption = marginal propensity to consume times disposable income + sum level of autonomous consumption . plus sum level of autonomous consumption . this actually takes us back to the basics . this takes us back to our very original situation here where we had some autonomous consumption plus our marginal propensity to consume times disposable income . if we wanted to plot it this way as a function of disposable income , not aggregate income then it would look like this . this is consumption , and now this is an aggregate income , this is disposable income which is the same thing as ( 1 - t ) y . now , still our vertical intercept is c [ not ] and our line slope is the marginal propensity to consume . this is c1 just like that . all of these are completely valid consumption functions and i thank nilsor1337 for bringing up a topic that actually was a cause of confusion for me because it really does depend . because i thought the way , he or she , originally thought about the problem . well , taxes are a function and a lot of econ books tend to treat this as a constant . that is actually just an assumption they make to often simplify the calculations . if they do n't want to make that assumption you can still show that it is a linear function , that aggregate consumption is still a linear function of aggregate income .
|
we get c = c1 x y . marginal propensity to consume times aggregate income and i 'm going to write this one . minus the marginal propensity to consume times ...
|
how is someone able to consume without income ?
|
in the last video where we generalized the linear consumption function . i said that the tax , the total amount of taxes , the aggregate taxes are constant , all of these were constants right here . you can merge them into a constant that ended up being our independent variable intercept right over here . youtube user nilsor1337 asks a very interesting and good question . `` are n't taxes in some way a function of aggregate income ? `` in most modern economies `` people pay a percentage of their income . `` in general , the tax base grows as aggregate income `` or as gdp grows . `` is it appropriate to make this constant ? '' the simple answer is it depends on how carefully you want to model it . in some cases you might just say , `` well , let 's just assume that this is a bulk tax . `` we 're just trying to understand one aspect of it . '' you will see that in some economics courses or some economics textbooks . the other way is you could actually model it a little bit more realistic . you could say , `` hey , taxes really are `` a function of aggregate income . '' we could say that t really is going to be equal to some tax rate . i 'll write that as a lower case t times aggregate income . in a place like the u.s. , this might be close to the 30 % of aggregate income or 20 % . whatever it might be or aggregate income is what is going to go for taxes . if you do it this way , and you substitute back to this you could actually get an expression for consumption in terms of aggregate income that takes into consideration the idea that taxes are function of aggregate income . just to do that algebraically , we can rewrite this expression up here . you have aggregate consumption = my marginal propensity to consume times aggregate income + autonomous consumption , the amount that would be consumed no matter what . minus the marginal propensity to consume , shows up again . instead of writing t right over here , i 'm going to write lower case t x y , tax rate times aggregate income . times the tax rate times aggregate income . i just took this , instead of writing upper case t , i wrote lower case t times aggregate income and they should be the same thing . but now we 've expressed t as a function of aggregate income . now we can merge both of these , these are something times aggregate income . we can combine those 2 terms . this one and this one write over here . if we factor our a common factor of c1 x y , we get , let me write it this way . actually , let me just combine them first so that the algebra does n't confuse you . we get c = c1 x y . marginal propensity to consume times aggregate income and i 'm going to write this one . minus the marginal propensity to consume times ... i 'll switch the order here . well , let me not switch the order , times the tax rate , not just the aggregate total tax value but the actual tax rate times aggregate income . that 's those 2 terms there and then we 're just left with the autonomous consumption . so , plus the autonomous consumption . over here , we have a common factor . we can factor out the c1 and the y , or essentially the marginal propensity to consume and the aggregate income . this is just algebraic manipulation right over here . we get aggregate consumption is equal to , let 's see , we could write this c1 ( 1 - t ) y . you can multiply this out to verify . if you multiply it all out then the 1st term is c1 ( 1 ) y is this right over here and c1 ( -t ) y is this term right over here . then you 're left with your autonomous consumption . this actually makes a lot of sense because when you write it like this , when you write it like this you could look at this term right over here . what is this term right over here ? well , ( 1 - t ) y , if the tax rate is 30 % then this 1 - 30 % is going to be 70 % . 70 % x aggregate income , that 's essentially what people get in their pockets . this whole term right over here is essentially disposable income . disposable income right over here . we could actually , if we wanted to write this as some other variable we could just put that variable right over there and say it 's disposable income and then it actually becomes a very simple thing to graph . we could graph this 2 different ways . if we wanted to write a function of aggregate income we would graph it like this . now , when we express it this way , taxes as a function of aggregate income now our vertical intercept . this is aggregate consumption . our vertical intercept is this term right over here . that is c [ not ] and our slope is all of this business . the slope of our line is going to be c1 ( 1 - t ) and this right over here , the independent variable is aggregate income . another option , we could set some other variable to what we could say disposable income . let me call it y disposable = ( 1 - t ) y then we could write this . it 's essentially equal to this business right over there . then we could rewrite the consumption function as aggregate consumption = marginal propensity to consume times disposable income + sum level of autonomous consumption . plus sum level of autonomous consumption . this actually takes us back to the basics . this takes us back to our very original situation here where we had some autonomous consumption plus our marginal propensity to consume times disposable income . if we wanted to plot it this way as a function of disposable income , not aggregate income then it would look like this . this is consumption , and now this is an aggregate income , this is disposable income which is the same thing as ( 1 - t ) y . now , still our vertical intercept is c [ not ] and our line slope is the marginal propensity to consume . this is c1 just like that . all of these are completely valid consumption functions and i thank nilsor1337 for bringing up a topic that actually was a cause of confusion for me because it really does depend . because i thought the way , he or she , originally thought about the problem . well , taxes are a function and a lot of econ books tend to treat this as a constant . that is actually just an assumption they make to often simplify the calculations . if they do n't want to make that assumption you can still show that it is a linear function , that aggregate consumption is still a linear function of aggregate income .
|
you can merge them into a constant that ended up being our independent variable intercept right over here . youtube user nilsor1337 asks a very interesting and good question . `` are n't taxes in some way a function of aggregate income ? `` in most modern economies `` people pay a percentage of their income .
|
hi , i need help please with the following question that i 'm struggling with : if tax function is given as t= -108+0.32y , how much would the government collect in taxes when the economy remains equilibrium ?
|
in the last video where we generalized the linear consumption function . i said that the tax , the total amount of taxes , the aggregate taxes are constant , all of these were constants right here . you can merge them into a constant that ended up being our independent variable intercept right over here . youtube user nilsor1337 asks a very interesting and good question . `` are n't taxes in some way a function of aggregate income ? `` in most modern economies `` people pay a percentage of their income . `` in general , the tax base grows as aggregate income `` or as gdp grows . `` is it appropriate to make this constant ? '' the simple answer is it depends on how carefully you want to model it . in some cases you might just say , `` well , let 's just assume that this is a bulk tax . `` we 're just trying to understand one aspect of it . '' you will see that in some economics courses or some economics textbooks . the other way is you could actually model it a little bit more realistic . you could say , `` hey , taxes really are `` a function of aggregate income . '' we could say that t really is going to be equal to some tax rate . i 'll write that as a lower case t times aggregate income . in a place like the u.s. , this might be close to the 30 % of aggregate income or 20 % . whatever it might be or aggregate income is what is going to go for taxes . if you do it this way , and you substitute back to this you could actually get an expression for consumption in terms of aggregate income that takes into consideration the idea that taxes are function of aggregate income . just to do that algebraically , we can rewrite this expression up here . you have aggregate consumption = my marginal propensity to consume times aggregate income + autonomous consumption , the amount that would be consumed no matter what . minus the marginal propensity to consume , shows up again . instead of writing t right over here , i 'm going to write lower case t x y , tax rate times aggregate income . times the tax rate times aggregate income . i just took this , instead of writing upper case t , i wrote lower case t times aggregate income and they should be the same thing . but now we 've expressed t as a function of aggregate income . now we can merge both of these , these are something times aggregate income . we can combine those 2 terms . this one and this one write over here . if we factor our a common factor of c1 x y , we get , let me write it this way . actually , let me just combine them first so that the algebra does n't confuse you . we get c = c1 x y . marginal propensity to consume times aggregate income and i 'm going to write this one . minus the marginal propensity to consume times ... i 'll switch the order here . well , let me not switch the order , times the tax rate , not just the aggregate total tax value but the actual tax rate times aggregate income . that 's those 2 terms there and then we 're just left with the autonomous consumption . so , plus the autonomous consumption . over here , we have a common factor . we can factor out the c1 and the y , or essentially the marginal propensity to consume and the aggregate income . this is just algebraic manipulation right over here . we get aggregate consumption is equal to , let 's see , we could write this c1 ( 1 - t ) y . you can multiply this out to verify . if you multiply it all out then the 1st term is c1 ( 1 ) y is this right over here and c1 ( -t ) y is this term right over here . then you 're left with your autonomous consumption . this actually makes a lot of sense because when you write it like this , when you write it like this you could look at this term right over here . what is this term right over here ? well , ( 1 - t ) y , if the tax rate is 30 % then this 1 - 30 % is going to be 70 % . 70 % x aggregate income , that 's essentially what people get in their pockets . this whole term right over here is essentially disposable income . disposable income right over here . we could actually , if we wanted to write this as some other variable we could just put that variable right over there and say it 's disposable income and then it actually becomes a very simple thing to graph . we could graph this 2 different ways . if we wanted to write a function of aggregate income we would graph it like this . now , when we express it this way , taxes as a function of aggregate income now our vertical intercept . this is aggregate consumption . our vertical intercept is this term right over here . that is c [ not ] and our slope is all of this business . the slope of our line is going to be c1 ( 1 - t ) and this right over here , the independent variable is aggregate income . another option , we could set some other variable to what we could say disposable income . let me call it y disposable = ( 1 - t ) y then we could write this . it 's essentially equal to this business right over there . then we could rewrite the consumption function as aggregate consumption = marginal propensity to consume times disposable income + sum level of autonomous consumption . plus sum level of autonomous consumption . this actually takes us back to the basics . this takes us back to our very original situation here where we had some autonomous consumption plus our marginal propensity to consume times disposable income . if we wanted to plot it this way as a function of disposable income , not aggregate income then it would look like this . this is consumption , and now this is an aggregate income , this is disposable income which is the same thing as ( 1 - t ) y . now , still our vertical intercept is c [ not ] and our line slope is the marginal propensity to consume . this is c1 just like that . all of these are completely valid consumption functions and i thank nilsor1337 for bringing up a topic that actually was a cause of confusion for me because it really does depend . because i thought the way , he or she , originally thought about the problem . well , taxes are a function and a lot of econ books tend to treat this as a constant . that is actually just an assumption they make to often simplify the calculations . if they do n't want to make that assumption you can still show that it is a linear function , that aggregate consumption is still a linear function of aggregate income .
|
i 'll switch the order here . well , let me not switch the order , times the tax rate , not just the aggregate total tax value but the actual tax rate times aggregate income . that 's those 2 terms there and then we 're just left with the autonomous consumption .
|
other information that is given is the proportional tax rate at 32 % the thing that confuses me is how do i use the given tax rate into the tax function that i 'm required to determine , should i substitute t by ty ?
|
in the last video where we generalized the linear consumption function . i said that the tax , the total amount of taxes , the aggregate taxes are constant , all of these were constants right here . you can merge them into a constant that ended up being our independent variable intercept right over here . youtube user nilsor1337 asks a very interesting and good question . `` are n't taxes in some way a function of aggregate income ? `` in most modern economies `` people pay a percentage of their income . `` in general , the tax base grows as aggregate income `` or as gdp grows . `` is it appropriate to make this constant ? '' the simple answer is it depends on how carefully you want to model it . in some cases you might just say , `` well , let 's just assume that this is a bulk tax . `` we 're just trying to understand one aspect of it . '' you will see that in some economics courses or some economics textbooks . the other way is you could actually model it a little bit more realistic . you could say , `` hey , taxes really are `` a function of aggregate income . '' we could say that t really is going to be equal to some tax rate . i 'll write that as a lower case t times aggregate income . in a place like the u.s. , this might be close to the 30 % of aggregate income or 20 % . whatever it might be or aggregate income is what is going to go for taxes . if you do it this way , and you substitute back to this you could actually get an expression for consumption in terms of aggregate income that takes into consideration the idea that taxes are function of aggregate income . just to do that algebraically , we can rewrite this expression up here . you have aggregate consumption = my marginal propensity to consume times aggregate income + autonomous consumption , the amount that would be consumed no matter what . minus the marginal propensity to consume , shows up again . instead of writing t right over here , i 'm going to write lower case t x y , tax rate times aggregate income . times the tax rate times aggregate income . i just took this , instead of writing upper case t , i wrote lower case t times aggregate income and they should be the same thing . but now we 've expressed t as a function of aggregate income . now we can merge both of these , these are something times aggregate income . we can combine those 2 terms . this one and this one write over here . if we factor our a common factor of c1 x y , we get , let me write it this way . actually , let me just combine them first so that the algebra does n't confuse you . we get c = c1 x y . marginal propensity to consume times aggregate income and i 'm going to write this one . minus the marginal propensity to consume times ... i 'll switch the order here . well , let me not switch the order , times the tax rate , not just the aggregate total tax value but the actual tax rate times aggregate income . that 's those 2 terms there and then we 're just left with the autonomous consumption . so , plus the autonomous consumption . over here , we have a common factor . we can factor out the c1 and the y , or essentially the marginal propensity to consume and the aggregate income . this is just algebraic manipulation right over here . we get aggregate consumption is equal to , let 's see , we could write this c1 ( 1 - t ) y . you can multiply this out to verify . if you multiply it all out then the 1st term is c1 ( 1 ) y is this right over here and c1 ( -t ) y is this term right over here . then you 're left with your autonomous consumption . this actually makes a lot of sense because when you write it like this , when you write it like this you could look at this term right over here . what is this term right over here ? well , ( 1 - t ) y , if the tax rate is 30 % then this 1 - 30 % is going to be 70 % . 70 % x aggregate income , that 's essentially what people get in their pockets . this whole term right over here is essentially disposable income . disposable income right over here . we could actually , if we wanted to write this as some other variable we could just put that variable right over there and say it 's disposable income and then it actually becomes a very simple thing to graph . we could graph this 2 different ways . if we wanted to write a function of aggregate income we would graph it like this . now , when we express it this way , taxes as a function of aggregate income now our vertical intercept . this is aggregate consumption . our vertical intercept is this term right over here . that is c [ not ] and our slope is all of this business . the slope of our line is going to be c1 ( 1 - t ) and this right over here , the independent variable is aggregate income . another option , we could set some other variable to what we could say disposable income . let me call it y disposable = ( 1 - t ) y then we could write this . it 's essentially equal to this business right over there . then we could rewrite the consumption function as aggregate consumption = marginal propensity to consume times disposable income + sum level of autonomous consumption . plus sum level of autonomous consumption . this actually takes us back to the basics . this takes us back to our very original situation here where we had some autonomous consumption plus our marginal propensity to consume times disposable income . if we wanted to plot it this way as a function of disposable income , not aggregate income then it would look like this . this is consumption , and now this is an aggregate income , this is disposable income which is the same thing as ( 1 - t ) y . now , still our vertical intercept is c [ not ] and our line slope is the marginal propensity to consume . this is c1 just like that . all of these are completely valid consumption functions and i thank nilsor1337 for bringing up a topic that actually was a cause of confusion for me because it really does depend . because i thought the way , he or she , originally thought about the problem . well , taxes are a function and a lot of econ books tend to treat this as a constant . that is actually just an assumption they make to often simplify the calculations . if they do n't want to make that assumption you can still show that it is a linear function , that aggregate consumption is still a linear function of aggregate income .
|
it 's essentially equal to this business right over there . then we could rewrite the consumption function as aggregate consumption = marginal propensity to consume times disposable income + sum level of autonomous consumption . plus sum level of autonomous consumption .
|
how consumption and saving function shifts downward when increase in indirect tax ?
|
alright , so last video i showed you guys this really crazy fact . we have our usual setup here for this constrained optimization situation . we have a function we wan na maximize , which i 'm thinking of as revenues for some company . a constraint , which i 'm thinking of as some kinda budget for that company . and , as you know if you 've gotten to this video , one way to solve this constraint optimization problem is to define this function here , the lagrangian , which involves taking this function that you 're trying to maximize , in this case the revenue , and subtracting a new variable , lambda , what 's called the lagrange multiplier , times this quantity , which is the budget function , you know , however much you spend as a function of your input parameters , minus the budget itself , which you might think of as $ 10,000 in our example . so that 's all the usual setup , and the crazy fact , which i just declared , is that when you set this gradient equal to zero , and you find some solution , and there will be three variables in this solution , h star , s star , and lambda star , that this lambda star is not meaningless . it 's not just a proportionality constant between these gradient vectors , but it will actually tell you how much the maximum possible revenue changes as a function of your budget . and the way to start writing all of that in formulas would be to make explicit the fact that , if you consider this value , the $ 10,000 that is your budget , which i 'm calling b , a variable and not a constant , then you have to acknowledge that h star and s star are dependent on b . it 's a very implicit relationship , something that 's kind of hard to think about at first because as you change b , it changes what the lagrangian is , which is gon na change where its gradient equals zero , which changes what h star , s star , and lambda star are . but in principle , they are some function of that budget , of b . and the maximum possible revenue is whatever you get when you just plug in that solution to your function , r , and the claim i made that i just pulled out of the hat is that lambda star , the lambda value that comes packaged in with these two when you set the gradient of the lagrangian equal to zero , equals the derivative of this maximum value , thought of as a function of b , maybe i should emphasize that , we 're thinking of this maximum value as a function of b , with respect to b . so that 's kind of a mouthful . it takes a lot just to even phrase what 's going on , but in the context of an economic example , it has a very clear , precise meaning , which is , if you increase your budget by $ 1 , right , if you increase it from $ 10,000 to $ 10,001 , you 're wondering for that tiny change in budget , that tiny db , what is the ratio of the resulting change in revenue . in a sense , this lambda star tells you , for every dollar that you increase the budget , how much can your revenue increase if you 're always maximizing it . why on earth is this true ? this just seems like it comes out of nowhere . there are a couple clever observations that go into proving this . the first is to notice what happens if we evaluate this lagrangian function itself at this critical point when you input h star , s star , and lambda star . and remember the way that these guys are defined is that you look at all of the values where the gradient of the lagrangian equals the zero vector , and then if you get multiple options , you know sometimes when you set the gradient equal to zero you get multiple solutions , and whichever one maximizes r , that is h star , s star , lambda star . so now i 'm just asking , if you plug that not into the gradient of the lagrangian , but to the lagrangian itself , what do you get ? you 're going to get , we just look at its definition up here , r evaluated at h star and s star . and we subtract off lambda star times b of h star , s star minus the constant that is your budget , something you might think of as $ 10,000 . whatever you set , it 'll be equal to . okay grant , you might say , why does this tell us anything ? you 're just plugging in stars instead of the usual variables . but the key is that , if you plug in h star and s star , this value has to equal zero because h star and s star have to satisfy the constraint . remember , one of the cool parts about this lagrangian function as a whole is that when you take its partial derivative with respect to lambda , all that 's left is this constraint function minus the constraint portion . when you set the gradient of the lagrangian equal to the zero vector , one component of that is to set the partial derivative with respect to lambda equal to zero . and if you remember from the lagrangian video , all that really boils down to is the fact that the constraint holds , which would be your budget achieves $ 10,000 . when you plug in the appropriate h star and s star to this value , you are hitting this constrained amount of money that you can spend . by virtue of how h star and s star are defined , the fact that they are solutions to the constrained optimization problem means this whole portion goes to zero . we can just kind of cancel all that out , and what 's left here is the maximum possible revenue . evidently , when you evaluate the lagrangian at this critical point , at h star , s star , and lambda star , it equals m star . it equals the maximum possible value for the function you 're trying to maximize . ultimately what we want is to understand how that maximum value changes when you consider it a function of the budget . evidently what we can look for is to just ask how the lagrangian changes as you consider it a function of the budget . now , this is an interesting thing to observe because if we just look up at the definition of the lagrangian , if you just look at this formula , if i told you to take the derivative of this with respect to little b , how much does this change with respect to little b , you would notice that this goes to zero . it does n't have a little b . this would also go to zero . and all you 'd be left with would be negative lambda times negative b , and the derivative of that with respect to b would be lambda . so you might say , oh yeah , of course , of course , the derivative of that lagrangian with respect to b , once we work it all out , the only term that was left there was the lambda . and that 's compelling , but ultimately it 's not entirely right . that overlooks the fact that l is not actually defined as a function of b . when we defined the lagrangian , we were considering b to be a constant . so if you really wan na consider this to be a function that involves b , the way we should write it , and i 'll go ahead and erase this guy , the way we should write this lagrangian is to say , you are a function of h star , which itself is dependent on b , and s star , which is also a function of b . as soon as we start considering b a variable and not a constant , we have to acknowledge that this critical point , h star , s star , and lambda star , depends on the value of b . so likewise , that lambda star is also gon na be a function of b , and then we can consider , as a fourth variable , so we 're adding on yet another variable to this function , the value of b itself here . now , when we wan na know what is the value of the lagrangian at the critical point , h star , s star , lambda star , as a function of b , so that can be kinda confusing . what you basically have is this function that only really depends on one value . it only depends on b , but it kinda goes through a four variable function . and so just to make it explicit , this would equal the value of r as a function of h star and s star , and each one of those is a function of little b . so this term is saying what 's your revenue evaluated on the maximizing h and s for the given budget , and then you subtract off lambda star , oh here , i should probably ... i 'm not gon na have room here , am i ? so what you subtract off , minus lambda star at b of h star and s star , but each of these guys is also a function of little b , minus little b . so you have this large , kind of complicated multivariable function . it 's defined in terms of h stars and s stars , which are themselves very implicit . we just say , by definition these are whatever values make the gradient of l equal zero , so very hard to think about what that means concretely . but all of this is really just dependent on the single value , little b . and from here , if we wan na evaluate the derivative of l , we wan na evaluate the derivative of this lagrangian with respect to little b , which is really the only thing it depends on , it 's just via all of these other variables , we use the multivariable chain rule . and at this point , if you do n't know the multivariable chain rule , i have a video on that . definitely pause , go take a look , make sure that it all makes sense . but right here i 'm just gon na be assuming that you know what the multivariable chain rule is . so what it is , is we take the , we 're gon na look at the partial derivatives with respect to all four of these inputs . so we 'll start with the partial derivative of l with respect to h star , and we 're gon na multiple that by the derivative of h star with respect to b . and this might seem like a very hard thing to think about . how do we know how h star changes as b star changes ? but do n't worry about it , you 'll see something magic happen in just a moment . and then we add in partial derivative of l with respect to that second variable , s star , with respect to whatever the second variable is , multiplied by the derivative of s star with respect to b . you can see how you really need to know what the multivariable chain rule is . this would all seem kind of out of the blue . what we now add in is the partial derivative of l with respect to that lambda star , multiplied by the derivative of lambda star with respect to little b . and then finally , we take the partial derivative of this lagrangian with respect to that little b , which we 're now considering a variable . is n't that right ? we 're no longer considering that b a constant . multiplied by , well , something kinda silly . the derivative of b with respect to itself . now if you 're thinking that this is gon na be horrifying to compute , i can understand where you 're coming from . you have to know the derivative of lambda star with respect to b ? you have to somehow intimately be familiar with how this lambda star changes as you change b ? and like i said , that 's such an implicit relationship . we just said that lambda star is , by definition , whatever the solution to this gradient equation is , so somehow you 're supposed to know how that changes when you slightly alter b over here ? well , you do n't really have to worry about things because , by definition , h star , s star , and lambda star are whatever values make the gradient of l equal to zero . but if you think about that , what does it mean for the gradient of l to equal the zero vector ? what it means is that when you take its derivative with respect to that first variable , h star , it equals zero . when you take its derivative with respect to the second variable , that equals zero as well . and with respect to this third variable , that 's gon na equal zero . by definition , h star , s star , and lambda star are whatever values make it the case so that when you plug them in , the partial derivative of the lagrangian with respect to any one of those variables equals zero . so we do n't even have to worry about most of this equation . the only part that matters here is the partial derivative of l with respect to b , that we 're now considering a variable , multiplied by , well , what 's db db ? what is the rate of change of a variable with respect to itself ? it 's one . it is one . so all of this stuff , this entire multivariable chain rule boils down to a single , innocent-looking factor , which is the partial derivative of l with respect to little b . there 's something very subtle here because this might seem obvious . i 'm saying the derivative of l with respect to b equals the derivative of l with respect to b . but maybe i should give a different notation here because here , when i 'm taking the derivative , really i 'm considering l as a single variable function . i 'm considering not what happens as you can freely change all four of these variables . three of them are locked into place by b . so maybe i should really give that a different name . i should call that l star . l star is a single variable function , whereas this l is a multivariable function . this is the function where you can freely change the values of h , and s , and lambda , and b as you put them in . so if we scroll up to look at its definition , which i 've written all over i guess . here , lem me actually rewrite its definition . i think that 'll be useful . i 'm gon na rewrite the l if i consider it as a four variable function of h , s , lambda , and b , that what that equals is r evaluated h and s , minus lambda multiplied by this constraint function , b evaluated at h and s , minus little b . and this is now when i 'm considering little b to be a variable . so this is the lagrangian when you consider all four of these to be freely changing as you want , whereas the thing up here that i 'm considering a single variable function has three of its inputs locked into place , so effectively it 's just a single variable function with respect to b . so it 's actually quite miraculous that the single variable derivative of that l , here , i should , l star , with respect to b , ends up being the same as the partial derivative of l , this l where you 're free to change all the variables , that these should be the same . usually , in any usual circumstance , all of these other terms would 've come into play somehow . but what 's special here is that , by the definition of this l star , the specific way in which these h star , s star , and lambda stars are locked into place happens to be one in which all of these partial derivatives go to zero . so that 's pretty subtle , and i think it 's quite clever . and what it leaves us with is that we just have to evaluate this partial derivative , which is quite simple because we look down here , and you say , what 's the partial derivative of l with respect to b . well , this r has no bs in it , so do n't need to care about that . this term over here , its partial derivative is negative one just because there 's a b here , and that 's multiplied by the constant lambda , so that all just equals lambda . but if we 're in the situation where lambda is locked into place as a function of little b , then we 'd write lambda star as a function of little b . if that feels a little notationally confusing , i 'm right there with you , but the important part here , the important thing to remember , is that we just started considering b as a variable , and we were looking at the h star , s star , and lambda star as they depended on that variable . we made the observation that the lagrangian evaluated at that critical point equals the revenue evaluated at that critical point . the rest of the stuff just cancels out . if you wan na know the derivative of m star , the maximizing revenue , with respect to the budget , how much does your maximum revenue change for tiny changes in your budget , that 's the same as looking at the derivative of the lagrangian with respect to the budget , so long as you 're considering it only on values h star , s star , lambda star , that are critical points of the lagrangian . and all of that really nicely boils down to just taking a simple , partial derivative that gives us the relation we want .
|
i 'm not gon na have room here , am i ? so what you subtract off , minus lambda star at b of h star and s star , but each of these guys is also a function of little b , minus little b . so you have this large , kind of complicated multivariable function .
|
is it possible to find an expression for lambda star as a function of b ?
|
alright , so last video i showed you guys this really crazy fact . we have our usual setup here for this constrained optimization situation . we have a function we wan na maximize , which i 'm thinking of as revenues for some company . a constraint , which i 'm thinking of as some kinda budget for that company . and , as you know if you 've gotten to this video , one way to solve this constraint optimization problem is to define this function here , the lagrangian , which involves taking this function that you 're trying to maximize , in this case the revenue , and subtracting a new variable , lambda , what 's called the lagrange multiplier , times this quantity , which is the budget function , you know , however much you spend as a function of your input parameters , minus the budget itself , which you might think of as $ 10,000 in our example . so that 's all the usual setup , and the crazy fact , which i just declared , is that when you set this gradient equal to zero , and you find some solution , and there will be three variables in this solution , h star , s star , and lambda star , that this lambda star is not meaningless . it 's not just a proportionality constant between these gradient vectors , but it will actually tell you how much the maximum possible revenue changes as a function of your budget . and the way to start writing all of that in formulas would be to make explicit the fact that , if you consider this value , the $ 10,000 that is your budget , which i 'm calling b , a variable and not a constant , then you have to acknowledge that h star and s star are dependent on b . it 's a very implicit relationship , something that 's kind of hard to think about at first because as you change b , it changes what the lagrangian is , which is gon na change where its gradient equals zero , which changes what h star , s star , and lambda star are . but in principle , they are some function of that budget , of b . and the maximum possible revenue is whatever you get when you just plug in that solution to your function , r , and the claim i made that i just pulled out of the hat is that lambda star , the lambda value that comes packaged in with these two when you set the gradient of the lagrangian equal to zero , equals the derivative of this maximum value , thought of as a function of b , maybe i should emphasize that , we 're thinking of this maximum value as a function of b , with respect to b . so that 's kind of a mouthful . it takes a lot just to even phrase what 's going on , but in the context of an economic example , it has a very clear , precise meaning , which is , if you increase your budget by $ 1 , right , if you increase it from $ 10,000 to $ 10,001 , you 're wondering for that tiny change in budget , that tiny db , what is the ratio of the resulting change in revenue . in a sense , this lambda star tells you , for every dollar that you increase the budget , how much can your revenue increase if you 're always maximizing it . why on earth is this true ? this just seems like it comes out of nowhere . there are a couple clever observations that go into proving this . the first is to notice what happens if we evaluate this lagrangian function itself at this critical point when you input h star , s star , and lambda star . and remember the way that these guys are defined is that you look at all of the values where the gradient of the lagrangian equals the zero vector , and then if you get multiple options , you know sometimes when you set the gradient equal to zero you get multiple solutions , and whichever one maximizes r , that is h star , s star , lambda star . so now i 'm just asking , if you plug that not into the gradient of the lagrangian , but to the lagrangian itself , what do you get ? you 're going to get , we just look at its definition up here , r evaluated at h star and s star . and we subtract off lambda star times b of h star , s star minus the constant that is your budget , something you might think of as $ 10,000 . whatever you set , it 'll be equal to . okay grant , you might say , why does this tell us anything ? you 're just plugging in stars instead of the usual variables . but the key is that , if you plug in h star and s star , this value has to equal zero because h star and s star have to satisfy the constraint . remember , one of the cool parts about this lagrangian function as a whole is that when you take its partial derivative with respect to lambda , all that 's left is this constraint function minus the constraint portion . when you set the gradient of the lagrangian equal to the zero vector , one component of that is to set the partial derivative with respect to lambda equal to zero . and if you remember from the lagrangian video , all that really boils down to is the fact that the constraint holds , which would be your budget achieves $ 10,000 . when you plug in the appropriate h star and s star to this value , you are hitting this constrained amount of money that you can spend . by virtue of how h star and s star are defined , the fact that they are solutions to the constrained optimization problem means this whole portion goes to zero . we can just kind of cancel all that out , and what 's left here is the maximum possible revenue . evidently , when you evaluate the lagrangian at this critical point , at h star , s star , and lambda star , it equals m star . it equals the maximum possible value for the function you 're trying to maximize . ultimately what we want is to understand how that maximum value changes when you consider it a function of the budget . evidently what we can look for is to just ask how the lagrangian changes as you consider it a function of the budget . now , this is an interesting thing to observe because if we just look up at the definition of the lagrangian , if you just look at this formula , if i told you to take the derivative of this with respect to little b , how much does this change with respect to little b , you would notice that this goes to zero . it does n't have a little b . this would also go to zero . and all you 'd be left with would be negative lambda times negative b , and the derivative of that with respect to b would be lambda . so you might say , oh yeah , of course , of course , the derivative of that lagrangian with respect to b , once we work it all out , the only term that was left there was the lambda . and that 's compelling , but ultimately it 's not entirely right . that overlooks the fact that l is not actually defined as a function of b . when we defined the lagrangian , we were considering b to be a constant . so if you really wan na consider this to be a function that involves b , the way we should write it , and i 'll go ahead and erase this guy , the way we should write this lagrangian is to say , you are a function of h star , which itself is dependent on b , and s star , which is also a function of b . as soon as we start considering b a variable and not a constant , we have to acknowledge that this critical point , h star , s star , and lambda star , depends on the value of b . so likewise , that lambda star is also gon na be a function of b , and then we can consider , as a fourth variable , so we 're adding on yet another variable to this function , the value of b itself here . now , when we wan na know what is the value of the lagrangian at the critical point , h star , s star , lambda star , as a function of b , so that can be kinda confusing . what you basically have is this function that only really depends on one value . it only depends on b , but it kinda goes through a four variable function . and so just to make it explicit , this would equal the value of r as a function of h star and s star , and each one of those is a function of little b . so this term is saying what 's your revenue evaluated on the maximizing h and s for the given budget , and then you subtract off lambda star , oh here , i should probably ... i 'm not gon na have room here , am i ? so what you subtract off , minus lambda star at b of h star and s star , but each of these guys is also a function of little b , minus little b . so you have this large , kind of complicated multivariable function . it 's defined in terms of h stars and s stars , which are themselves very implicit . we just say , by definition these are whatever values make the gradient of l equal zero , so very hard to think about what that means concretely . but all of this is really just dependent on the single value , little b . and from here , if we wan na evaluate the derivative of l , we wan na evaluate the derivative of this lagrangian with respect to little b , which is really the only thing it depends on , it 's just via all of these other variables , we use the multivariable chain rule . and at this point , if you do n't know the multivariable chain rule , i have a video on that . definitely pause , go take a look , make sure that it all makes sense . but right here i 'm just gon na be assuming that you know what the multivariable chain rule is . so what it is , is we take the , we 're gon na look at the partial derivatives with respect to all four of these inputs . so we 'll start with the partial derivative of l with respect to h star , and we 're gon na multiple that by the derivative of h star with respect to b . and this might seem like a very hard thing to think about . how do we know how h star changes as b star changes ? but do n't worry about it , you 'll see something magic happen in just a moment . and then we add in partial derivative of l with respect to that second variable , s star , with respect to whatever the second variable is , multiplied by the derivative of s star with respect to b . you can see how you really need to know what the multivariable chain rule is . this would all seem kind of out of the blue . what we now add in is the partial derivative of l with respect to that lambda star , multiplied by the derivative of lambda star with respect to little b . and then finally , we take the partial derivative of this lagrangian with respect to that little b , which we 're now considering a variable . is n't that right ? we 're no longer considering that b a constant . multiplied by , well , something kinda silly . the derivative of b with respect to itself . now if you 're thinking that this is gon na be horrifying to compute , i can understand where you 're coming from . you have to know the derivative of lambda star with respect to b ? you have to somehow intimately be familiar with how this lambda star changes as you change b ? and like i said , that 's such an implicit relationship . we just said that lambda star is , by definition , whatever the solution to this gradient equation is , so somehow you 're supposed to know how that changes when you slightly alter b over here ? well , you do n't really have to worry about things because , by definition , h star , s star , and lambda star are whatever values make the gradient of l equal to zero . but if you think about that , what does it mean for the gradient of l to equal the zero vector ? what it means is that when you take its derivative with respect to that first variable , h star , it equals zero . when you take its derivative with respect to the second variable , that equals zero as well . and with respect to this third variable , that 's gon na equal zero . by definition , h star , s star , and lambda star are whatever values make it the case so that when you plug them in , the partial derivative of the lagrangian with respect to any one of those variables equals zero . so we do n't even have to worry about most of this equation . the only part that matters here is the partial derivative of l with respect to b , that we 're now considering a variable , multiplied by , well , what 's db db ? what is the rate of change of a variable with respect to itself ? it 's one . it is one . so all of this stuff , this entire multivariable chain rule boils down to a single , innocent-looking factor , which is the partial derivative of l with respect to little b . there 's something very subtle here because this might seem obvious . i 'm saying the derivative of l with respect to b equals the derivative of l with respect to b . but maybe i should give a different notation here because here , when i 'm taking the derivative , really i 'm considering l as a single variable function . i 'm considering not what happens as you can freely change all four of these variables . three of them are locked into place by b . so maybe i should really give that a different name . i should call that l star . l star is a single variable function , whereas this l is a multivariable function . this is the function where you can freely change the values of h , and s , and lambda , and b as you put them in . so if we scroll up to look at its definition , which i 've written all over i guess . here , lem me actually rewrite its definition . i think that 'll be useful . i 'm gon na rewrite the l if i consider it as a four variable function of h , s , lambda , and b , that what that equals is r evaluated h and s , minus lambda multiplied by this constraint function , b evaluated at h and s , minus little b . and this is now when i 'm considering little b to be a variable . so this is the lagrangian when you consider all four of these to be freely changing as you want , whereas the thing up here that i 'm considering a single variable function has three of its inputs locked into place , so effectively it 's just a single variable function with respect to b . so it 's actually quite miraculous that the single variable derivative of that l , here , i should , l star , with respect to b , ends up being the same as the partial derivative of l , this l where you 're free to change all the variables , that these should be the same . usually , in any usual circumstance , all of these other terms would 've come into play somehow . but what 's special here is that , by the definition of this l star , the specific way in which these h star , s star , and lambda stars are locked into place happens to be one in which all of these partial derivatives go to zero . so that 's pretty subtle , and i think it 's quite clever . and what it leaves us with is that we just have to evaluate this partial derivative , which is quite simple because we look down here , and you say , what 's the partial derivative of l with respect to b . well , this r has no bs in it , so do n't need to care about that . this term over here , its partial derivative is negative one just because there 's a b here , and that 's multiplied by the constant lambda , so that all just equals lambda . but if we 're in the situation where lambda is locked into place as a function of little b , then we 'd write lambda star as a function of little b . if that feels a little notationally confusing , i 'm right there with you , but the important part here , the important thing to remember , is that we just started considering b as a variable , and we were looking at the h star , s star , and lambda star as they depended on that variable . we made the observation that the lagrangian evaluated at that critical point equals the revenue evaluated at that critical point . the rest of the stuff just cancels out . if you wan na know the derivative of m star , the maximizing revenue , with respect to the budget , how much does your maximum revenue change for tiny changes in your budget , that 's the same as looking at the derivative of the lagrangian with respect to the budget , so long as you 're considering it only on values h star , s star , lambda star , that are critical points of the lagrangian . and all of that really nicely boils down to just taking a simple , partial derivative that gives us the relation we want .
|
i think that 'll be useful . i 'm gon na rewrite the l if i consider it as a four variable function of h , s , lambda , and b , that what that equals is r evaluated h and s , minus lambda multiplied by this constraint function , b evaluated at h and s , minus little b . and this is now when i 'm considering little b to be a variable .
|
why would lambda* be written as a constant lambda* , rather than a function lambda* ( b ) , as the other variables h* ( b ) and s* ( b ) ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this .
|
why does capillary action increase when the diameter of the vessel becomes thinner ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface .
|
also , i understand that adhesion helps the water molecules stick to the walls of the container , but how does it help the water molecules to keep climbing higher ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above .
|
so what happens in the absence of gravity , like in space ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ?
|
how would water stay in a glass container ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup .
|
is surface tension what causes strands of wet hair to stick together in air ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical .
|
how many free surfaces are there when a needle floats on liquid at rest ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action .
|
what will happen when cohesive force is equal to adhesive force ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion .
|
is surface tension due to the surface molecules or due to the bulk of liquid ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup .
|
surface tension is more in concave or plane surface ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup .
|
what exactly is breaking the surface tension ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion .
|
how can a mercury drop inside water have two free surfaces and in air have onl one free surface ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion .
|
what does the length refer to , especially in something like the surface of a glass of water ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup .
|
why does less surfactant cause an increase in alveolar surface tension ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface .
|
if we put mercury on top op water ... will it float or sink ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this .
|
why makes a concave or convex shape in capillary ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup .
|
what is surface energy and how is it related with surface tension ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position .
|
then why ca n't we pick mercury with our bare hands ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw .
|
what explains the tendency of two fluids to combine when they are brought together in a container without application of another factor ; for example , as happens with cream or milk added to coffee in a cup before any stirring is done ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should .
|
in the video , the lecturer explains that bile in urine lowers the surface tension of urine- how does it exactly work and what effects does it have ( by lowering the surface tension , how does bile help our body ) ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup .
|
what happens to the surface tension of a liquid after addition of some type of impurity ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go .
|
2.if work done in blowing a soap bubble of volume 'v ' is w , then the work done in blowing a soap bubble of volume 2v is ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup .
|
adhesion forces have no role in surface tension ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup .
|
what is the direction of surface tension ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup .
|
is capillary action just surface tension but on the sides of the liquid ?
|
if you took a glass of water and a needle , and you took that needle and you very carefully , very carefully dropped it on the water , it would stay there , and it 's not because it 's floating . this needle would not be floating on the water . this needle is more dense than water , and we know that if it 's more dense , then it should sink . so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup . so , why does water have this property of surface tension ? it has to do with the fact that the water molecules within this liquid are attracted to each other . this water molecule can form hydrogen bonds with the other water molecules around it , and it gets pulled toward them , and there 's a term for this . we call this cohesion . so , the fact that water molecules and other liquid molecules are attracted to each other is called cohesion . but what does this have to do with surface tension ? well , the key is these water molecules would like to bunch together . they want to group together , if they can . so , what would this water molecule do ? i mean , which way is he going to go ? how does he pick which one to group with ? that 's a problem . here in the bulk of the liquid , he ca n't decide , or in other words , let 's just say he got pulled toward this molecule . well , it 's also getting pulled to the left by all of this , by this one pulling it back to its original position . this one 's pulling it back to its original position , because there will be a component of that force that will point in the direction of its original position , as well as this one to the left . so , these are restricted . these molecules here in the bulk of the liquid have too many other water molecules around them dictating where they need to be , because if they tried to get displaced , it 'd pull them back to that position . however , at the surface there 's no water molecules above them . these are freer . they 're less restricted . so , that allows these water molecules on the surface to group together a little better , form stronger tighter bonds , closer spacing at the surface in such a way that they form a tension that 's not present in the bulk of the liquid . yes , these water molecules down below will prevent them from just grouping into one big clump in the center , but since they 're less restricted , they can form these tighter bonds here at the surface , and this allows it to support a pressure from above . so , this allows it to support a certain amount of weight , which allows the needle to rest on the surface . a few practical applications of this , one clinical . if there 's bile present in urine , you can detect its presence because it lowers the surface tension of urine . so , it gives you a test of whether the liver is metabolizing things the way it should . another application is if you go camping , and you 're in the tent . it 's raining , and the tent gets rain drops on it . most tents will keep the water from seeping through , but you 're going to be tempted . you 're going to be sitting in here . you 're going to be like , that looks cool , and you 're going to touch it , but you 're not supposed to touch it , because as soon as you touch it , you may break the surface tension , and once you break the surface tension , that water is dripping into your tent from that spot that you touched it , and you 're probably not going to have a good night . so , resist the urge to break the surface tension on your tent if it 's raining out . and when you wash your hands , when we use detergents . if you washed your hands with just regular water and that 's it , sometimes the surface tension 's too great . these water molecules are too bound to each other . they form too big of a clump . it does n't look like it . it looks perfectly smooth , but on a microscopic level , the water 's not as diffuse as it could be . it 's forming these clumps , because the water has cohesion , and it joins together , but if you add a little soap to the scenario , that breaks the surface tension . it lowers the surface tension , which means these water molecules do n't clump together as much , and if they 're not clumping together , they can get into the small cracks , which kicks out the dirt in your hands , and this water is better able to penetrate into the smaller cracks and get where it needs to go . so , surface tension is due to cohesion between the water molecules at the surface of a liquid , but water molecules are n't just attracted to each other . they 're actually attracted to the container too and other materials , and that 's called adhesion . so , the fact that water molecules are attracted to other materials as well is called adhesion . so , what happens is , this water molecule is n't just attracted to the other water molecules , it 's attracted to the wall , and these water molecules climb the wall a little bit . so , that 's why you 'll see when you fill a container with water , or you 're measuring an amount of liquid in a small burette , it 's not perfectly level at the surface . it actually forms this kind of shape like that . this is exaggerated , but the sides will be a little higher than the middle . so , you have to be careful when you 're measuring . this is usually called the meniscus , and it 's caused by the adhesion , the attraction of water molecules to the container that it 's in . this adhesive force , this adhesion force , is important . it causes something called capillary action . so , let me get rid of this . if you have a container with liquid , or say water , and you took another container . you put it in here like a straw . if you just stick it in , what you 'll see is that because the liquid is attracted to the walls of this inner container , it does n't just stay at this level , it 'll rise above . it pulls this up a little bit above the surface level of the water . and if you took an even smaller diameter tube and put it in there , the smaller the tube the greater this effect , and you 'd get this water rising to an even higher level within this tube , due to the adhesion to the walls of this container . and the name for this effect is capillary action , which is important in a variety of biological and non-biological examples where fluid is being aided in transport partially by the attraction to the walls of the container or the tube that it 's flowing in .
|
so , it 's not floating . it 's actually just sitting on the surface , because there 's surface tension . water is a liquid that 's capable of having a significant amount of surface tension , and you know it 's surface tension because if you were to come in here and exert a little force down , breaking the surface tension , or pushing this needle just below the surface , then it would sink . it would sink like a stone and just drop immediately to the bottom of the cup .
|
they how could this `` surface tension '' be parallel to the surface when its origin is due to downward forces ?
|
: with non-cyanotic heart dieseae , you have some type of a congenital defect . congenital just means that the individual is born with it , but what happens as a result is that blood moves from the left side of the heart to the right side of the heart . in this example , you see that we have a little hole here in the wall between the left ventricle and the right ventricle . since the pressure is higher on this left side that 's sending the blood throughout the entire body , that is going to cause blood to go from the left to the right ventricle . now , my question is , how does the doctor diagnose that an individual has some non-cyanotic heart defect ? well , one of the first things is that you can hear it . so , let 's draw a little ear here . you 'll be able to hear it , and also , you should be able see it . we 'll talk about how you can do those things ... let 's put a little pupil here . all right , so , you 'll be able to hear it , and you 'll be able to see it . now for the hearing , well , just think about it this way . let 's say you have a garden hose . this is my garden hose , and we have water that 's flowing through that garden hose , and all of a sudden , we decide `` hey we 're going to put a little tiny hole in the hose . '' so , right here we have a little hole . what 's going to happen ? well , of course , you 're going to have water flying out in places that you do n't want it to go , and it 's going to kind of squirt in this direction . if you come closely here , you 'll be able to hear that . right ? yeah ! of course , that makes sense . well , how does a doctor do that ? well , the doctor ca n't go in and put his ear right by that hole . what he can do is take this little handy device that we 're all so familiar with , that 's called a stethoscope , and this end , it 's going in his ears . then , you have this tube , and then , you have this chest piece , and where you can listen to the sounds of the heart . depending on the type of non-cyanotic heart disease that individual might have , he 'll be able to hear the squirting or some type of a characteristic sound that 's the result of that defect . this process , i 'll give you a fancy name for it , it called auscultation . all right , so , that is when the doctor comes with the stethoscope and since this is a congenital defect , when the baby is just born , he listens to the sound of the heart , and say , `` hey . i 'm hearing something that 's it 's not exactly what i would like to hear . '' so , that is one way , by listening to the heart . then , you can see the heart . how do you see the heart ? well , by taking a picture . unfortunately , you ca n't just take a regular camera . you need a more expensive machine , and that expensive machine is going to allow you to be able to visualize the chest area , and with that , it 's just like we 're taking a picture . it 's just a little different . it 's not going to have all the nice fancy colors , and you 'll be able to see the heart . all right , so , this is my heart . this is called a chest x-ray . all right . you going x-ray machine . you put the baby in the x-ray machine . you take a picture , and you look to see , all right , is there some type of a structural defect that 's not suppose to be there ? that 's one way to visualize the heart . there 's a second way to visualize the heart that 's even better . yeah , you can take a picture , or you can take a video . right ? with a fetal or postnatal ... so , fetal is while the fetus is still inside the mother 's womb , and postnatal , once that baby is born , you take an echocardiogram . so , echo ... ooh , that does n't look right . echocardiogram . what that does is you 're using sound waves , and you 're projecting it onto a screen , so , that you can see the heart . you see the heart as it 's beating . you see it contracting . you see the valves closing . you can also see in real time if there are defects that should not be there . so , that 's number two . we can visualize the heart by either using a chest x-ray or a fetal or postnatal echocardiogram . there are some other issues that we might notice with non-cyanotic heart disease . we said that blood is going from the left side to the right side , and if you have more and more blood going to the right side where it 's ultimately going to your lungs , so , you have more gong to your lungs some coming back but not going as much to the body , eventually , you 're going to get buildup in pressure in your lungs . if you get a buildup in pressure in your lungs , that can feed back to the right side causing buildup in pressure over here too . if we have that buildup in pressure over here , the ventricle has to do much more work . now , if you go to the gym , and you 're exercising , and you 're doing a lot of work , what 's going to happen to your muscles ? well , their going to get larger . their going to get significantly stronger . that 's going to start to happen on the right side where you have a larger heart muscle . if you have larger heart muscle , you will notice this when a doctor comes and does an electrocardiogram . so , we take an electrocardiogram . cardiogram where we are looking at the electrical signals throughout the heart . with that , i 'm going to just sketch one out . right now we have our p wave , and then , our qrs complex , and then , we have our t wave . if i look at that , so , this p wave , our qrs complex , and then , we have our t wave . the p wave gives me the electrical activity of the atria . the qrs complex is given you the electrical activity of the ventricles . all right . i 'm not going to go into all the details . i 'm just going to kind of make it just that simple for now . if you have enlargement of the ventricles , or the right ventricle , what 's that going to do to the signal ? do you expect to see the same signal , a larger signal , a smaller signal ? well , if you have a bigger muscle , i would expect to see a significantly larger signal here with the ventricles . if that feeds back to your atria , and you have a larger right atrium , well , you might see this being a larger , a little broader , a little wider . there are characteristics features that you can see in the electrocardiogram , the ecg or ekg , depending on where you are in the world . that can give you an indication as to whether there is some type of a dysfunction in the heart , as a result of the load that 's placed on the right ventricle , and the right atrium , and enlargement of those structures . so , you can hear it . you can see it . there are some functional things that you can notice in the electrocardiogram to help diagnose a non-cyanotic heart defect .
|
all right , so , this is my heart . this is called a chest x-ray . all right .
|
why are x-rays harmful and how much damage does one chest x-ray produce ?
|
alright i 'll tackle . in the last video we did the first part of part a , now , so the second part of part a . so , the second part of part a , they say , `` calculate the number of moles of ethene that would be produced if the dehydration reaction went to completion '' . well , this is the dehydration reaction right over here , and they 're telling us , they 're telling us that we start with 0.200 grams of ethanol , so , if we start with 0.200 grams of ethanol , and if we figure out how many moles of ethanol that is , well , for every mole of ethanol , if we have the reaction go to , if the dehydration reaction goes to completion , for every mole of ethanol that we start with , we 're going to have a mole of ethene , and a mole of water . so , if we can just figure out how many moles of ethanol this is , then we 'll say , `` okay , if this were completely react , we would have that many moles of ethene '' . so , let 's figure this out . so if we say , so , we have ethanol , so for ethanol , we are starting with zero .200 grams , and we wan na convert this to moles , so we wan na multiply this times , we want grams in the denominator to cancel out with this grams , and moles in the numerator . so , one mole of ethanol is , as a mass of how many grams , well , they tell us that earlier on the problem , they say , `` ethanol , molar mass 46.1 grams per mol '' , so , ethanol , molar mass of 46.1 grams per mol , or another way to thinking about it , one mole would have mass of 46.1 grams of 46.1 grams , and so if we do this , we are going to get 0.200 over 46.1 , and then grams cancel with the grams , and that going to be how many moles we have , and this is going to be equal to , we have three significant digits that we 're gon na be with three significant digits divided by three significant digits , so this is going to be all right , so we clear this , so .2 , i could write 00 , but it 's going to , for the calculator 's purposes this is the same thing , divided by 46.1 is equal to 0.0043 , i want three significant figures here , so 43 i 'm gon na round up , 434 , .00434 so 0.00434 moles . so , we 've seen so far , if the ethanol were ( mumbling ) the reaction , if we have this many moles of ethanol , well , and if they completely react , well , then we should end up with that many moles of ethene , and so if we have , if it we get a dehydration , i 'm gon na write it this way , if dehydration dehydration reaction goes to completion goes to completion every every mole of ethanol would be converted to a mole of ethene and a mole of water . i should n't write the shorthand there , a mole , if i 'm writing it out , mole of and a mole water . so 0.00434 mole of ethanol would yield , that same number of moles , 0.00434 moles of ethene . so , if the reaction went to completion that how many moles it would produce . what we actually measure is a smaller number than that , so the reaction did n't go fully to completion . so now let 's tackle part b , let 's tackle part b , and they ask us , `` calculate he percent yield of ethene in the experiment '' . well , the percent yield is going to be how much we got , divide by how much we would ideally have gotten if the reaction went fully to completion . so yield yield is going to be equal to how much we actually got , which we figured out in part one , so 0.00264 moles over what we actually got , i 'm sorry , what we actually got over what we 'd have ideally gotten if the reaction went to completion , so divided by 0.00434 moles , and this is going to be equal to this is going to be equal to so , 00264 divided by 00434 , is equal to , and let 's see , we have three significant digits here , so 60 , i can say .608 , or i could say 60.8 % yield . so , i 'm gon na write this as actually this is gon na , i 'm rounding , so i can say 60.8 % yield , and there you go .
|
so yield yield is going to be equal to how much we actually got , which we figured out in part one , so 0.00264 moles over what we actually got , i 'm sorry , what we actually got over what we 'd have ideally gotten if the reaction went to completion , so divided by 0.00434 moles , and this is going to be equal to this is going to be equal to so , 00264 divided by 00434 , is equal to , and let 's see , we have three significant digits here , so 60 , i can say .608 , or i could say 60.8 % yield . so , i 'm gon na write this as actually this is gon na , i 'm rounding , so i can say 60.8 % yield , and there you go .
|
may you tell me where did the rest of yield go ?
|
alright i 'll tackle . in the last video we did the first part of part a , now , so the second part of part a . so , the second part of part a , they say , `` calculate the number of moles of ethene that would be produced if the dehydration reaction went to completion '' . well , this is the dehydration reaction right over here , and they 're telling us , they 're telling us that we start with 0.200 grams of ethanol , so , if we start with 0.200 grams of ethanol , and if we figure out how many moles of ethanol that is , well , for every mole of ethanol , if we have the reaction go to , if the dehydration reaction goes to completion , for every mole of ethanol that we start with , we 're going to have a mole of ethene , and a mole of water . so , if we can just figure out how many moles of ethanol this is , then we 'll say , `` okay , if this were completely react , we would have that many moles of ethene '' . so , let 's figure this out . so if we say , so , we have ethanol , so for ethanol , we are starting with zero .200 grams , and we wan na convert this to moles , so we wan na multiply this times , we want grams in the denominator to cancel out with this grams , and moles in the numerator . so , one mole of ethanol is , as a mass of how many grams , well , they tell us that earlier on the problem , they say , `` ethanol , molar mass 46.1 grams per mol '' , so , ethanol , molar mass of 46.1 grams per mol , or another way to thinking about it , one mole would have mass of 46.1 grams of 46.1 grams , and so if we do this , we are going to get 0.200 over 46.1 , and then grams cancel with the grams , and that going to be how many moles we have , and this is going to be equal to , we have three significant digits that we 're gon na be with three significant digits divided by three significant digits , so this is going to be all right , so we clear this , so .2 , i could write 00 , but it 's going to , for the calculator 's purposes this is the same thing , divided by 46.1 is equal to 0.0043 , i want three significant figures here , so 43 i 'm gon na round up , 434 , .00434 so 0.00434 moles . so , we 've seen so far , if the ethanol were ( mumbling ) the reaction , if we have this many moles of ethanol , well , and if they completely react , well , then we should end up with that many moles of ethene , and so if we have , if it we get a dehydration , i 'm gon na write it this way , if dehydration dehydration reaction goes to completion goes to completion every every mole of ethanol would be converted to a mole of ethene and a mole of water . i should n't write the shorthand there , a mole , if i 'm writing it out , mole of and a mole water . so 0.00434 mole of ethanol would yield , that same number of moles , 0.00434 moles of ethene . so , if the reaction went to completion that how many moles it would produce . what we actually measure is a smaller number than that , so the reaction did n't go fully to completion . so now let 's tackle part b , let 's tackle part b , and they ask us , `` calculate he percent yield of ethene in the experiment '' . well , the percent yield is going to be how much we got , divide by how much we would ideally have gotten if the reaction went fully to completion . so yield yield is going to be equal to how much we actually got , which we figured out in part one , so 0.00264 moles over what we actually got , i 'm sorry , what we actually got over what we 'd have ideally gotten if the reaction went to completion , so divided by 0.00434 moles , and this is going to be equal to this is going to be equal to so , 00264 divided by 00434 , is equal to , and let 's see , we have three significant digits here , so 60 , i can say .608 , or i could say 60.8 % yield . so , i 'm gon na write this as actually this is gon na , i 'm rounding , so i can say 60.8 % yield , and there you go .
|
so , one mole of ethanol is , as a mass of how many grams , well , they tell us that earlier on the problem , they say , `` ethanol , molar mass 46.1 grams per mol '' , so , ethanol , molar mass of 46.1 grams per mol , or another way to thinking about it , one mole would have mass of 46.1 grams of 46.1 grams , and so if we do this , we are going to get 0.200 over 46.1 , and then grams cancel with the grams , and that going to be how many moles we have , and this is going to be equal to , we have three significant digits that we 're gon na be with three significant digits divided by three significant digits , so this is going to be all right , so we clear this , so .2 , i could write 00 , but it 's going to , for the calculator 's purposes this is the same thing , divided by 46.1 is equal to 0.0043 , i want three significant figures here , so 43 i 'm gon na round up , 434 , .00434 so 0.00434 moles . so , we 've seen so far , if the ethanol were ( mumbling ) the reaction , if we have this many moles of ethanol , well , and if they completely react , well , then we should end up with that many moles of ethene , and so if we have , if it we get a dehydration , i 'm gon na write it this way , if dehydration dehydration reaction goes to completion goes to completion every every mole of ethanol would be converted to a mole of ethene and a mole of water . i should n't write the shorthand there , a mole , if i 'm writing it out , mole of and a mole water .
|
what is the average time it takes to complete dehydration ?
|
welcome back . we 're ready to do part d , and let me copy and paste that in as well . see , i do n't think that 's going to need this graph , so let me just remove that with a color other than yellow . it 's copy and pasted . i do n't know if you can read it , but it 's helpful for me to review the problem on our clipboard . ok . the rate at which tickets were sold for t -- for over this range is modeled by r of t -- let me write that in case you ca n't see it -- is the rate at which tickets were sold . r of t is equal to 550 te to the minus t over 2 tickets per hour . based on the model , how many tickets were sold by 3:00 pm ? so my t equals 3 -- to the nearest whole number ? so that 's sometimes important . you do n't want to give a decimal answer . so this is the rate at which tickets are sold . so this is the derivative of the total tickets sold function . or another way that we could write it is the total tickets sold -- so let 's call that , i do n't know , capital t sub -- well let me -- i do n't want to do t of t , that 's [ unintelligible ] so let 's say the tickets sold as a function of time is going to be equal to the definite integral -- well , we could say is at any time t , the tickets sold -- and this is the fundamental theorems calculus , i think it might be one of its correlaries or actually sometimes it is the fundamental theorem of calculus , i always forget my definitions . between time equals 0 and t -- or if we want to know the tickets sold , between time equals 0 and t is equal to the integral of the rate at which the tickets sold was changing . so that 's equal to 550te to the minus t over 2dt . right ? that 's it . and so if we want to know how many tickets were sold at time equals 3 , that 's just equal to the definite integral from 0 to 3 , or we could also view it as the area under this curve , from time equals 0 to time equal to 3 of 550te to the minus t over 2dt . now this integral right here , you can solve it analytically using integration of parts , which i just called the reverse product rule , but you only have 45 minutes to do all three of these problems , and they 'll let you use your graphing calculator , and your graphic calculator is excellent at doing definite integrals , and they just want the number , right ? so let 's use our graphic calculators to get that number . let 's see . i do n't want to copy , so how do we do that ? we just do second the division button but that 's calc -- definite , let me use the definite integral , and like what was , let 's see , let me make sure i have that -- 550 let 's just use x . 550 times x times second e to the minus x divided by 2 . i think that 's the whole function . and let 's see . my independent variable is x , i 've just swapped t for x there , and i 'm taking the integral from 0 to 3 . click enter , let the calculator do the work . this would have taken you quite a while if you had to actually do the integral yourself . 972.78 , and they want us to round to the nearest whole number . so the nearest whole number is 973 . so we say 973 tickets sold by 3:00 pm . and we 're done . that only took us four minutes . and it would have taken us even less if we did n't have to explain it . anyway . i will see you in problem number three .
|
and so if we want to know how many tickets were sold at time equals 3 , that 's just equal to the definite integral from 0 to 3 , or we could also view it as the area under this curve , from time equals 0 to time equal to 3 of 550te to the minus t over 2dt . now this integral right here , you can solve it analytically using integration of parts , which i just called the reverse product rule , but you only have 45 minutes to do all three of these problems , and they 'll let you use your graphing calculator , and your graphic calculator is excellent at doing definite integrals , and they just want the number , right ? so let 's use our graphic calculators to get that number .
|
how to solve the last integral expression without using a calculator ?
|
so let 's start thinking about partial derivatives of vector fields . so a vector field is a function . i 'll just do a two dimensional example here . it 's gon na be something that has a two dimensional input . and then the output has the same number of dimensions . that 's the important part . and each of these components in the output is gon na depend somehow on the input variables . so the example i have in mind will be x times y as that first component , and then y squared minus x squared as that second component . and you can compute the partial derivative of a guy like this , right ? you 'll take the partial derivative with respect to one of the input variables . i 'll choose x . it 's always a nice one to start with . partial derivative with respect to x . and if we were to actually compute it , in this case , it 's another , it 's a function of x and y . what you do is you take the partial derivative component wise . so you to each component in the first one . you say , okay . x looks like a variable . y looks like a constant . the derivative will just be that constant . and then the partial derivative of the second component . that y squared looks like a constant . derivative of negative x squared with respect to x . negative two x . so analytically , if you know how to take a partial derivative , you already know how to take a partial derivative of vector valued functions and hence vector fields , but the fun part , the important part here . how do you actually interpret this ? and this has everything to do with visualizing it in some way . so the vector field , the reason we call it a vector field , is you kind of take the whole x y plane and you 're gon na fill it with vectors . and concretely , what i mean by that , you 'll take a given input . what 's an input you wan na look at ? i 'll say , maybe one , two . yeah , let 's do that . let 's do one , two . which would mean you kinda go x equals one . and then y equals two this input point . then we want to associate that with the output vector in some way . and so , let 's just compute what it should equal . so when we plug in x equals one , and y equals two , x times y becomes two . y squared minus x squared becomes two squared minus one squared , so four minus one is three . so we have this vector two , three that we want to associate with that input point . and vector fields , you just attach the two points . i 'm gon na take the vector two , three and attach it to this guy . so we should have an x component of two and then a y component of three . so it 's going to end up looking something like , let 's see , so y component of three , something like this . so that 'll be the vector and we attach it to that point . and in principal , you do this to all the different points . and if you did , what you 'd get would be something like this . and remember when we represent these , especially with computers , it tends to lie , where each represented vector is much , much shorter than it should be in reality , but you want to squish them all onto the same page so they do n't over run each other . and here , color is supposed to give a general , vague sense of relative length . so ones that are blue should thought of as much shorter than the ones that are yellow , but that does n't really give a specific thought for how long they should be . but , for partial derivatives , we actually care a lot about the specifics . and if you think back to how we interpret partial derivatives in a lot of other contexts , what want to do is imagine this partial x here as a slight nudge in the x direction , right . so this was our original input , so you might imagine just nudging it a little bit , and the size of that nudge , as a number , would be your partial x . so then the question is , what 's the resulting change to the output ? and because the output is a vector , the change to the output is also going to be a vector . so what we want is to say there 's going to be some other vector attached to this point , right ? it 's going to look very similar . maybe it looks like , maybe it looks something like this . so something similar , but maybe a little bit different . and you want to take that difference in vector form . and i 'll describe what i mean by that in just a moment , and then divide by the size of that original nudge . so to be much more specific about what i mean here , if you 're comparing two different vectors and they 're rooted in two different spots , i think a good way to start is to just move them to a new space where they 're rooted in the same spot . so in this case , i 'm gon na kinda just draw a separate space over here . and be thinking of this as a place for these vectors to live . and i 'm gon na them both on this plane , but i 'm gon na root them each in the origin . so this first one that has components two , three , now let 's give it a name , right . let 's call this guy v one , okay . so that 'll be v one . and then the nudged output , the second one , i 'll call v two . and let 's say v two is also in this space , and i might exaggerate the difference , just so we can see it here . let 's say it was different in some way . in reality , if it 's a small nudge , it 'll be different in only a very small way . but let 's say these were our two vectors . the difference between these guys is going to be a vector that connects the tips . and i 'm gon na call that guy partial v. and the way you can be thinking about this is to say that v one , v one , that original guy , plus , that tiny nudge , the difference between them is equal to the two , you know , the nudged output . and in terms of tip to tail with vectors , you 've seen that . kind of the green vector plus that blue vector is the same as that pink vector that connects the tail of the original one to the tip of the new one . so when we 're thinking of a partial derivative , you 're basically saying , `` hey , what happens if we take this , the nudge , the size of the nudge of the output , and then we divide it by the nudge of the input ? '' so let 's thinking of that original nudge as being , i do n't know , of a size of one half , like zero point five . as the change in the x direction . then that would mean , when you go over here and say what 's that dv ? that changing vector v divided by the x , you 'd be dividing it by zero point five , and in principle , you 'd be thinking of , that would mean that your kind of scaling this by two . as if to say , this little dv is one half of some other vector . and that other vector is what the partial derivative is . so this other vector here , the full blue guy , would be dv , you know , scaled down or scaled up , however you want to think about it , by that partial x . and that 's what makes it such the , you know , in principle if this partial x change was really small , like one 100th and the output nudge was also really small , it 's like one 100th , or you know something on that order , it would n't be specifically that . then the dvdx , that change , would still be a normal sized vector . and the direction that it points is still kind of an indication of the direction that this green vector should change as you 're scooting over . so just be concrete and actually compute this guy , let 's say we were to take this partial derivative partial v with respect to x and evaluate it at that point one , two that we 're just dealing with , one , two . what that would mean , y is equal to two , so that first component is two and then x is equal to one , so that next should be negative two . and then we can see just how wrong my drawing was to start here . i was just kind of guessing what the pink vector would be , but i guess it changes in the direction of two , negative two . so that should be something , here i 'll erase the , what turns out to be , the wrong direction here . get rid of this guy . and i guess the change would be in the direction kind of two as the x component , and then negative two , that 's a negative two , as the y component . so the derivative vector should look something like this . which means all corresponding little dv nudges , will be slight changes , will be slight changes on that . so these will be your , your dvs . something in that direction . and what that means in our vector field then , as you move in the x direction and consider the various vectors attached to each point , as you kind of passing through the point one , two , the way that the vectors are changing , should be somehow down and to the right . the tip should move down and to the right . so if this starts highly up and to the right , then it should be getting kind of shorter , but then longer to the right . so then the v two , if i were to have drawn it more accurately here , you know , what they nudged output should look like , it would really be something that kind of like i do n't know , like this , where it 's getting shorter in the y direction , but then longer in x direction , as per that blue nudging arrow . and then in the next video i 'll kind of go through more examples of how you might think of this . how you think of it in terms of what each component means . which becomes very important for later topics , like divergence and curl . and i 'll see you next video .
|
and i 'm gon na call that guy partial v. and the way you can be thinking about this is to say that v one , v one , that original guy , plus , that tiny nudge , the difference between them is equal to the two , you know , the nudged output . and in terms of tip to tail with vectors , you 've seen that . kind of the green vector plus that blue vector is the same as that pink vector that connects the tail of the original one to the tip of the new one . so when we 're thinking of a partial derivative , you 're basically saying , `` hey , what happens if we take this , the nudge , the size of the nudge of the output , and then we divide it by the nudge of the input ? ''
|
since v1+dv=v2 , should n't the tip of the second pink vector touch the tip of the differential blue vector ?
|
imagine you had a monatomic ideal gas in this cylinder here , an there was this tightly fitted piston above it that prevented any gas from getting out . well we know that the total internal energy for a monatomic ideal gas is just three halves p times v or three halves nkt , or three halves little nrt , and we know that saying u internal the internal energy is really just code for the total kinetic energy of the monatomic ideal gas , that these are the same thing . when we talk about internal energy we 're talking about how fast are these particles moving , in other words , what 's the total kinetic energy of all of these particles added up . my question is how do we go about changing the internal energy ? let 's say we wanted to increase the total kinetic energy , what could we do ? well , we could say increase the pressure , or the volume , or the temperature , yeah but i mean physically , actually , in the lab , what do we do ? and there 's basically two ways to change the internal energy . if you want to add internal energy , i.e . get these particles moving faster , we can heat it up so put this above a flame or on a hot plate , and heat will flow into the gas which will cause these particles to move faster and faster . that 's one way to do it , to add heat . the other way to do it is to do work on the gas . i could take this piston and push it down , and if you push this down hard enough it will squash this gas together , and those impacts with this piston while it 's moving down will cause them to start moving faster and faster , that will also add internal energy to the gas . so if we wanted to write down a formula that told us how you could get a change in the internal energy , if i want to change the internal energy , delta u , which is really just saying changing the kinetic energy , well there 's two ways to do it . i can add heat . if i added ten joules of heat i 'd add ten joules to the internal energy , but i 've also got to take into account this work being done , and so i can do plus the work done on the gas , and that 's it , this is actually the first law of thermodynamics , it 's the law of conservation of energy it says there 's only two ways to add energy , internal energy to a gas . let me talk a little bit more about this work done though cause getting the sign right is important . if you 're doing work on the gas compressing it you 're adding energy to the gas , but if you let the gas push up on the piston and this gas expands pushing the piston up , then the gas is doing the work , that 's energy leaving the system . so if the gas does work you have to subtract work done by the gas . if the outside force does work on the gas you add that to the internal energy . so you got to pay attention to which way the energy is flowing . work done on gas , energy goes in . work done by the gas , energy goes out , and you 'd have to subtract that over here . let 's say the gas did expand . let 's say the gas in here was under so much pressure that the force it exerted on this piston was enough to push that piston upward by a certain amount . so let 's say it started right here and it went up to here so that piston went from here to there no gasses escaping cause this is tightly fitting , but the gas was able to push it up a certain distance d , how much work was done ? you know the definition of work . work is defined to be the force times the distance through which that force was applied . so the work that the gas did was f times d , but we want this to be in terms of thermal quantities like pressure , and volume , and temperature . so what could we do ? we can say that this volume , not only did the piston raise up , but there was an extra volume generated within here that i 'm going to call delta v , and i know that this delta v has got to equal the area of the piston times the distance through which that piston moved because this height times that area gives me this volume right in here . why am i doing this ? cause look i can write d as equal to delta v over a , and i can take this , i can substitute this formula for d into here , and something magical happens , i 'll get work equals f times delta v over a , but look f over a , we know what f over a is , that 's pressure so i get that the work done by the gas is the pressure times delta v. this is an equation that i like because it 's in terms of thermodynamic quantities that we 're already dealing with . so work done you can figure out by taking p times delta v but strictly speaking this is only true if this pressure remained constant , right ? if the pressure was changing , then what am i supposed to plug in here , the initial pressure , the final pressure ? if the pressure 's staying constant this gives you an exact way to find the work done . you might object and say wait , how is it possible for a gas to expand and remain at the same pressure ? well , you basically have to heat it up while the gas expands , that allows the pressure to remain constant as the gas expands . and now we 're finally ready to talk about heat capacities . so let 's get rid of this , and heat capacity is defined to be , imagine you had a certain amount of heat being added . so a certain amount of heat gets added to your gas . how much does the temperature increase ? that 's what the heat capacity tells you . so capital c is heat capacity and it 's defined to be the amount of heat that you 've added to the gas , divided by the amount of change in the temperature of that gas . and actually , something you 'll hear about often is the molar heat capacity , which is actually divided by an extra n here . so instead of q over delta t it 's q over n the number of moles times delta t. pretty simple but think about it . if we had a piston in here , are we going to allow that piston to move while we add the heat , or are we not going to allow the piston to move ? there 's different ways that this can happen , and because of that there 's different heat capacities . if we do n't allow this piston to move , if we weld this thing shut so it ca n't move we 've got heat capacity at constant volume , and if we do allow this piston to move freely while we add the heat so that the pressure inside of here remains constant , we 'd have the heat capacity at constant pressure . and these are similar but different , and they 're related , and we can figure them out . so let 's clear this away , let 's get a nice , here we go , two pistons inside of cylinders . we 'll put a piston in here , but i 'm going to weld this one shut . this one ca n't move . we 'll have another one over here , it can move freely . so over on this side , we 'll have the definition of heat capacity , regular heat capacity , is the amount of heat you add divided by the change in temperature that you get . so on this side we 're adding heat , let 's say heat goes in , but the piston does not move and so the gas in here is stuck , it ca n't move , no work can be done . since this piston ca n't move , external forces ca n't do work on the gas , and the gas ca n't do work and allow energy to leave . q is the only thing adding energy into this system , or in other words , we 've got heat capacity at constant volume is going to equal , well , remember the first law of thermodynamics said that delta u , the only way to add internal energy , or take it away is that you can add or subtract heat , and you can do work on the gas . in this case , q , if i subtract w from both sides i get delta u minus w over delta t , but since we 're not allowing this piston to move the work done has got to be zero . so there 's no work done at all so the heat capacity at constant volume is going to be delta u over delta t , what 's delta u ? let 's just assume this is a monatomic ideal gas , if it 's monatomic we 've got a formula for this . delta u is just three halves , p times v over delta t. that 's not the only way i can write it . remember i can also write it as three halves nk delta t over delta t , and something magical happens , check it out the delta t 's go away and you get that this is a constant . that the heat capacity for any monatomic ideal gas is just going to be three halves , capital nk , boltzmann 's constant , n is the total number of molecules . or you could have rewrote this as little n r delta t. the t 's would still have cancelled and you would have got three halves , little n , the number of moles , times r , the gas constant . so the heat capacity at constant volume for any monatomic ideal gas is just three halves nr , and if you wanted the molar heat capacity remember that 's just divide by an extra mole here so everything gets divided by moles everywhere divided by moles , that just cancels this out , and the molar heat capacity at constant volume is just three halves r. so that 's heat capacity at constant volume , what about heat capacity at constant pressure ? now we 're going to look at this side . again , we 're going to allow this gas to have heat enter the cylinder , but we 're going to allow this piston to move up while it does that so that the pressure inside of here remains constant and this is going to be the heat capacity at constant pressure . well , again , we 're going to get that it 's q over delta t , and just like the first law said , q has to equal delta u minus w. so we get delta u minus w , the work done , over delta t , this time w is not zero . what 's w going to be ? remember w is p times delta v. so this is a way we can find the work done by the gas , p times delta v , so this is going to equal delta u , we know what that is . if this is again , a monatomic ideal gas , this is going to equal three halves nr delta t plus this is p times delta v , but we have to be careful , in this formula this work is referring to work done on the gas , but in this case , work is being done by the gas , so i need another negative . technically the work done on the gas would be a negative amount of this since energy is leaving the system . so that negative cancels this negative and i get plus p times delta v , all of that over delta t , phew . so what do we get ? three halves nr delta t plus i want to rewrite p times delta v , but i know how to do that . the ideal gas law says pv equals nrt , well if that 's true , then p times delta v is going to equal nr delta t. so can rewrite this as nr delta t divided by delta t , almost there , all of the delta t 's go away . look what i 'm left with . i 'm left with c. heat capacity at constant pressure is going to be equal to three halves nr plus nr , that 's just five halves nr , and if i wanted the molar heat capacity again i could divide everything , everything around here by little n , and that would just give me the molar heat capacity constant pressure would be five halves r. and notice they 're almost the same . the heat capacity at constant volume is three halves nr , and the heat capacity at constant pressure is five halves nr . they just differ by nr . so the difference between the heat capacity at constant volume which is three halves nr , and the heat capacity at constant pressure which is five halves nr , is just cp minus cv which is nr , just nr , and if you wanted to take the difference between the molar heat capacities at constant volume and pressure , it would just be r. the difference would just be r because everything would get divided by the number of moles . so there 's a relationship , an important relationship . it tells you the difference between the heat capacity at constant pressure and the heat capacity at constant volume .
|
or you could have rewrote this as little n r delta t. the t 's would still have cancelled and you would have got three halves , little n , the number of moles , times r , the gas constant . so the heat capacity at constant volume for any monatomic ideal gas is just three halves nr , and if you wanted the molar heat capacity remember that 's just divide by an extra mole here so everything gets divided by moles everywhere divided by moles , that just cancels this out , and the molar heat capacity at constant volume is just three halves r. so that 's heat capacity at constant volume , what about heat capacity at constant pressure ? now we 're going to look at this side .
|
what would be the interpretation of molar heat capacity being infinite at constant temperature ?
|
imagine you had a monatomic ideal gas in this cylinder here , an there was this tightly fitted piston above it that prevented any gas from getting out . well we know that the total internal energy for a monatomic ideal gas is just three halves p times v or three halves nkt , or three halves little nrt , and we know that saying u internal the internal energy is really just code for the total kinetic energy of the monatomic ideal gas , that these are the same thing . when we talk about internal energy we 're talking about how fast are these particles moving , in other words , what 's the total kinetic energy of all of these particles added up . my question is how do we go about changing the internal energy ? let 's say we wanted to increase the total kinetic energy , what could we do ? well , we could say increase the pressure , or the volume , or the temperature , yeah but i mean physically , actually , in the lab , what do we do ? and there 's basically two ways to change the internal energy . if you want to add internal energy , i.e . get these particles moving faster , we can heat it up so put this above a flame or on a hot plate , and heat will flow into the gas which will cause these particles to move faster and faster . that 's one way to do it , to add heat . the other way to do it is to do work on the gas . i could take this piston and push it down , and if you push this down hard enough it will squash this gas together , and those impacts with this piston while it 's moving down will cause them to start moving faster and faster , that will also add internal energy to the gas . so if we wanted to write down a formula that told us how you could get a change in the internal energy , if i want to change the internal energy , delta u , which is really just saying changing the kinetic energy , well there 's two ways to do it . i can add heat . if i added ten joules of heat i 'd add ten joules to the internal energy , but i 've also got to take into account this work being done , and so i can do plus the work done on the gas , and that 's it , this is actually the first law of thermodynamics , it 's the law of conservation of energy it says there 's only two ways to add energy , internal energy to a gas . let me talk a little bit more about this work done though cause getting the sign right is important . if you 're doing work on the gas compressing it you 're adding energy to the gas , but if you let the gas push up on the piston and this gas expands pushing the piston up , then the gas is doing the work , that 's energy leaving the system . so if the gas does work you have to subtract work done by the gas . if the outside force does work on the gas you add that to the internal energy . so you got to pay attention to which way the energy is flowing . work done on gas , energy goes in . work done by the gas , energy goes out , and you 'd have to subtract that over here . let 's say the gas did expand . let 's say the gas in here was under so much pressure that the force it exerted on this piston was enough to push that piston upward by a certain amount . so let 's say it started right here and it went up to here so that piston went from here to there no gasses escaping cause this is tightly fitting , but the gas was able to push it up a certain distance d , how much work was done ? you know the definition of work . work is defined to be the force times the distance through which that force was applied . so the work that the gas did was f times d , but we want this to be in terms of thermal quantities like pressure , and volume , and temperature . so what could we do ? we can say that this volume , not only did the piston raise up , but there was an extra volume generated within here that i 'm going to call delta v , and i know that this delta v has got to equal the area of the piston times the distance through which that piston moved because this height times that area gives me this volume right in here . why am i doing this ? cause look i can write d as equal to delta v over a , and i can take this , i can substitute this formula for d into here , and something magical happens , i 'll get work equals f times delta v over a , but look f over a , we know what f over a is , that 's pressure so i get that the work done by the gas is the pressure times delta v. this is an equation that i like because it 's in terms of thermodynamic quantities that we 're already dealing with . so work done you can figure out by taking p times delta v but strictly speaking this is only true if this pressure remained constant , right ? if the pressure was changing , then what am i supposed to plug in here , the initial pressure , the final pressure ? if the pressure 's staying constant this gives you an exact way to find the work done . you might object and say wait , how is it possible for a gas to expand and remain at the same pressure ? well , you basically have to heat it up while the gas expands , that allows the pressure to remain constant as the gas expands . and now we 're finally ready to talk about heat capacities . so let 's get rid of this , and heat capacity is defined to be , imagine you had a certain amount of heat being added . so a certain amount of heat gets added to your gas . how much does the temperature increase ? that 's what the heat capacity tells you . so capital c is heat capacity and it 's defined to be the amount of heat that you 've added to the gas , divided by the amount of change in the temperature of that gas . and actually , something you 'll hear about often is the molar heat capacity , which is actually divided by an extra n here . so instead of q over delta t it 's q over n the number of moles times delta t. pretty simple but think about it . if we had a piston in here , are we going to allow that piston to move while we add the heat , or are we not going to allow the piston to move ? there 's different ways that this can happen , and because of that there 's different heat capacities . if we do n't allow this piston to move , if we weld this thing shut so it ca n't move we 've got heat capacity at constant volume , and if we do allow this piston to move freely while we add the heat so that the pressure inside of here remains constant , we 'd have the heat capacity at constant pressure . and these are similar but different , and they 're related , and we can figure them out . so let 's clear this away , let 's get a nice , here we go , two pistons inside of cylinders . we 'll put a piston in here , but i 'm going to weld this one shut . this one ca n't move . we 'll have another one over here , it can move freely . so over on this side , we 'll have the definition of heat capacity , regular heat capacity , is the amount of heat you add divided by the change in temperature that you get . so on this side we 're adding heat , let 's say heat goes in , but the piston does not move and so the gas in here is stuck , it ca n't move , no work can be done . since this piston ca n't move , external forces ca n't do work on the gas , and the gas ca n't do work and allow energy to leave . q is the only thing adding energy into this system , or in other words , we 've got heat capacity at constant volume is going to equal , well , remember the first law of thermodynamics said that delta u , the only way to add internal energy , or take it away is that you can add or subtract heat , and you can do work on the gas . in this case , q , if i subtract w from both sides i get delta u minus w over delta t , but since we 're not allowing this piston to move the work done has got to be zero . so there 's no work done at all so the heat capacity at constant volume is going to be delta u over delta t , what 's delta u ? let 's just assume this is a monatomic ideal gas , if it 's monatomic we 've got a formula for this . delta u is just three halves , p times v over delta t. that 's not the only way i can write it . remember i can also write it as three halves nk delta t over delta t , and something magical happens , check it out the delta t 's go away and you get that this is a constant . that the heat capacity for any monatomic ideal gas is just going to be three halves , capital nk , boltzmann 's constant , n is the total number of molecules . or you could have rewrote this as little n r delta t. the t 's would still have cancelled and you would have got three halves , little n , the number of moles , times r , the gas constant . so the heat capacity at constant volume for any monatomic ideal gas is just three halves nr , and if you wanted the molar heat capacity remember that 's just divide by an extra mole here so everything gets divided by moles everywhere divided by moles , that just cancels this out , and the molar heat capacity at constant volume is just three halves r. so that 's heat capacity at constant volume , what about heat capacity at constant pressure ? now we 're going to look at this side . again , we 're going to allow this gas to have heat enter the cylinder , but we 're going to allow this piston to move up while it does that so that the pressure inside of here remains constant and this is going to be the heat capacity at constant pressure . well , again , we 're going to get that it 's q over delta t , and just like the first law said , q has to equal delta u minus w. so we get delta u minus w , the work done , over delta t , this time w is not zero . what 's w going to be ? remember w is p times delta v. so this is a way we can find the work done by the gas , p times delta v , so this is going to equal delta u , we know what that is . if this is again , a monatomic ideal gas , this is going to equal three halves nr delta t plus this is p times delta v , but we have to be careful , in this formula this work is referring to work done on the gas , but in this case , work is being done by the gas , so i need another negative . technically the work done on the gas would be a negative amount of this since energy is leaving the system . so that negative cancels this negative and i get plus p times delta v , all of that over delta t , phew . so what do we get ? three halves nr delta t plus i want to rewrite p times delta v , but i know how to do that . the ideal gas law says pv equals nrt , well if that 's true , then p times delta v is going to equal nr delta t. so can rewrite this as nr delta t divided by delta t , almost there , all of the delta t 's go away . look what i 'm left with . i 'm left with c. heat capacity at constant pressure is going to be equal to three halves nr plus nr , that 's just five halves nr , and if i wanted the molar heat capacity again i could divide everything , everything around here by little n , and that would just give me the molar heat capacity constant pressure would be five halves r. and notice they 're almost the same . the heat capacity at constant volume is three halves nr , and the heat capacity at constant pressure is five halves nr . they just differ by nr . so the difference between the heat capacity at constant volume which is three halves nr , and the heat capacity at constant pressure which is five halves nr , is just cp minus cv which is nr , just nr , and if you wanted to take the difference between the molar heat capacities at constant volume and pressure , it would just be r. the difference would just be r because everything would get divided by the number of moles . so there 's a relationship , an important relationship . it tells you the difference between the heat capacity at constant pressure and the heat capacity at constant volume .
|
or you could have rewrote this as little n r delta t. the t 's would still have cancelled and you would have got three halves , little n , the number of moles , times r , the gas constant . so the heat capacity at constant volume for any monatomic ideal gas is just three halves nr , and if you wanted the molar heat capacity remember that 's just divide by an extra mole here so everything gets divided by moles everywhere divided by moles , that just cancels this out , and the molar heat capacity at constant volume is just three halves r. so that 's heat capacity at constant volume , what about heat capacity at constant pressure ? now we 're going to look at this side .
|
how would you figure out the heat capacity of a liquid or solid or a realistic ( instead of ideal ) gas ?
|
imagine you had a monatomic ideal gas in this cylinder here , an there was this tightly fitted piston above it that prevented any gas from getting out . well we know that the total internal energy for a monatomic ideal gas is just three halves p times v or three halves nkt , or three halves little nrt , and we know that saying u internal the internal energy is really just code for the total kinetic energy of the monatomic ideal gas , that these are the same thing . when we talk about internal energy we 're talking about how fast are these particles moving , in other words , what 's the total kinetic energy of all of these particles added up . my question is how do we go about changing the internal energy ? let 's say we wanted to increase the total kinetic energy , what could we do ? well , we could say increase the pressure , or the volume , or the temperature , yeah but i mean physically , actually , in the lab , what do we do ? and there 's basically two ways to change the internal energy . if you want to add internal energy , i.e . get these particles moving faster , we can heat it up so put this above a flame or on a hot plate , and heat will flow into the gas which will cause these particles to move faster and faster . that 's one way to do it , to add heat . the other way to do it is to do work on the gas . i could take this piston and push it down , and if you push this down hard enough it will squash this gas together , and those impacts with this piston while it 's moving down will cause them to start moving faster and faster , that will also add internal energy to the gas . so if we wanted to write down a formula that told us how you could get a change in the internal energy , if i want to change the internal energy , delta u , which is really just saying changing the kinetic energy , well there 's two ways to do it . i can add heat . if i added ten joules of heat i 'd add ten joules to the internal energy , but i 've also got to take into account this work being done , and so i can do plus the work done on the gas , and that 's it , this is actually the first law of thermodynamics , it 's the law of conservation of energy it says there 's only two ways to add energy , internal energy to a gas . let me talk a little bit more about this work done though cause getting the sign right is important . if you 're doing work on the gas compressing it you 're adding energy to the gas , but if you let the gas push up on the piston and this gas expands pushing the piston up , then the gas is doing the work , that 's energy leaving the system . so if the gas does work you have to subtract work done by the gas . if the outside force does work on the gas you add that to the internal energy . so you got to pay attention to which way the energy is flowing . work done on gas , energy goes in . work done by the gas , energy goes out , and you 'd have to subtract that over here . let 's say the gas did expand . let 's say the gas in here was under so much pressure that the force it exerted on this piston was enough to push that piston upward by a certain amount . so let 's say it started right here and it went up to here so that piston went from here to there no gasses escaping cause this is tightly fitting , but the gas was able to push it up a certain distance d , how much work was done ? you know the definition of work . work is defined to be the force times the distance through which that force was applied . so the work that the gas did was f times d , but we want this to be in terms of thermal quantities like pressure , and volume , and temperature . so what could we do ? we can say that this volume , not only did the piston raise up , but there was an extra volume generated within here that i 'm going to call delta v , and i know that this delta v has got to equal the area of the piston times the distance through which that piston moved because this height times that area gives me this volume right in here . why am i doing this ? cause look i can write d as equal to delta v over a , and i can take this , i can substitute this formula for d into here , and something magical happens , i 'll get work equals f times delta v over a , but look f over a , we know what f over a is , that 's pressure so i get that the work done by the gas is the pressure times delta v. this is an equation that i like because it 's in terms of thermodynamic quantities that we 're already dealing with . so work done you can figure out by taking p times delta v but strictly speaking this is only true if this pressure remained constant , right ? if the pressure was changing , then what am i supposed to plug in here , the initial pressure , the final pressure ? if the pressure 's staying constant this gives you an exact way to find the work done . you might object and say wait , how is it possible for a gas to expand and remain at the same pressure ? well , you basically have to heat it up while the gas expands , that allows the pressure to remain constant as the gas expands . and now we 're finally ready to talk about heat capacities . so let 's get rid of this , and heat capacity is defined to be , imagine you had a certain amount of heat being added . so a certain amount of heat gets added to your gas . how much does the temperature increase ? that 's what the heat capacity tells you . so capital c is heat capacity and it 's defined to be the amount of heat that you 've added to the gas , divided by the amount of change in the temperature of that gas . and actually , something you 'll hear about often is the molar heat capacity , which is actually divided by an extra n here . so instead of q over delta t it 's q over n the number of moles times delta t. pretty simple but think about it . if we had a piston in here , are we going to allow that piston to move while we add the heat , or are we not going to allow the piston to move ? there 's different ways that this can happen , and because of that there 's different heat capacities . if we do n't allow this piston to move , if we weld this thing shut so it ca n't move we 've got heat capacity at constant volume , and if we do allow this piston to move freely while we add the heat so that the pressure inside of here remains constant , we 'd have the heat capacity at constant pressure . and these are similar but different , and they 're related , and we can figure them out . so let 's clear this away , let 's get a nice , here we go , two pistons inside of cylinders . we 'll put a piston in here , but i 'm going to weld this one shut . this one ca n't move . we 'll have another one over here , it can move freely . so over on this side , we 'll have the definition of heat capacity , regular heat capacity , is the amount of heat you add divided by the change in temperature that you get . so on this side we 're adding heat , let 's say heat goes in , but the piston does not move and so the gas in here is stuck , it ca n't move , no work can be done . since this piston ca n't move , external forces ca n't do work on the gas , and the gas ca n't do work and allow energy to leave . q is the only thing adding energy into this system , or in other words , we 've got heat capacity at constant volume is going to equal , well , remember the first law of thermodynamics said that delta u , the only way to add internal energy , or take it away is that you can add or subtract heat , and you can do work on the gas . in this case , q , if i subtract w from both sides i get delta u minus w over delta t , but since we 're not allowing this piston to move the work done has got to be zero . so there 's no work done at all so the heat capacity at constant volume is going to be delta u over delta t , what 's delta u ? let 's just assume this is a monatomic ideal gas , if it 's monatomic we 've got a formula for this . delta u is just three halves , p times v over delta t. that 's not the only way i can write it . remember i can also write it as three halves nk delta t over delta t , and something magical happens , check it out the delta t 's go away and you get that this is a constant . that the heat capacity for any monatomic ideal gas is just going to be three halves , capital nk , boltzmann 's constant , n is the total number of molecules . or you could have rewrote this as little n r delta t. the t 's would still have cancelled and you would have got three halves , little n , the number of moles , times r , the gas constant . so the heat capacity at constant volume for any monatomic ideal gas is just three halves nr , and if you wanted the molar heat capacity remember that 's just divide by an extra mole here so everything gets divided by moles everywhere divided by moles , that just cancels this out , and the molar heat capacity at constant volume is just three halves r. so that 's heat capacity at constant volume , what about heat capacity at constant pressure ? now we 're going to look at this side . again , we 're going to allow this gas to have heat enter the cylinder , but we 're going to allow this piston to move up while it does that so that the pressure inside of here remains constant and this is going to be the heat capacity at constant pressure . well , again , we 're going to get that it 's q over delta t , and just like the first law said , q has to equal delta u minus w. so we get delta u minus w , the work done , over delta t , this time w is not zero . what 's w going to be ? remember w is p times delta v. so this is a way we can find the work done by the gas , p times delta v , so this is going to equal delta u , we know what that is . if this is again , a monatomic ideal gas , this is going to equal three halves nr delta t plus this is p times delta v , but we have to be careful , in this formula this work is referring to work done on the gas , but in this case , work is being done by the gas , so i need another negative . technically the work done on the gas would be a negative amount of this since energy is leaving the system . so that negative cancels this negative and i get plus p times delta v , all of that over delta t , phew . so what do we get ? three halves nr delta t plus i want to rewrite p times delta v , but i know how to do that . the ideal gas law says pv equals nrt , well if that 's true , then p times delta v is going to equal nr delta t. so can rewrite this as nr delta t divided by delta t , almost there , all of the delta t 's go away . look what i 'm left with . i 'm left with c. heat capacity at constant pressure is going to be equal to three halves nr plus nr , that 's just five halves nr , and if i wanted the molar heat capacity again i could divide everything , everything around here by little n , and that would just give me the molar heat capacity constant pressure would be five halves r. and notice they 're almost the same . the heat capacity at constant volume is three halves nr , and the heat capacity at constant pressure is five halves nr . they just differ by nr . so the difference between the heat capacity at constant volume which is three halves nr , and the heat capacity at constant pressure which is five halves nr , is just cp minus cv which is nr , just nr , and if you wanted to take the difference between the molar heat capacities at constant volume and pressure , it would just be r. the difference would just be r because everything would get divided by the number of moles . so there 's a relationship , an important relationship . it tells you the difference between the heat capacity at constant pressure and the heat capacity at constant volume .
|
that the heat capacity for any monatomic ideal gas is just going to be three halves , capital nk , boltzmann 's constant , n is the total number of molecules . or you could have rewrote this as little n r delta t. the t 's would still have cancelled and you would have got three halves , little n , the number of moles , times r , the gas constant . so the heat capacity at constant volume for any monatomic ideal gas is just three halves nr , and if you wanted the molar heat capacity remember that 's just divide by an extra mole here so everything gets divided by moles everywhere divided by moles , that just cancels this out , and the molar heat capacity at constant volume is just three halves r. so that 's heat capacity at constant volume , what about heat capacity at constant pressure ?
|
pardon me as this is basic maths , but i can just do 2.5 x n x r and 1.5 x n x r right ?
|
imagine you had a monatomic ideal gas in this cylinder here , an there was this tightly fitted piston above it that prevented any gas from getting out . well we know that the total internal energy for a monatomic ideal gas is just three halves p times v or three halves nkt , or three halves little nrt , and we know that saying u internal the internal energy is really just code for the total kinetic energy of the monatomic ideal gas , that these are the same thing . when we talk about internal energy we 're talking about how fast are these particles moving , in other words , what 's the total kinetic energy of all of these particles added up . my question is how do we go about changing the internal energy ? let 's say we wanted to increase the total kinetic energy , what could we do ? well , we could say increase the pressure , or the volume , or the temperature , yeah but i mean physically , actually , in the lab , what do we do ? and there 's basically two ways to change the internal energy . if you want to add internal energy , i.e . get these particles moving faster , we can heat it up so put this above a flame or on a hot plate , and heat will flow into the gas which will cause these particles to move faster and faster . that 's one way to do it , to add heat . the other way to do it is to do work on the gas . i could take this piston and push it down , and if you push this down hard enough it will squash this gas together , and those impacts with this piston while it 's moving down will cause them to start moving faster and faster , that will also add internal energy to the gas . so if we wanted to write down a formula that told us how you could get a change in the internal energy , if i want to change the internal energy , delta u , which is really just saying changing the kinetic energy , well there 's two ways to do it . i can add heat . if i added ten joules of heat i 'd add ten joules to the internal energy , but i 've also got to take into account this work being done , and so i can do plus the work done on the gas , and that 's it , this is actually the first law of thermodynamics , it 's the law of conservation of energy it says there 's only two ways to add energy , internal energy to a gas . let me talk a little bit more about this work done though cause getting the sign right is important . if you 're doing work on the gas compressing it you 're adding energy to the gas , but if you let the gas push up on the piston and this gas expands pushing the piston up , then the gas is doing the work , that 's energy leaving the system . so if the gas does work you have to subtract work done by the gas . if the outside force does work on the gas you add that to the internal energy . so you got to pay attention to which way the energy is flowing . work done on gas , energy goes in . work done by the gas , energy goes out , and you 'd have to subtract that over here . let 's say the gas did expand . let 's say the gas in here was under so much pressure that the force it exerted on this piston was enough to push that piston upward by a certain amount . so let 's say it started right here and it went up to here so that piston went from here to there no gasses escaping cause this is tightly fitting , but the gas was able to push it up a certain distance d , how much work was done ? you know the definition of work . work is defined to be the force times the distance through which that force was applied . so the work that the gas did was f times d , but we want this to be in terms of thermal quantities like pressure , and volume , and temperature . so what could we do ? we can say that this volume , not only did the piston raise up , but there was an extra volume generated within here that i 'm going to call delta v , and i know that this delta v has got to equal the area of the piston times the distance through which that piston moved because this height times that area gives me this volume right in here . why am i doing this ? cause look i can write d as equal to delta v over a , and i can take this , i can substitute this formula for d into here , and something magical happens , i 'll get work equals f times delta v over a , but look f over a , we know what f over a is , that 's pressure so i get that the work done by the gas is the pressure times delta v. this is an equation that i like because it 's in terms of thermodynamic quantities that we 're already dealing with . so work done you can figure out by taking p times delta v but strictly speaking this is only true if this pressure remained constant , right ? if the pressure was changing , then what am i supposed to plug in here , the initial pressure , the final pressure ? if the pressure 's staying constant this gives you an exact way to find the work done . you might object and say wait , how is it possible for a gas to expand and remain at the same pressure ? well , you basically have to heat it up while the gas expands , that allows the pressure to remain constant as the gas expands . and now we 're finally ready to talk about heat capacities . so let 's get rid of this , and heat capacity is defined to be , imagine you had a certain amount of heat being added . so a certain amount of heat gets added to your gas . how much does the temperature increase ? that 's what the heat capacity tells you . so capital c is heat capacity and it 's defined to be the amount of heat that you 've added to the gas , divided by the amount of change in the temperature of that gas . and actually , something you 'll hear about often is the molar heat capacity , which is actually divided by an extra n here . so instead of q over delta t it 's q over n the number of moles times delta t. pretty simple but think about it . if we had a piston in here , are we going to allow that piston to move while we add the heat , or are we not going to allow the piston to move ? there 's different ways that this can happen , and because of that there 's different heat capacities . if we do n't allow this piston to move , if we weld this thing shut so it ca n't move we 've got heat capacity at constant volume , and if we do allow this piston to move freely while we add the heat so that the pressure inside of here remains constant , we 'd have the heat capacity at constant pressure . and these are similar but different , and they 're related , and we can figure them out . so let 's clear this away , let 's get a nice , here we go , two pistons inside of cylinders . we 'll put a piston in here , but i 'm going to weld this one shut . this one ca n't move . we 'll have another one over here , it can move freely . so over on this side , we 'll have the definition of heat capacity , regular heat capacity , is the amount of heat you add divided by the change in temperature that you get . so on this side we 're adding heat , let 's say heat goes in , but the piston does not move and so the gas in here is stuck , it ca n't move , no work can be done . since this piston ca n't move , external forces ca n't do work on the gas , and the gas ca n't do work and allow energy to leave . q is the only thing adding energy into this system , or in other words , we 've got heat capacity at constant volume is going to equal , well , remember the first law of thermodynamics said that delta u , the only way to add internal energy , or take it away is that you can add or subtract heat , and you can do work on the gas . in this case , q , if i subtract w from both sides i get delta u minus w over delta t , but since we 're not allowing this piston to move the work done has got to be zero . so there 's no work done at all so the heat capacity at constant volume is going to be delta u over delta t , what 's delta u ? let 's just assume this is a monatomic ideal gas , if it 's monatomic we 've got a formula for this . delta u is just three halves , p times v over delta t. that 's not the only way i can write it . remember i can also write it as three halves nk delta t over delta t , and something magical happens , check it out the delta t 's go away and you get that this is a constant . that the heat capacity for any monatomic ideal gas is just going to be three halves , capital nk , boltzmann 's constant , n is the total number of molecules . or you could have rewrote this as little n r delta t. the t 's would still have cancelled and you would have got three halves , little n , the number of moles , times r , the gas constant . so the heat capacity at constant volume for any monatomic ideal gas is just three halves nr , and if you wanted the molar heat capacity remember that 's just divide by an extra mole here so everything gets divided by moles everywhere divided by moles , that just cancels this out , and the molar heat capacity at constant volume is just three halves r. so that 's heat capacity at constant volume , what about heat capacity at constant pressure ? now we 're going to look at this side . again , we 're going to allow this gas to have heat enter the cylinder , but we 're going to allow this piston to move up while it does that so that the pressure inside of here remains constant and this is going to be the heat capacity at constant pressure . well , again , we 're going to get that it 's q over delta t , and just like the first law said , q has to equal delta u minus w. so we get delta u minus w , the work done , over delta t , this time w is not zero . what 's w going to be ? remember w is p times delta v. so this is a way we can find the work done by the gas , p times delta v , so this is going to equal delta u , we know what that is . if this is again , a monatomic ideal gas , this is going to equal three halves nr delta t plus this is p times delta v , but we have to be careful , in this formula this work is referring to work done on the gas , but in this case , work is being done by the gas , so i need another negative . technically the work done on the gas would be a negative amount of this since energy is leaving the system . so that negative cancels this negative and i get plus p times delta v , all of that over delta t , phew . so what do we get ? three halves nr delta t plus i want to rewrite p times delta v , but i know how to do that . the ideal gas law says pv equals nrt , well if that 's true , then p times delta v is going to equal nr delta t. so can rewrite this as nr delta t divided by delta t , almost there , all of the delta t 's go away . look what i 'm left with . i 'm left with c. heat capacity at constant pressure is going to be equal to three halves nr plus nr , that 's just five halves nr , and if i wanted the molar heat capacity again i could divide everything , everything around here by little n , and that would just give me the molar heat capacity constant pressure would be five halves r. and notice they 're almost the same . the heat capacity at constant volume is three halves nr , and the heat capacity at constant pressure is five halves nr . they just differ by nr . so the difference between the heat capacity at constant volume which is three halves nr , and the heat capacity at constant pressure which is five halves nr , is just cp minus cv which is nr , just nr , and if you wanted to take the difference between the molar heat capacities at constant volume and pressure , it would just be r. the difference would just be r because everything would get divided by the number of moles . so there 's a relationship , an important relationship . it tells you the difference between the heat capacity at constant pressure and the heat capacity at constant volume .
|
so there 's a relationship , an important relationship . it tells you the difference between the heat capacity at constant pressure and the heat capacity at constant volume .
|
so does it mean that at constant pressure more heat is required to increase the temperature than whats required at constant volume ?
|
imagine you had a monatomic ideal gas in this cylinder here , an there was this tightly fitted piston above it that prevented any gas from getting out . well we know that the total internal energy for a monatomic ideal gas is just three halves p times v or three halves nkt , or three halves little nrt , and we know that saying u internal the internal energy is really just code for the total kinetic energy of the monatomic ideal gas , that these are the same thing . when we talk about internal energy we 're talking about how fast are these particles moving , in other words , what 's the total kinetic energy of all of these particles added up . my question is how do we go about changing the internal energy ? let 's say we wanted to increase the total kinetic energy , what could we do ? well , we could say increase the pressure , or the volume , or the temperature , yeah but i mean physically , actually , in the lab , what do we do ? and there 's basically two ways to change the internal energy . if you want to add internal energy , i.e . get these particles moving faster , we can heat it up so put this above a flame or on a hot plate , and heat will flow into the gas which will cause these particles to move faster and faster . that 's one way to do it , to add heat . the other way to do it is to do work on the gas . i could take this piston and push it down , and if you push this down hard enough it will squash this gas together , and those impacts with this piston while it 's moving down will cause them to start moving faster and faster , that will also add internal energy to the gas . so if we wanted to write down a formula that told us how you could get a change in the internal energy , if i want to change the internal energy , delta u , which is really just saying changing the kinetic energy , well there 's two ways to do it . i can add heat . if i added ten joules of heat i 'd add ten joules to the internal energy , but i 've also got to take into account this work being done , and so i can do plus the work done on the gas , and that 's it , this is actually the first law of thermodynamics , it 's the law of conservation of energy it says there 's only two ways to add energy , internal energy to a gas . let me talk a little bit more about this work done though cause getting the sign right is important . if you 're doing work on the gas compressing it you 're adding energy to the gas , but if you let the gas push up on the piston and this gas expands pushing the piston up , then the gas is doing the work , that 's energy leaving the system . so if the gas does work you have to subtract work done by the gas . if the outside force does work on the gas you add that to the internal energy . so you got to pay attention to which way the energy is flowing . work done on gas , energy goes in . work done by the gas , energy goes out , and you 'd have to subtract that over here . let 's say the gas did expand . let 's say the gas in here was under so much pressure that the force it exerted on this piston was enough to push that piston upward by a certain amount . so let 's say it started right here and it went up to here so that piston went from here to there no gasses escaping cause this is tightly fitting , but the gas was able to push it up a certain distance d , how much work was done ? you know the definition of work . work is defined to be the force times the distance through which that force was applied . so the work that the gas did was f times d , but we want this to be in terms of thermal quantities like pressure , and volume , and temperature . so what could we do ? we can say that this volume , not only did the piston raise up , but there was an extra volume generated within here that i 'm going to call delta v , and i know that this delta v has got to equal the area of the piston times the distance through which that piston moved because this height times that area gives me this volume right in here . why am i doing this ? cause look i can write d as equal to delta v over a , and i can take this , i can substitute this formula for d into here , and something magical happens , i 'll get work equals f times delta v over a , but look f over a , we know what f over a is , that 's pressure so i get that the work done by the gas is the pressure times delta v. this is an equation that i like because it 's in terms of thermodynamic quantities that we 're already dealing with . so work done you can figure out by taking p times delta v but strictly speaking this is only true if this pressure remained constant , right ? if the pressure was changing , then what am i supposed to plug in here , the initial pressure , the final pressure ? if the pressure 's staying constant this gives you an exact way to find the work done . you might object and say wait , how is it possible for a gas to expand and remain at the same pressure ? well , you basically have to heat it up while the gas expands , that allows the pressure to remain constant as the gas expands . and now we 're finally ready to talk about heat capacities . so let 's get rid of this , and heat capacity is defined to be , imagine you had a certain amount of heat being added . so a certain amount of heat gets added to your gas . how much does the temperature increase ? that 's what the heat capacity tells you . so capital c is heat capacity and it 's defined to be the amount of heat that you 've added to the gas , divided by the amount of change in the temperature of that gas . and actually , something you 'll hear about often is the molar heat capacity , which is actually divided by an extra n here . so instead of q over delta t it 's q over n the number of moles times delta t. pretty simple but think about it . if we had a piston in here , are we going to allow that piston to move while we add the heat , or are we not going to allow the piston to move ? there 's different ways that this can happen , and because of that there 's different heat capacities . if we do n't allow this piston to move , if we weld this thing shut so it ca n't move we 've got heat capacity at constant volume , and if we do allow this piston to move freely while we add the heat so that the pressure inside of here remains constant , we 'd have the heat capacity at constant pressure . and these are similar but different , and they 're related , and we can figure them out . so let 's clear this away , let 's get a nice , here we go , two pistons inside of cylinders . we 'll put a piston in here , but i 'm going to weld this one shut . this one ca n't move . we 'll have another one over here , it can move freely . so over on this side , we 'll have the definition of heat capacity , regular heat capacity , is the amount of heat you add divided by the change in temperature that you get . so on this side we 're adding heat , let 's say heat goes in , but the piston does not move and so the gas in here is stuck , it ca n't move , no work can be done . since this piston ca n't move , external forces ca n't do work on the gas , and the gas ca n't do work and allow energy to leave . q is the only thing adding energy into this system , or in other words , we 've got heat capacity at constant volume is going to equal , well , remember the first law of thermodynamics said that delta u , the only way to add internal energy , or take it away is that you can add or subtract heat , and you can do work on the gas . in this case , q , if i subtract w from both sides i get delta u minus w over delta t , but since we 're not allowing this piston to move the work done has got to be zero . so there 's no work done at all so the heat capacity at constant volume is going to be delta u over delta t , what 's delta u ? let 's just assume this is a monatomic ideal gas , if it 's monatomic we 've got a formula for this . delta u is just three halves , p times v over delta t. that 's not the only way i can write it . remember i can also write it as three halves nk delta t over delta t , and something magical happens , check it out the delta t 's go away and you get that this is a constant . that the heat capacity for any monatomic ideal gas is just going to be three halves , capital nk , boltzmann 's constant , n is the total number of molecules . or you could have rewrote this as little n r delta t. the t 's would still have cancelled and you would have got three halves , little n , the number of moles , times r , the gas constant . so the heat capacity at constant volume for any monatomic ideal gas is just three halves nr , and if you wanted the molar heat capacity remember that 's just divide by an extra mole here so everything gets divided by moles everywhere divided by moles , that just cancels this out , and the molar heat capacity at constant volume is just three halves r. so that 's heat capacity at constant volume , what about heat capacity at constant pressure ? now we 're going to look at this side . again , we 're going to allow this gas to have heat enter the cylinder , but we 're going to allow this piston to move up while it does that so that the pressure inside of here remains constant and this is going to be the heat capacity at constant pressure . well , again , we 're going to get that it 's q over delta t , and just like the first law said , q has to equal delta u minus w. so we get delta u minus w , the work done , over delta t , this time w is not zero . what 's w going to be ? remember w is p times delta v. so this is a way we can find the work done by the gas , p times delta v , so this is going to equal delta u , we know what that is . if this is again , a monatomic ideal gas , this is going to equal three halves nr delta t plus this is p times delta v , but we have to be careful , in this formula this work is referring to work done on the gas , but in this case , work is being done by the gas , so i need another negative . technically the work done on the gas would be a negative amount of this since energy is leaving the system . so that negative cancels this negative and i get plus p times delta v , all of that over delta t , phew . so what do we get ? three halves nr delta t plus i want to rewrite p times delta v , but i know how to do that . the ideal gas law says pv equals nrt , well if that 's true , then p times delta v is going to equal nr delta t. so can rewrite this as nr delta t divided by delta t , almost there , all of the delta t 's go away . look what i 'm left with . i 'm left with c. heat capacity at constant pressure is going to be equal to three halves nr plus nr , that 's just five halves nr , and if i wanted the molar heat capacity again i could divide everything , everything around here by little n , and that would just give me the molar heat capacity constant pressure would be five halves r. and notice they 're almost the same . the heat capacity at constant volume is three halves nr , and the heat capacity at constant pressure is five halves nr . they just differ by nr . so the difference between the heat capacity at constant volume which is three halves nr , and the heat capacity at constant pressure which is five halves nr , is just cp minus cv which is nr , just nr , and if you wanted to take the difference between the molar heat capacities at constant volume and pressure , it would just be r. the difference would just be r because everything would get divided by the number of moles . so there 's a relationship , an important relationship . it tells you the difference between the heat capacity at constant pressure and the heat capacity at constant volume .
|
or you could have rewrote this as little n r delta t. the t 's would still have cancelled and you would have got three halves , little n , the number of moles , times r , the gas constant . so the heat capacity at constant volume for any monatomic ideal gas is just three halves nr , and if you wanted the molar heat capacity remember that 's just divide by an extra mole here so everything gets divided by moles everywhere divided by moles , that just cancels this out , and the molar heat capacity at constant volume is just three halves r. so that 's heat capacity at constant volume , what about heat capacity at constant pressure ? now we 're going to look at this side .
|
does a monatomic gas have lower or higher heat capacity than a diatomic , or polyatomic ?
|
imagine you had a monatomic ideal gas in this cylinder here , an there was this tightly fitted piston above it that prevented any gas from getting out . well we know that the total internal energy for a monatomic ideal gas is just three halves p times v or three halves nkt , or three halves little nrt , and we know that saying u internal the internal energy is really just code for the total kinetic energy of the monatomic ideal gas , that these are the same thing . when we talk about internal energy we 're talking about how fast are these particles moving , in other words , what 's the total kinetic energy of all of these particles added up . my question is how do we go about changing the internal energy ? let 's say we wanted to increase the total kinetic energy , what could we do ? well , we could say increase the pressure , or the volume , or the temperature , yeah but i mean physically , actually , in the lab , what do we do ? and there 's basically two ways to change the internal energy . if you want to add internal energy , i.e . get these particles moving faster , we can heat it up so put this above a flame or on a hot plate , and heat will flow into the gas which will cause these particles to move faster and faster . that 's one way to do it , to add heat . the other way to do it is to do work on the gas . i could take this piston and push it down , and if you push this down hard enough it will squash this gas together , and those impacts with this piston while it 's moving down will cause them to start moving faster and faster , that will also add internal energy to the gas . so if we wanted to write down a formula that told us how you could get a change in the internal energy , if i want to change the internal energy , delta u , which is really just saying changing the kinetic energy , well there 's two ways to do it . i can add heat . if i added ten joules of heat i 'd add ten joules to the internal energy , but i 've also got to take into account this work being done , and so i can do plus the work done on the gas , and that 's it , this is actually the first law of thermodynamics , it 's the law of conservation of energy it says there 's only two ways to add energy , internal energy to a gas . let me talk a little bit more about this work done though cause getting the sign right is important . if you 're doing work on the gas compressing it you 're adding energy to the gas , but if you let the gas push up on the piston and this gas expands pushing the piston up , then the gas is doing the work , that 's energy leaving the system . so if the gas does work you have to subtract work done by the gas . if the outside force does work on the gas you add that to the internal energy . so you got to pay attention to which way the energy is flowing . work done on gas , energy goes in . work done by the gas , energy goes out , and you 'd have to subtract that over here . let 's say the gas did expand . let 's say the gas in here was under so much pressure that the force it exerted on this piston was enough to push that piston upward by a certain amount . so let 's say it started right here and it went up to here so that piston went from here to there no gasses escaping cause this is tightly fitting , but the gas was able to push it up a certain distance d , how much work was done ? you know the definition of work . work is defined to be the force times the distance through which that force was applied . so the work that the gas did was f times d , but we want this to be in terms of thermal quantities like pressure , and volume , and temperature . so what could we do ? we can say that this volume , not only did the piston raise up , but there was an extra volume generated within here that i 'm going to call delta v , and i know that this delta v has got to equal the area of the piston times the distance through which that piston moved because this height times that area gives me this volume right in here . why am i doing this ? cause look i can write d as equal to delta v over a , and i can take this , i can substitute this formula for d into here , and something magical happens , i 'll get work equals f times delta v over a , but look f over a , we know what f over a is , that 's pressure so i get that the work done by the gas is the pressure times delta v. this is an equation that i like because it 's in terms of thermodynamic quantities that we 're already dealing with . so work done you can figure out by taking p times delta v but strictly speaking this is only true if this pressure remained constant , right ? if the pressure was changing , then what am i supposed to plug in here , the initial pressure , the final pressure ? if the pressure 's staying constant this gives you an exact way to find the work done . you might object and say wait , how is it possible for a gas to expand and remain at the same pressure ? well , you basically have to heat it up while the gas expands , that allows the pressure to remain constant as the gas expands . and now we 're finally ready to talk about heat capacities . so let 's get rid of this , and heat capacity is defined to be , imagine you had a certain amount of heat being added . so a certain amount of heat gets added to your gas . how much does the temperature increase ? that 's what the heat capacity tells you . so capital c is heat capacity and it 's defined to be the amount of heat that you 've added to the gas , divided by the amount of change in the temperature of that gas . and actually , something you 'll hear about often is the molar heat capacity , which is actually divided by an extra n here . so instead of q over delta t it 's q over n the number of moles times delta t. pretty simple but think about it . if we had a piston in here , are we going to allow that piston to move while we add the heat , or are we not going to allow the piston to move ? there 's different ways that this can happen , and because of that there 's different heat capacities . if we do n't allow this piston to move , if we weld this thing shut so it ca n't move we 've got heat capacity at constant volume , and if we do allow this piston to move freely while we add the heat so that the pressure inside of here remains constant , we 'd have the heat capacity at constant pressure . and these are similar but different , and they 're related , and we can figure them out . so let 's clear this away , let 's get a nice , here we go , two pistons inside of cylinders . we 'll put a piston in here , but i 'm going to weld this one shut . this one ca n't move . we 'll have another one over here , it can move freely . so over on this side , we 'll have the definition of heat capacity , regular heat capacity , is the amount of heat you add divided by the change in temperature that you get . so on this side we 're adding heat , let 's say heat goes in , but the piston does not move and so the gas in here is stuck , it ca n't move , no work can be done . since this piston ca n't move , external forces ca n't do work on the gas , and the gas ca n't do work and allow energy to leave . q is the only thing adding energy into this system , or in other words , we 've got heat capacity at constant volume is going to equal , well , remember the first law of thermodynamics said that delta u , the only way to add internal energy , or take it away is that you can add or subtract heat , and you can do work on the gas . in this case , q , if i subtract w from both sides i get delta u minus w over delta t , but since we 're not allowing this piston to move the work done has got to be zero . so there 's no work done at all so the heat capacity at constant volume is going to be delta u over delta t , what 's delta u ? let 's just assume this is a monatomic ideal gas , if it 's monatomic we 've got a formula for this . delta u is just three halves , p times v over delta t. that 's not the only way i can write it . remember i can also write it as three halves nk delta t over delta t , and something magical happens , check it out the delta t 's go away and you get that this is a constant . that the heat capacity for any monatomic ideal gas is just going to be three halves , capital nk , boltzmann 's constant , n is the total number of molecules . or you could have rewrote this as little n r delta t. the t 's would still have cancelled and you would have got three halves , little n , the number of moles , times r , the gas constant . so the heat capacity at constant volume for any monatomic ideal gas is just three halves nr , and if you wanted the molar heat capacity remember that 's just divide by an extra mole here so everything gets divided by moles everywhere divided by moles , that just cancels this out , and the molar heat capacity at constant volume is just three halves r. so that 's heat capacity at constant volume , what about heat capacity at constant pressure ? now we 're going to look at this side . again , we 're going to allow this gas to have heat enter the cylinder , but we 're going to allow this piston to move up while it does that so that the pressure inside of here remains constant and this is going to be the heat capacity at constant pressure . well , again , we 're going to get that it 's q over delta t , and just like the first law said , q has to equal delta u minus w. so we get delta u minus w , the work done , over delta t , this time w is not zero . what 's w going to be ? remember w is p times delta v. so this is a way we can find the work done by the gas , p times delta v , so this is going to equal delta u , we know what that is . if this is again , a monatomic ideal gas , this is going to equal three halves nr delta t plus this is p times delta v , but we have to be careful , in this formula this work is referring to work done on the gas , but in this case , work is being done by the gas , so i need another negative . technically the work done on the gas would be a negative amount of this since energy is leaving the system . so that negative cancels this negative and i get plus p times delta v , all of that over delta t , phew . so what do we get ? three halves nr delta t plus i want to rewrite p times delta v , but i know how to do that . the ideal gas law says pv equals nrt , well if that 's true , then p times delta v is going to equal nr delta t. so can rewrite this as nr delta t divided by delta t , almost there , all of the delta t 's go away . look what i 'm left with . i 'm left with c. heat capacity at constant pressure is going to be equal to three halves nr plus nr , that 's just five halves nr , and if i wanted the molar heat capacity again i could divide everything , everything around here by little n , and that would just give me the molar heat capacity constant pressure would be five halves r. and notice they 're almost the same . the heat capacity at constant volume is three halves nr , and the heat capacity at constant pressure is five halves nr . they just differ by nr . so the difference between the heat capacity at constant volume which is three halves nr , and the heat capacity at constant pressure which is five halves nr , is just cp minus cv which is nr , just nr , and if you wanted to take the difference between the molar heat capacities at constant volume and pressure , it would just be r. the difference would just be r because everything would get divided by the number of moles . so there 's a relationship , an important relationship . it tells you the difference between the heat capacity at constant pressure and the heat capacity at constant volume .
|
so a certain amount of heat gets added to your gas . how much does the temperature increase ? that 's what the heat capacity tells you .
|
stumpped the mass of a hydrogen atom is 1.67 x 10-27 kilograms , and venus ' exosphere has a temperature of about 350 k. what is the thermal speed in venus ' exosphere ?
|
imagine you had a monatomic ideal gas in this cylinder here , an there was this tightly fitted piston above it that prevented any gas from getting out . well we know that the total internal energy for a monatomic ideal gas is just three halves p times v or three halves nkt , or three halves little nrt , and we know that saying u internal the internal energy is really just code for the total kinetic energy of the monatomic ideal gas , that these are the same thing . when we talk about internal energy we 're talking about how fast are these particles moving , in other words , what 's the total kinetic energy of all of these particles added up . my question is how do we go about changing the internal energy ? let 's say we wanted to increase the total kinetic energy , what could we do ? well , we could say increase the pressure , or the volume , or the temperature , yeah but i mean physically , actually , in the lab , what do we do ? and there 's basically two ways to change the internal energy . if you want to add internal energy , i.e . get these particles moving faster , we can heat it up so put this above a flame or on a hot plate , and heat will flow into the gas which will cause these particles to move faster and faster . that 's one way to do it , to add heat . the other way to do it is to do work on the gas . i could take this piston and push it down , and if you push this down hard enough it will squash this gas together , and those impacts with this piston while it 's moving down will cause them to start moving faster and faster , that will also add internal energy to the gas . so if we wanted to write down a formula that told us how you could get a change in the internal energy , if i want to change the internal energy , delta u , which is really just saying changing the kinetic energy , well there 's two ways to do it . i can add heat . if i added ten joules of heat i 'd add ten joules to the internal energy , but i 've also got to take into account this work being done , and so i can do plus the work done on the gas , and that 's it , this is actually the first law of thermodynamics , it 's the law of conservation of energy it says there 's only two ways to add energy , internal energy to a gas . let me talk a little bit more about this work done though cause getting the sign right is important . if you 're doing work on the gas compressing it you 're adding energy to the gas , but if you let the gas push up on the piston and this gas expands pushing the piston up , then the gas is doing the work , that 's energy leaving the system . so if the gas does work you have to subtract work done by the gas . if the outside force does work on the gas you add that to the internal energy . so you got to pay attention to which way the energy is flowing . work done on gas , energy goes in . work done by the gas , energy goes out , and you 'd have to subtract that over here . let 's say the gas did expand . let 's say the gas in here was under so much pressure that the force it exerted on this piston was enough to push that piston upward by a certain amount . so let 's say it started right here and it went up to here so that piston went from here to there no gasses escaping cause this is tightly fitting , but the gas was able to push it up a certain distance d , how much work was done ? you know the definition of work . work is defined to be the force times the distance through which that force was applied . so the work that the gas did was f times d , but we want this to be in terms of thermal quantities like pressure , and volume , and temperature . so what could we do ? we can say that this volume , not only did the piston raise up , but there was an extra volume generated within here that i 'm going to call delta v , and i know that this delta v has got to equal the area of the piston times the distance through which that piston moved because this height times that area gives me this volume right in here . why am i doing this ? cause look i can write d as equal to delta v over a , and i can take this , i can substitute this formula for d into here , and something magical happens , i 'll get work equals f times delta v over a , but look f over a , we know what f over a is , that 's pressure so i get that the work done by the gas is the pressure times delta v. this is an equation that i like because it 's in terms of thermodynamic quantities that we 're already dealing with . so work done you can figure out by taking p times delta v but strictly speaking this is only true if this pressure remained constant , right ? if the pressure was changing , then what am i supposed to plug in here , the initial pressure , the final pressure ? if the pressure 's staying constant this gives you an exact way to find the work done . you might object and say wait , how is it possible for a gas to expand and remain at the same pressure ? well , you basically have to heat it up while the gas expands , that allows the pressure to remain constant as the gas expands . and now we 're finally ready to talk about heat capacities . so let 's get rid of this , and heat capacity is defined to be , imagine you had a certain amount of heat being added . so a certain amount of heat gets added to your gas . how much does the temperature increase ? that 's what the heat capacity tells you . so capital c is heat capacity and it 's defined to be the amount of heat that you 've added to the gas , divided by the amount of change in the temperature of that gas . and actually , something you 'll hear about often is the molar heat capacity , which is actually divided by an extra n here . so instead of q over delta t it 's q over n the number of moles times delta t. pretty simple but think about it . if we had a piston in here , are we going to allow that piston to move while we add the heat , or are we not going to allow the piston to move ? there 's different ways that this can happen , and because of that there 's different heat capacities . if we do n't allow this piston to move , if we weld this thing shut so it ca n't move we 've got heat capacity at constant volume , and if we do allow this piston to move freely while we add the heat so that the pressure inside of here remains constant , we 'd have the heat capacity at constant pressure . and these are similar but different , and they 're related , and we can figure them out . so let 's clear this away , let 's get a nice , here we go , two pistons inside of cylinders . we 'll put a piston in here , but i 'm going to weld this one shut . this one ca n't move . we 'll have another one over here , it can move freely . so over on this side , we 'll have the definition of heat capacity , regular heat capacity , is the amount of heat you add divided by the change in temperature that you get . so on this side we 're adding heat , let 's say heat goes in , but the piston does not move and so the gas in here is stuck , it ca n't move , no work can be done . since this piston ca n't move , external forces ca n't do work on the gas , and the gas ca n't do work and allow energy to leave . q is the only thing adding energy into this system , or in other words , we 've got heat capacity at constant volume is going to equal , well , remember the first law of thermodynamics said that delta u , the only way to add internal energy , or take it away is that you can add or subtract heat , and you can do work on the gas . in this case , q , if i subtract w from both sides i get delta u minus w over delta t , but since we 're not allowing this piston to move the work done has got to be zero . so there 's no work done at all so the heat capacity at constant volume is going to be delta u over delta t , what 's delta u ? let 's just assume this is a monatomic ideal gas , if it 's monatomic we 've got a formula for this . delta u is just three halves , p times v over delta t. that 's not the only way i can write it . remember i can also write it as three halves nk delta t over delta t , and something magical happens , check it out the delta t 's go away and you get that this is a constant . that the heat capacity for any monatomic ideal gas is just going to be three halves , capital nk , boltzmann 's constant , n is the total number of molecules . or you could have rewrote this as little n r delta t. the t 's would still have cancelled and you would have got three halves , little n , the number of moles , times r , the gas constant . so the heat capacity at constant volume for any monatomic ideal gas is just three halves nr , and if you wanted the molar heat capacity remember that 's just divide by an extra mole here so everything gets divided by moles everywhere divided by moles , that just cancels this out , and the molar heat capacity at constant volume is just three halves r. so that 's heat capacity at constant volume , what about heat capacity at constant pressure ? now we 're going to look at this side . again , we 're going to allow this gas to have heat enter the cylinder , but we 're going to allow this piston to move up while it does that so that the pressure inside of here remains constant and this is going to be the heat capacity at constant pressure . well , again , we 're going to get that it 's q over delta t , and just like the first law said , q has to equal delta u minus w. so we get delta u minus w , the work done , over delta t , this time w is not zero . what 's w going to be ? remember w is p times delta v. so this is a way we can find the work done by the gas , p times delta v , so this is going to equal delta u , we know what that is . if this is again , a monatomic ideal gas , this is going to equal three halves nr delta t plus this is p times delta v , but we have to be careful , in this formula this work is referring to work done on the gas , but in this case , work is being done by the gas , so i need another negative . technically the work done on the gas would be a negative amount of this since energy is leaving the system . so that negative cancels this negative and i get plus p times delta v , all of that over delta t , phew . so what do we get ? three halves nr delta t plus i want to rewrite p times delta v , but i know how to do that . the ideal gas law says pv equals nrt , well if that 's true , then p times delta v is going to equal nr delta t. so can rewrite this as nr delta t divided by delta t , almost there , all of the delta t 's go away . look what i 'm left with . i 'm left with c. heat capacity at constant pressure is going to be equal to three halves nr plus nr , that 's just five halves nr , and if i wanted the molar heat capacity again i could divide everything , everything around here by little n , and that would just give me the molar heat capacity constant pressure would be five halves r. and notice they 're almost the same . the heat capacity at constant volume is three halves nr , and the heat capacity at constant pressure is five halves nr . they just differ by nr . so the difference between the heat capacity at constant volume which is three halves nr , and the heat capacity at constant pressure which is five halves nr , is just cp minus cv which is nr , just nr , and if you wanted to take the difference between the molar heat capacities at constant volume and pressure , it would just be r. the difference would just be r because everything would get divided by the number of moles . so there 's a relationship , an important relationship . it tells you the difference between the heat capacity at constant pressure and the heat capacity at constant volume .
|
so what do we get ? three halves nr delta t plus i want to rewrite p times delta v , but i know how to do that . the ideal gas law says pv equals nrt , well if that 's true , then p times delta v is going to equal nr delta t. so can rewrite this as nr delta t divided by delta t , almost there , all of the delta t 's go away . look what i 'm left with .
|
the volume doenst change so how can you express the cv with p delta v over delta t ?
|
imagine you had a monatomic ideal gas in this cylinder here , an there was this tightly fitted piston above it that prevented any gas from getting out . well we know that the total internal energy for a monatomic ideal gas is just three halves p times v or three halves nkt , or three halves little nrt , and we know that saying u internal the internal energy is really just code for the total kinetic energy of the monatomic ideal gas , that these are the same thing . when we talk about internal energy we 're talking about how fast are these particles moving , in other words , what 's the total kinetic energy of all of these particles added up . my question is how do we go about changing the internal energy ? let 's say we wanted to increase the total kinetic energy , what could we do ? well , we could say increase the pressure , or the volume , or the temperature , yeah but i mean physically , actually , in the lab , what do we do ? and there 's basically two ways to change the internal energy . if you want to add internal energy , i.e . get these particles moving faster , we can heat it up so put this above a flame or on a hot plate , and heat will flow into the gas which will cause these particles to move faster and faster . that 's one way to do it , to add heat . the other way to do it is to do work on the gas . i could take this piston and push it down , and if you push this down hard enough it will squash this gas together , and those impacts with this piston while it 's moving down will cause them to start moving faster and faster , that will also add internal energy to the gas . so if we wanted to write down a formula that told us how you could get a change in the internal energy , if i want to change the internal energy , delta u , which is really just saying changing the kinetic energy , well there 's two ways to do it . i can add heat . if i added ten joules of heat i 'd add ten joules to the internal energy , but i 've also got to take into account this work being done , and so i can do plus the work done on the gas , and that 's it , this is actually the first law of thermodynamics , it 's the law of conservation of energy it says there 's only two ways to add energy , internal energy to a gas . let me talk a little bit more about this work done though cause getting the sign right is important . if you 're doing work on the gas compressing it you 're adding energy to the gas , but if you let the gas push up on the piston and this gas expands pushing the piston up , then the gas is doing the work , that 's energy leaving the system . so if the gas does work you have to subtract work done by the gas . if the outside force does work on the gas you add that to the internal energy . so you got to pay attention to which way the energy is flowing . work done on gas , energy goes in . work done by the gas , energy goes out , and you 'd have to subtract that over here . let 's say the gas did expand . let 's say the gas in here was under so much pressure that the force it exerted on this piston was enough to push that piston upward by a certain amount . so let 's say it started right here and it went up to here so that piston went from here to there no gasses escaping cause this is tightly fitting , but the gas was able to push it up a certain distance d , how much work was done ? you know the definition of work . work is defined to be the force times the distance through which that force was applied . so the work that the gas did was f times d , but we want this to be in terms of thermal quantities like pressure , and volume , and temperature . so what could we do ? we can say that this volume , not only did the piston raise up , but there was an extra volume generated within here that i 'm going to call delta v , and i know that this delta v has got to equal the area of the piston times the distance through which that piston moved because this height times that area gives me this volume right in here . why am i doing this ? cause look i can write d as equal to delta v over a , and i can take this , i can substitute this formula for d into here , and something magical happens , i 'll get work equals f times delta v over a , but look f over a , we know what f over a is , that 's pressure so i get that the work done by the gas is the pressure times delta v. this is an equation that i like because it 's in terms of thermodynamic quantities that we 're already dealing with . so work done you can figure out by taking p times delta v but strictly speaking this is only true if this pressure remained constant , right ? if the pressure was changing , then what am i supposed to plug in here , the initial pressure , the final pressure ? if the pressure 's staying constant this gives you an exact way to find the work done . you might object and say wait , how is it possible for a gas to expand and remain at the same pressure ? well , you basically have to heat it up while the gas expands , that allows the pressure to remain constant as the gas expands . and now we 're finally ready to talk about heat capacities . so let 's get rid of this , and heat capacity is defined to be , imagine you had a certain amount of heat being added . so a certain amount of heat gets added to your gas . how much does the temperature increase ? that 's what the heat capacity tells you . so capital c is heat capacity and it 's defined to be the amount of heat that you 've added to the gas , divided by the amount of change in the temperature of that gas . and actually , something you 'll hear about often is the molar heat capacity , which is actually divided by an extra n here . so instead of q over delta t it 's q over n the number of moles times delta t. pretty simple but think about it . if we had a piston in here , are we going to allow that piston to move while we add the heat , or are we not going to allow the piston to move ? there 's different ways that this can happen , and because of that there 's different heat capacities . if we do n't allow this piston to move , if we weld this thing shut so it ca n't move we 've got heat capacity at constant volume , and if we do allow this piston to move freely while we add the heat so that the pressure inside of here remains constant , we 'd have the heat capacity at constant pressure . and these are similar but different , and they 're related , and we can figure them out . so let 's clear this away , let 's get a nice , here we go , two pistons inside of cylinders . we 'll put a piston in here , but i 'm going to weld this one shut . this one ca n't move . we 'll have another one over here , it can move freely . so over on this side , we 'll have the definition of heat capacity , regular heat capacity , is the amount of heat you add divided by the change in temperature that you get . so on this side we 're adding heat , let 's say heat goes in , but the piston does not move and so the gas in here is stuck , it ca n't move , no work can be done . since this piston ca n't move , external forces ca n't do work on the gas , and the gas ca n't do work and allow energy to leave . q is the only thing adding energy into this system , or in other words , we 've got heat capacity at constant volume is going to equal , well , remember the first law of thermodynamics said that delta u , the only way to add internal energy , or take it away is that you can add or subtract heat , and you can do work on the gas . in this case , q , if i subtract w from both sides i get delta u minus w over delta t , but since we 're not allowing this piston to move the work done has got to be zero . so there 's no work done at all so the heat capacity at constant volume is going to be delta u over delta t , what 's delta u ? let 's just assume this is a monatomic ideal gas , if it 's monatomic we 've got a formula for this . delta u is just three halves , p times v over delta t. that 's not the only way i can write it . remember i can also write it as three halves nk delta t over delta t , and something magical happens , check it out the delta t 's go away and you get that this is a constant . that the heat capacity for any monatomic ideal gas is just going to be three halves , capital nk , boltzmann 's constant , n is the total number of molecules . or you could have rewrote this as little n r delta t. the t 's would still have cancelled and you would have got three halves , little n , the number of moles , times r , the gas constant . so the heat capacity at constant volume for any monatomic ideal gas is just three halves nr , and if you wanted the molar heat capacity remember that 's just divide by an extra mole here so everything gets divided by moles everywhere divided by moles , that just cancels this out , and the molar heat capacity at constant volume is just three halves r. so that 's heat capacity at constant volume , what about heat capacity at constant pressure ? now we 're going to look at this side . again , we 're going to allow this gas to have heat enter the cylinder , but we 're going to allow this piston to move up while it does that so that the pressure inside of here remains constant and this is going to be the heat capacity at constant pressure . well , again , we 're going to get that it 's q over delta t , and just like the first law said , q has to equal delta u minus w. so we get delta u minus w , the work done , over delta t , this time w is not zero . what 's w going to be ? remember w is p times delta v. so this is a way we can find the work done by the gas , p times delta v , so this is going to equal delta u , we know what that is . if this is again , a monatomic ideal gas , this is going to equal three halves nr delta t plus this is p times delta v , but we have to be careful , in this formula this work is referring to work done on the gas , but in this case , work is being done by the gas , so i need another negative . technically the work done on the gas would be a negative amount of this since energy is leaving the system . so that negative cancels this negative and i get plus p times delta v , all of that over delta t , phew . so what do we get ? three halves nr delta t plus i want to rewrite p times delta v , but i know how to do that . the ideal gas law says pv equals nrt , well if that 's true , then p times delta v is going to equal nr delta t. so can rewrite this as nr delta t divided by delta t , almost there , all of the delta t 's go away . look what i 'm left with . i 'm left with c. heat capacity at constant pressure is going to be equal to three halves nr plus nr , that 's just five halves nr , and if i wanted the molar heat capacity again i could divide everything , everything around here by little n , and that would just give me the molar heat capacity constant pressure would be five halves r. and notice they 're almost the same . the heat capacity at constant volume is three halves nr , and the heat capacity at constant pressure is five halves nr . they just differ by nr . so the difference between the heat capacity at constant volume which is three halves nr , and the heat capacity at constant pressure which is five halves nr , is just cp minus cv which is nr , just nr , and if you wanted to take the difference between the molar heat capacities at constant volume and pressure , it would just be r. the difference would just be r because everything would get divided by the number of moles . so there 's a relationship , an important relationship . it tells you the difference between the heat capacity at constant pressure and the heat capacity at constant volume .
|
so there 's a relationship , an important relationship . it tells you the difference between the heat capacity at constant pressure and the heat capacity at constant volume .
|
i think this would detract from the total internal energy ... does this imply that heat energy is allowed to exit in the constant pressure scenario but not in the constant volume scenario ?
|
imagine you had a monatomic ideal gas in this cylinder here , an there was this tightly fitted piston above it that prevented any gas from getting out . well we know that the total internal energy for a monatomic ideal gas is just three halves p times v or three halves nkt , or three halves little nrt , and we know that saying u internal the internal energy is really just code for the total kinetic energy of the monatomic ideal gas , that these are the same thing . when we talk about internal energy we 're talking about how fast are these particles moving , in other words , what 's the total kinetic energy of all of these particles added up . my question is how do we go about changing the internal energy ? let 's say we wanted to increase the total kinetic energy , what could we do ? well , we could say increase the pressure , or the volume , or the temperature , yeah but i mean physically , actually , in the lab , what do we do ? and there 's basically two ways to change the internal energy . if you want to add internal energy , i.e . get these particles moving faster , we can heat it up so put this above a flame or on a hot plate , and heat will flow into the gas which will cause these particles to move faster and faster . that 's one way to do it , to add heat . the other way to do it is to do work on the gas . i could take this piston and push it down , and if you push this down hard enough it will squash this gas together , and those impacts with this piston while it 's moving down will cause them to start moving faster and faster , that will also add internal energy to the gas . so if we wanted to write down a formula that told us how you could get a change in the internal energy , if i want to change the internal energy , delta u , which is really just saying changing the kinetic energy , well there 's two ways to do it . i can add heat . if i added ten joules of heat i 'd add ten joules to the internal energy , but i 've also got to take into account this work being done , and so i can do plus the work done on the gas , and that 's it , this is actually the first law of thermodynamics , it 's the law of conservation of energy it says there 's only two ways to add energy , internal energy to a gas . let me talk a little bit more about this work done though cause getting the sign right is important . if you 're doing work on the gas compressing it you 're adding energy to the gas , but if you let the gas push up on the piston and this gas expands pushing the piston up , then the gas is doing the work , that 's energy leaving the system . so if the gas does work you have to subtract work done by the gas . if the outside force does work on the gas you add that to the internal energy . so you got to pay attention to which way the energy is flowing . work done on gas , energy goes in . work done by the gas , energy goes out , and you 'd have to subtract that over here . let 's say the gas did expand . let 's say the gas in here was under so much pressure that the force it exerted on this piston was enough to push that piston upward by a certain amount . so let 's say it started right here and it went up to here so that piston went from here to there no gasses escaping cause this is tightly fitting , but the gas was able to push it up a certain distance d , how much work was done ? you know the definition of work . work is defined to be the force times the distance through which that force was applied . so the work that the gas did was f times d , but we want this to be in terms of thermal quantities like pressure , and volume , and temperature . so what could we do ? we can say that this volume , not only did the piston raise up , but there was an extra volume generated within here that i 'm going to call delta v , and i know that this delta v has got to equal the area of the piston times the distance through which that piston moved because this height times that area gives me this volume right in here . why am i doing this ? cause look i can write d as equal to delta v over a , and i can take this , i can substitute this formula for d into here , and something magical happens , i 'll get work equals f times delta v over a , but look f over a , we know what f over a is , that 's pressure so i get that the work done by the gas is the pressure times delta v. this is an equation that i like because it 's in terms of thermodynamic quantities that we 're already dealing with . so work done you can figure out by taking p times delta v but strictly speaking this is only true if this pressure remained constant , right ? if the pressure was changing , then what am i supposed to plug in here , the initial pressure , the final pressure ? if the pressure 's staying constant this gives you an exact way to find the work done . you might object and say wait , how is it possible for a gas to expand and remain at the same pressure ? well , you basically have to heat it up while the gas expands , that allows the pressure to remain constant as the gas expands . and now we 're finally ready to talk about heat capacities . so let 's get rid of this , and heat capacity is defined to be , imagine you had a certain amount of heat being added . so a certain amount of heat gets added to your gas . how much does the temperature increase ? that 's what the heat capacity tells you . so capital c is heat capacity and it 's defined to be the amount of heat that you 've added to the gas , divided by the amount of change in the temperature of that gas . and actually , something you 'll hear about often is the molar heat capacity , which is actually divided by an extra n here . so instead of q over delta t it 's q over n the number of moles times delta t. pretty simple but think about it . if we had a piston in here , are we going to allow that piston to move while we add the heat , or are we not going to allow the piston to move ? there 's different ways that this can happen , and because of that there 's different heat capacities . if we do n't allow this piston to move , if we weld this thing shut so it ca n't move we 've got heat capacity at constant volume , and if we do allow this piston to move freely while we add the heat so that the pressure inside of here remains constant , we 'd have the heat capacity at constant pressure . and these are similar but different , and they 're related , and we can figure them out . so let 's clear this away , let 's get a nice , here we go , two pistons inside of cylinders . we 'll put a piston in here , but i 'm going to weld this one shut . this one ca n't move . we 'll have another one over here , it can move freely . so over on this side , we 'll have the definition of heat capacity , regular heat capacity , is the amount of heat you add divided by the change in temperature that you get . so on this side we 're adding heat , let 's say heat goes in , but the piston does not move and so the gas in here is stuck , it ca n't move , no work can be done . since this piston ca n't move , external forces ca n't do work on the gas , and the gas ca n't do work and allow energy to leave . q is the only thing adding energy into this system , or in other words , we 've got heat capacity at constant volume is going to equal , well , remember the first law of thermodynamics said that delta u , the only way to add internal energy , or take it away is that you can add or subtract heat , and you can do work on the gas . in this case , q , if i subtract w from both sides i get delta u minus w over delta t , but since we 're not allowing this piston to move the work done has got to be zero . so there 's no work done at all so the heat capacity at constant volume is going to be delta u over delta t , what 's delta u ? let 's just assume this is a monatomic ideal gas , if it 's monatomic we 've got a formula for this . delta u is just three halves , p times v over delta t. that 's not the only way i can write it . remember i can also write it as three halves nk delta t over delta t , and something magical happens , check it out the delta t 's go away and you get that this is a constant . that the heat capacity for any monatomic ideal gas is just going to be three halves , capital nk , boltzmann 's constant , n is the total number of molecules . or you could have rewrote this as little n r delta t. the t 's would still have cancelled and you would have got three halves , little n , the number of moles , times r , the gas constant . so the heat capacity at constant volume for any monatomic ideal gas is just three halves nr , and if you wanted the molar heat capacity remember that 's just divide by an extra mole here so everything gets divided by moles everywhere divided by moles , that just cancels this out , and the molar heat capacity at constant volume is just three halves r. so that 's heat capacity at constant volume , what about heat capacity at constant pressure ? now we 're going to look at this side . again , we 're going to allow this gas to have heat enter the cylinder , but we 're going to allow this piston to move up while it does that so that the pressure inside of here remains constant and this is going to be the heat capacity at constant pressure . well , again , we 're going to get that it 's q over delta t , and just like the first law said , q has to equal delta u minus w. so we get delta u minus w , the work done , over delta t , this time w is not zero . what 's w going to be ? remember w is p times delta v. so this is a way we can find the work done by the gas , p times delta v , so this is going to equal delta u , we know what that is . if this is again , a monatomic ideal gas , this is going to equal three halves nr delta t plus this is p times delta v , but we have to be careful , in this formula this work is referring to work done on the gas , but in this case , work is being done by the gas , so i need another negative . technically the work done on the gas would be a negative amount of this since energy is leaving the system . so that negative cancels this negative and i get plus p times delta v , all of that over delta t , phew . so what do we get ? three halves nr delta t plus i want to rewrite p times delta v , but i know how to do that . the ideal gas law says pv equals nrt , well if that 's true , then p times delta v is going to equal nr delta t. so can rewrite this as nr delta t divided by delta t , almost there , all of the delta t 's go away . look what i 'm left with . i 'm left with c. heat capacity at constant pressure is going to be equal to three halves nr plus nr , that 's just five halves nr , and if i wanted the molar heat capacity again i could divide everything , everything around here by little n , and that would just give me the molar heat capacity constant pressure would be five halves r. and notice they 're almost the same . the heat capacity at constant volume is three halves nr , and the heat capacity at constant pressure is five halves nr . they just differ by nr . so the difference between the heat capacity at constant volume which is three halves nr , and the heat capacity at constant pressure which is five halves nr , is just cp minus cv which is nr , just nr , and if you wanted to take the difference between the molar heat capacities at constant volume and pressure , it would just be r. the difference would just be r because everything would get divided by the number of moles . so there 's a relationship , an important relationship . it tells you the difference between the heat capacity at constant pressure and the heat capacity at constant volume .
|
work done by the gas , energy goes out , and you 'd have to subtract that over here . let 's say the gas did expand . let 's say the gas in here was under so much pressure that the force it exerted on this piston was enough to push that piston upward by a certain amount .
|
everything expand on heating but why polythene shrinks on heating ?
|
let 's look at the mechanism for an e1 elimination reaction , and we 'll start with our substrate , so on the left . let 's say we 're dealing with alkyl halide . so the carbon that 's bonded to our halogen would be the alpha carbon , and the carbon next to that carbon would be the beta carbon , so we need a beta hydrogen for this reaction . the first step of an e1 elimination mechanism is loss of our leaving group , so loss of leaving group , let me just write that in here really quickly , and in this case , the electrons would come off onto our leaving group in the first step of the mechanism . so we 're taking a bond away from this carbon , the one that i 've circled in red here , so that carbon is going from being sp3 hybridized to being sp2 hybridized . so now we have a carbocation , and we know that carbocations , sp2 hybridized carbons have planar geometry around them , so i 've attempted to show the planar geometry around this carbocation . so that 's the first step , loss of the leaving group to form a carbocation . in the second step , our base comes along and takes this proton , which leaves these electrons behind , and those electrons move in to form our alkene , so this is the second step of the mechanism , which is the base takes , or abstracts , a proton , so base takes a proton to form our alkene . and let me go ahead and highlight those electrons , so these electrons here in magenta moved in to form our double bond , and we form our product , we form our alkene . so the first step of the mechanism , the loss of the leaving group , this turns out to be the rate determining step , so this is the slowest step of the mechanism . so if you 're writing a rate law , the rate of this reaction would be equal to the rate constant k times the concentration of your substrate , so that 's what studies have shown , that these mechanisms depend on the concentration of only your substrate , this over here on the left , so it 's first order with respect to the substrate . and that 's because of this rate determining step . the loss of the leaving group is the rate determining step , and so the concentration of your substrate , your starting material , that 's what matters . your base ca n't do anything until you lose your leaving group . and so , since the base does not participate in the rate determining step , it participates in the second step , the concentration of the base has no effect on the rate of the reaction , so it 's the concentration of the substrate only , and since it 's only dependent on the concentration of the substrate , that 's where the one comes from in e1 , so i 'm gon na go ahead and write this out here , so in e1 mechanism , the one comes from the fact this is a unimolecular , a unimolecular rate law here , and the e comes from the fact that this is an elimination reaction , so when you see e1 , that 's what you 're thinking about , it 's an elimination reaction , and it 's unimolecular , the overall rate of the reaction only depends on the concentration of your substrate , so if you increase , let 's say you have , let 's say this was your substrate right here , and you increase the concentration of your substrate , let me just write this down , so if you increase the concentration of your substrate by a factor of two , you would also increase the rate of reaction by a factor of two , so it 's first order with respect to the substrate , so this is some general chemistry here . if you increase the concentration of your base by a factor of two , you would have no effect on the overall rate of the reaction . so let 's talk about one more point here in the mechanism , and that is the formation of this carbocation . since we have a carbocation in this mechanism , we need to think about the possibility of rearrangements in the mechanism , and you need to think what would form , what substrate would form a stable carbocation , so something like a tertiary substrate forming a tertiary carbocation would be favorable for an e1 mechanism . here we have a tertiary alkyl halides , and let 's say this tertiary alkyl halide undergoes an e1 elimination reaction . so the carbon that 's bonded to the iodine must be our alpha carbon , and then we would have three beta carbons , so that 's a beta carbon , that 's a beta carbon , and that 's a beta carbon . so the first step in an e1 mechanism is loss of our leaving group , so if i draw the lone pairs of electrons in here on iodine , i know that these electrons in this bond would come off onto iodine to form the iodide anion , so let me draw that in here , so we would make the iodide anion , and let me highlight our electron , so the electrons in this bond come off onto the iodine to form the iodide anion . and this is an excellent leaving group . iodide is an excellent leaving group , and you know that by looking at pka values . the iodide anion is the conjugate base of a very strong acid , hi , with a approximate pka value of negative 11 , so hi is very good at donating a proton , which must mean that the conjugate base is very stable , so the iodide anion is an excellent leaving group . so if we lose the iodide anion , that means we 're gon na have a carbocation , so we lost a bond to this carbon in red , so we 're gon na form a carbocation , let me go ahead and draw that in , so this is a planar carbocation , and so the carbon , let me go ahead and highlight it here , the carbon in red has a plus one formal charge , it lost a bond . so that 's the first step of an e1 elimination mechanism . the second step of an e1 elimination mechanism is the base comes along , and it takes a proton from a beta carbon , so our base in this case would be ethanol , so let me go ahead and draw in lone pairs of electrons on the oxygen , so notice we 're also heating this reaction , so the ethanol is gon na function as a base , so ethanol 's not a strong base , but it can take a proton , so let me go ahead and draw in a proton right here , and a lone pair of electrons on the oxygen is going to take this proton , and the electrons would move into here to form our alkene , so let me go ahead and draw our product , let me put that in here , and let me highlight some electrons , so the electrons in blue moved in here to form our double bond . so a couple of points about this reaction , one point is , when you 're looking at sn1 mechanisms , the first step is loss of a leaving group to form your carbocation , so when you get to this carbocation , you might think , well , why is ethanol acting as a base here ? why could n't it act as a nucleophile ? and the answer is , the ethanol certainly can act as a nucleophile , and it would attack the positively-charged carbon , and you would definitely get a substitution product for this reaction as well , so if ethanol acts as a nucleophile , you 're gon na get a substitution reaction , an sn1 mechanism . if the ethanol acts as a base , you 're gon na get an e1 elimination mechanism , so here , we 're just gon na focus on the elimination product , and we wo n't worry about the substitution product , but we will talk about this stuff in a later video , 'cause that would definitely happen . alright , something else i wan na talk about is we had three beta carbons over here , and if i look at these three beta carbons , and i just picked one of them , i just said that this carbon right here , let me highlight it , i just took a proton from this carbon , but it does n't matter which of those carbons that we take a proton off because of symmetry , let me go ahead and draw this in over here , so this is my carbocation , let 's say , and let 's say we took a proton from this carbon , so our weak base comes along , and takes a proton from here , and these electrons have moved into here , that would give us the same product , right ? so this would be , let me go and highlight those electrons , so these electrons in dark blue would move in to form our double bond , but this is the same as that product . alcohols can also react via an e1 mechanism . the carbon that 's bonded to the oh would be the alpha carbon , and the carbon next to that would be the beta carbon , so reacting an alcohol with sulfuric acid and heating up your reaction mixture will give you an alkene , and sometimes , phosphoric acid is used instead of sulfuric acid . so we saw the first step of an e1 mechanism was loss of a leaving group , but if that happens here , if these electrons come off onto the oxygen , that would form hydroxide as your leaving group , and the hydroxide anion is a poor leaving group , and we know that by looking at pka values . down here is the hydroxide anion , it is the conjugate base to water , but water is not a great asset , and we know that from the pka value here , so water is not great at donating a proton , which means that the hydroxide anion is not that stable , and since the hydroxide anion is not that stable , it 's not a great leaving group . so let 's go ahead and take off this arrow here , because the first step is not loss of a leaving group , the first step is a proton transfer . we have a strong acid here , sulfuric acid , and the alcohol will act as a base and take a proton from sulfuric acid . and that would form water as your leaving group , and water is a much better leaving group than the hydroxide anion , and again , we know that by pka values . water is the conjugate base to the hydronium ion , h3o+ , which is much better at donating a proton , the pka value is much , much lower . and that means that water is stable , so the first step , the first step when you are doing an e1 mechanism with an alcohol is to protonate the oh group . so here 's our alcohol , and the carbon bonded to the oh is our alpha carbon , and then these carbons next to the alpha carbon would all be beta carbons . we just saw the first step is a proton transfer , a lone pair of electrons on the oxygen take a proton from sulfuric acid , so we transfer a proton , and let 's go ahead and draw in what we would have now , so there 'd be a plus-one formal charge on the oxygen , so let 's highlight our electrons in magenta , these electrons took this proton to form this bond , and now we have water as a leaving group , let me just fix this hydrogen here really fast , and these electrons can come off onto our oxygen , so that gives us water as our leaving group , and let me go ahead and draw in the water molecule here , and let me highlight electrons , the electrons in light blue , in this bond , came off onto the oxygen , which forms water , and we know water is a good leaving group . we took a bond away from this carbon in red , so that carbon would now be a carbocation , so let me draw in our carbocation here , so the carbon in red is now positively charged , so let me draw in a plus-one formal charge on that carbon , the next step of our mechanism , we know a weak base comes along and takes a proton , one of the protons on one of the beta carbons over here , so let 's just say it 's this one , and i 'm just gon na draw in a generic base , so a generic base right here , which is gon na take this proton , and then these electrons are gon na move in to form our product , so let me draw our product in here , and let me highlight those electrons . so the electrons in , let 's use green this time , the electrons in green moved in here to form our double bond , to form our alkene . so i just put a generic base , let me go ahead and talk about the base for a second here . i just put in a generic base , sometimes you might see water acting as a base , sometimes you might see hso4- , right , the conjugate base to sulfuric acid acting as the base , different textbooks give you different things , i do n't think it really matters , but one of those acting as a weak base , it 's probably water , takes this proton to form your alkene . sometimes this reaction is called a dehydration reaction since we lost water in the process .
|
since we have a carbocation in this mechanism , we need to think about the possibility of rearrangements in the mechanism , and you need to think what would form , what substrate would form a stable carbocation , so something like a tertiary substrate forming a tertiary carbocation would be favorable for an e1 mechanism . here we have a tertiary alkyl halides , and let 's say this tertiary alkyl halide undergoes an e1 elimination reaction . so the carbon that 's bonded to the iodine must be our alpha carbon , and then we would have three beta carbons , so that 's a beta carbon , that 's a beta carbon , and that 's a beta carbon .
|
for the alkyl halide example ( starting ) , why would n't that undergo an sn1 reaction ?
|
let 's look at the mechanism for an e1 elimination reaction , and we 'll start with our substrate , so on the left . let 's say we 're dealing with alkyl halide . so the carbon that 's bonded to our halogen would be the alpha carbon , and the carbon next to that carbon would be the beta carbon , so we need a beta hydrogen for this reaction . the first step of an e1 elimination mechanism is loss of our leaving group , so loss of leaving group , let me just write that in here really quickly , and in this case , the electrons would come off onto our leaving group in the first step of the mechanism . so we 're taking a bond away from this carbon , the one that i 've circled in red here , so that carbon is going from being sp3 hybridized to being sp2 hybridized . so now we have a carbocation , and we know that carbocations , sp2 hybridized carbons have planar geometry around them , so i 've attempted to show the planar geometry around this carbocation . so that 's the first step , loss of the leaving group to form a carbocation . in the second step , our base comes along and takes this proton , which leaves these electrons behind , and those electrons move in to form our alkene , so this is the second step of the mechanism , which is the base takes , or abstracts , a proton , so base takes a proton to form our alkene . and let me go ahead and highlight those electrons , so these electrons here in magenta moved in to form our double bond , and we form our product , we form our alkene . so the first step of the mechanism , the loss of the leaving group , this turns out to be the rate determining step , so this is the slowest step of the mechanism . so if you 're writing a rate law , the rate of this reaction would be equal to the rate constant k times the concentration of your substrate , so that 's what studies have shown , that these mechanisms depend on the concentration of only your substrate , this over here on the left , so it 's first order with respect to the substrate . and that 's because of this rate determining step . the loss of the leaving group is the rate determining step , and so the concentration of your substrate , your starting material , that 's what matters . your base ca n't do anything until you lose your leaving group . and so , since the base does not participate in the rate determining step , it participates in the second step , the concentration of the base has no effect on the rate of the reaction , so it 's the concentration of the substrate only , and since it 's only dependent on the concentration of the substrate , that 's where the one comes from in e1 , so i 'm gon na go ahead and write this out here , so in e1 mechanism , the one comes from the fact this is a unimolecular , a unimolecular rate law here , and the e comes from the fact that this is an elimination reaction , so when you see e1 , that 's what you 're thinking about , it 's an elimination reaction , and it 's unimolecular , the overall rate of the reaction only depends on the concentration of your substrate , so if you increase , let 's say you have , let 's say this was your substrate right here , and you increase the concentration of your substrate , let me just write this down , so if you increase the concentration of your substrate by a factor of two , you would also increase the rate of reaction by a factor of two , so it 's first order with respect to the substrate , so this is some general chemistry here . if you increase the concentration of your base by a factor of two , you would have no effect on the overall rate of the reaction . so let 's talk about one more point here in the mechanism , and that is the formation of this carbocation . since we have a carbocation in this mechanism , we need to think about the possibility of rearrangements in the mechanism , and you need to think what would form , what substrate would form a stable carbocation , so something like a tertiary substrate forming a tertiary carbocation would be favorable for an e1 mechanism . here we have a tertiary alkyl halides , and let 's say this tertiary alkyl halide undergoes an e1 elimination reaction . so the carbon that 's bonded to the iodine must be our alpha carbon , and then we would have three beta carbons , so that 's a beta carbon , that 's a beta carbon , and that 's a beta carbon . so the first step in an e1 mechanism is loss of our leaving group , so if i draw the lone pairs of electrons in here on iodine , i know that these electrons in this bond would come off onto iodine to form the iodide anion , so let me draw that in here , so we would make the iodide anion , and let me highlight our electron , so the electrons in this bond come off onto the iodine to form the iodide anion . and this is an excellent leaving group . iodide is an excellent leaving group , and you know that by looking at pka values . the iodide anion is the conjugate base of a very strong acid , hi , with a approximate pka value of negative 11 , so hi is very good at donating a proton , which must mean that the conjugate base is very stable , so the iodide anion is an excellent leaving group . so if we lose the iodide anion , that means we 're gon na have a carbocation , so we lost a bond to this carbon in red , so we 're gon na form a carbocation , let me go ahead and draw that in , so this is a planar carbocation , and so the carbon , let me go ahead and highlight it here , the carbon in red has a plus one formal charge , it lost a bond . so that 's the first step of an e1 elimination mechanism . the second step of an e1 elimination mechanism is the base comes along , and it takes a proton from a beta carbon , so our base in this case would be ethanol , so let me go ahead and draw in lone pairs of electrons on the oxygen , so notice we 're also heating this reaction , so the ethanol is gon na function as a base , so ethanol 's not a strong base , but it can take a proton , so let me go ahead and draw in a proton right here , and a lone pair of electrons on the oxygen is going to take this proton , and the electrons would move into here to form our alkene , so let me go ahead and draw our product , let me put that in here , and let me highlight some electrons , so the electrons in blue moved in here to form our double bond . so a couple of points about this reaction , one point is , when you 're looking at sn1 mechanisms , the first step is loss of a leaving group to form your carbocation , so when you get to this carbocation , you might think , well , why is ethanol acting as a base here ? why could n't it act as a nucleophile ? and the answer is , the ethanol certainly can act as a nucleophile , and it would attack the positively-charged carbon , and you would definitely get a substitution product for this reaction as well , so if ethanol acts as a nucleophile , you 're gon na get a substitution reaction , an sn1 mechanism . if the ethanol acts as a base , you 're gon na get an e1 elimination mechanism , so here , we 're just gon na focus on the elimination product , and we wo n't worry about the substitution product , but we will talk about this stuff in a later video , 'cause that would definitely happen . alright , something else i wan na talk about is we had three beta carbons over here , and if i look at these three beta carbons , and i just picked one of them , i just said that this carbon right here , let me highlight it , i just took a proton from this carbon , but it does n't matter which of those carbons that we take a proton off because of symmetry , let me go ahead and draw this in over here , so this is my carbocation , let 's say , and let 's say we took a proton from this carbon , so our weak base comes along , and takes a proton from here , and these electrons have moved into here , that would give us the same product , right ? so this would be , let me go and highlight those electrons , so these electrons in dark blue would move in to form our double bond , but this is the same as that product . alcohols can also react via an e1 mechanism . the carbon that 's bonded to the oh would be the alpha carbon , and the carbon next to that would be the beta carbon , so reacting an alcohol with sulfuric acid and heating up your reaction mixture will give you an alkene , and sometimes , phosphoric acid is used instead of sulfuric acid . so we saw the first step of an e1 mechanism was loss of a leaving group , but if that happens here , if these electrons come off onto the oxygen , that would form hydroxide as your leaving group , and the hydroxide anion is a poor leaving group , and we know that by looking at pka values . down here is the hydroxide anion , it is the conjugate base to water , but water is not a great asset , and we know that from the pka value here , so water is not great at donating a proton , which means that the hydroxide anion is not that stable , and since the hydroxide anion is not that stable , it 's not a great leaving group . so let 's go ahead and take off this arrow here , because the first step is not loss of a leaving group , the first step is a proton transfer . we have a strong acid here , sulfuric acid , and the alcohol will act as a base and take a proton from sulfuric acid . and that would form water as your leaving group , and water is a much better leaving group than the hydroxide anion , and again , we know that by pka values . water is the conjugate base to the hydronium ion , h3o+ , which is much better at donating a proton , the pka value is much , much lower . and that means that water is stable , so the first step , the first step when you are doing an e1 mechanism with an alcohol is to protonate the oh group . so here 's our alcohol , and the carbon bonded to the oh is our alpha carbon , and then these carbons next to the alpha carbon would all be beta carbons . we just saw the first step is a proton transfer , a lone pair of electrons on the oxygen take a proton from sulfuric acid , so we transfer a proton , and let 's go ahead and draw in what we would have now , so there 'd be a plus-one formal charge on the oxygen , so let 's highlight our electrons in magenta , these electrons took this proton to form this bond , and now we have water as a leaving group , let me just fix this hydrogen here really fast , and these electrons can come off onto our oxygen , so that gives us water as our leaving group , and let me go ahead and draw in the water molecule here , and let me highlight electrons , the electrons in light blue , in this bond , came off onto the oxygen , which forms water , and we know water is a good leaving group . we took a bond away from this carbon in red , so that carbon would now be a carbocation , so let me draw in our carbocation here , so the carbon in red is now positively charged , so let me draw in a plus-one formal charge on that carbon , the next step of our mechanism , we know a weak base comes along and takes a proton , one of the protons on one of the beta carbons over here , so let 's just say it 's this one , and i 'm just gon na draw in a generic base , so a generic base right here , which is gon na take this proton , and then these electrons are gon na move in to form our product , so let me draw our product in here , and let me highlight those electrons . so the electrons in , let 's use green this time , the electrons in green moved in here to form our double bond , to form our alkene . so i just put a generic base , let me go ahead and talk about the base for a second here . i just put in a generic base , sometimes you might see water acting as a base , sometimes you might see hso4- , right , the conjugate base to sulfuric acid acting as the base , different textbooks give you different things , i do n't think it really matters , but one of those acting as a weak base , it 's probably water , takes this proton to form your alkene . sometimes this reaction is called a dehydration reaction since we lost water in the process .
|
and that means that water is stable , so the first step , the first step when you are doing an e1 mechanism with an alcohol is to protonate the oh group . so here 's our alcohol , and the carbon bonded to the oh is our alpha carbon , and then these carbons next to the alpha carbon would all be beta carbons . we just saw the first step is a proton transfer , a lone pair of electrons on the oxygen take a proton from sulfuric acid , so we transfer a proton , and let 's go ahead and draw in what we would have now , so there 'd be a plus-one formal charge on the oxygen , so let 's highlight our electrons in magenta , these electrons took this proton to form this bond , and now we have water as a leaving group , let me just fix this hydrogen here really fast , and these electrons can come off onto our oxygen , so that gives us water as our leaving group , and let me go ahead and draw in the water molecule here , and let me highlight electrons , the electrons in light blue , in this bond , came off onto the oxygen , which forms water , and we know water is a good leaving group . we took a bond away from this carbon in red , so that carbon would now be a carbocation , so let me draw in our carbocation here , so the carbon in red is now positively charged , so let me draw in a plus-one formal charge on that carbon , the next step of our mechanism , we know a weak base comes along and takes a proton , one of the protons on one of the beta carbons over here , so let 's just say it 's this one , and i 'm just gon na draw in a generic base , so a generic base right here , which is gon na take this proton , and then these electrons are gon na move in to form our product , so let me draw our product in here , and let me highlight those electrons .
|
how come the ch3 not on the ring not concidered as beta ?
|
let 's look at the mechanism for an e1 elimination reaction , and we 'll start with our substrate , so on the left . let 's say we 're dealing with alkyl halide . so the carbon that 's bonded to our halogen would be the alpha carbon , and the carbon next to that carbon would be the beta carbon , so we need a beta hydrogen for this reaction . the first step of an e1 elimination mechanism is loss of our leaving group , so loss of leaving group , let me just write that in here really quickly , and in this case , the electrons would come off onto our leaving group in the first step of the mechanism . so we 're taking a bond away from this carbon , the one that i 've circled in red here , so that carbon is going from being sp3 hybridized to being sp2 hybridized . so now we have a carbocation , and we know that carbocations , sp2 hybridized carbons have planar geometry around them , so i 've attempted to show the planar geometry around this carbocation . so that 's the first step , loss of the leaving group to form a carbocation . in the second step , our base comes along and takes this proton , which leaves these electrons behind , and those electrons move in to form our alkene , so this is the second step of the mechanism , which is the base takes , or abstracts , a proton , so base takes a proton to form our alkene . and let me go ahead and highlight those electrons , so these electrons here in magenta moved in to form our double bond , and we form our product , we form our alkene . so the first step of the mechanism , the loss of the leaving group , this turns out to be the rate determining step , so this is the slowest step of the mechanism . so if you 're writing a rate law , the rate of this reaction would be equal to the rate constant k times the concentration of your substrate , so that 's what studies have shown , that these mechanisms depend on the concentration of only your substrate , this over here on the left , so it 's first order with respect to the substrate . and that 's because of this rate determining step . the loss of the leaving group is the rate determining step , and so the concentration of your substrate , your starting material , that 's what matters . your base ca n't do anything until you lose your leaving group . and so , since the base does not participate in the rate determining step , it participates in the second step , the concentration of the base has no effect on the rate of the reaction , so it 's the concentration of the substrate only , and since it 's only dependent on the concentration of the substrate , that 's where the one comes from in e1 , so i 'm gon na go ahead and write this out here , so in e1 mechanism , the one comes from the fact this is a unimolecular , a unimolecular rate law here , and the e comes from the fact that this is an elimination reaction , so when you see e1 , that 's what you 're thinking about , it 's an elimination reaction , and it 's unimolecular , the overall rate of the reaction only depends on the concentration of your substrate , so if you increase , let 's say you have , let 's say this was your substrate right here , and you increase the concentration of your substrate , let me just write this down , so if you increase the concentration of your substrate by a factor of two , you would also increase the rate of reaction by a factor of two , so it 's first order with respect to the substrate , so this is some general chemistry here . if you increase the concentration of your base by a factor of two , you would have no effect on the overall rate of the reaction . so let 's talk about one more point here in the mechanism , and that is the formation of this carbocation . since we have a carbocation in this mechanism , we need to think about the possibility of rearrangements in the mechanism , and you need to think what would form , what substrate would form a stable carbocation , so something like a tertiary substrate forming a tertiary carbocation would be favorable for an e1 mechanism . here we have a tertiary alkyl halides , and let 's say this tertiary alkyl halide undergoes an e1 elimination reaction . so the carbon that 's bonded to the iodine must be our alpha carbon , and then we would have three beta carbons , so that 's a beta carbon , that 's a beta carbon , and that 's a beta carbon . so the first step in an e1 mechanism is loss of our leaving group , so if i draw the lone pairs of electrons in here on iodine , i know that these electrons in this bond would come off onto iodine to form the iodide anion , so let me draw that in here , so we would make the iodide anion , and let me highlight our electron , so the electrons in this bond come off onto the iodine to form the iodide anion . and this is an excellent leaving group . iodide is an excellent leaving group , and you know that by looking at pka values . the iodide anion is the conjugate base of a very strong acid , hi , with a approximate pka value of negative 11 , so hi is very good at donating a proton , which must mean that the conjugate base is very stable , so the iodide anion is an excellent leaving group . so if we lose the iodide anion , that means we 're gon na have a carbocation , so we lost a bond to this carbon in red , so we 're gon na form a carbocation , let me go ahead and draw that in , so this is a planar carbocation , and so the carbon , let me go ahead and highlight it here , the carbon in red has a plus one formal charge , it lost a bond . so that 's the first step of an e1 elimination mechanism . the second step of an e1 elimination mechanism is the base comes along , and it takes a proton from a beta carbon , so our base in this case would be ethanol , so let me go ahead and draw in lone pairs of electrons on the oxygen , so notice we 're also heating this reaction , so the ethanol is gon na function as a base , so ethanol 's not a strong base , but it can take a proton , so let me go ahead and draw in a proton right here , and a lone pair of electrons on the oxygen is going to take this proton , and the electrons would move into here to form our alkene , so let me go ahead and draw our product , let me put that in here , and let me highlight some electrons , so the electrons in blue moved in here to form our double bond . so a couple of points about this reaction , one point is , when you 're looking at sn1 mechanisms , the first step is loss of a leaving group to form your carbocation , so when you get to this carbocation , you might think , well , why is ethanol acting as a base here ? why could n't it act as a nucleophile ? and the answer is , the ethanol certainly can act as a nucleophile , and it would attack the positively-charged carbon , and you would definitely get a substitution product for this reaction as well , so if ethanol acts as a nucleophile , you 're gon na get a substitution reaction , an sn1 mechanism . if the ethanol acts as a base , you 're gon na get an e1 elimination mechanism , so here , we 're just gon na focus on the elimination product , and we wo n't worry about the substitution product , but we will talk about this stuff in a later video , 'cause that would definitely happen . alright , something else i wan na talk about is we had three beta carbons over here , and if i look at these three beta carbons , and i just picked one of them , i just said that this carbon right here , let me highlight it , i just took a proton from this carbon , but it does n't matter which of those carbons that we take a proton off because of symmetry , let me go ahead and draw this in over here , so this is my carbocation , let 's say , and let 's say we took a proton from this carbon , so our weak base comes along , and takes a proton from here , and these electrons have moved into here , that would give us the same product , right ? so this would be , let me go and highlight those electrons , so these electrons in dark blue would move in to form our double bond , but this is the same as that product . alcohols can also react via an e1 mechanism . the carbon that 's bonded to the oh would be the alpha carbon , and the carbon next to that would be the beta carbon , so reacting an alcohol with sulfuric acid and heating up your reaction mixture will give you an alkene , and sometimes , phosphoric acid is used instead of sulfuric acid . so we saw the first step of an e1 mechanism was loss of a leaving group , but if that happens here , if these electrons come off onto the oxygen , that would form hydroxide as your leaving group , and the hydroxide anion is a poor leaving group , and we know that by looking at pka values . down here is the hydroxide anion , it is the conjugate base to water , but water is not a great asset , and we know that from the pka value here , so water is not great at donating a proton , which means that the hydroxide anion is not that stable , and since the hydroxide anion is not that stable , it 's not a great leaving group . so let 's go ahead and take off this arrow here , because the first step is not loss of a leaving group , the first step is a proton transfer . we have a strong acid here , sulfuric acid , and the alcohol will act as a base and take a proton from sulfuric acid . and that would form water as your leaving group , and water is a much better leaving group than the hydroxide anion , and again , we know that by pka values . water is the conjugate base to the hydronium ion , h3o+ , which is much better at donating a proton , the pka value is much , much lower . and that means that water is stable , so the first step , the first step when you are doing an e1 mechanism with an alcohol is to protonate the oh group . so here 's our alcohol , and the carbon bonded to the oh is our alpha carbon , and then these carbons next to the alpha carbon would all be beta carbons . we just saw the first step is a proton transfer , a lone pair of electrons on the oxygen take a proton from sulfuric acid , so we transfer a proton , and let 's go ahead and draw in what we would have now , so there 'd be a plus-one formal charge on the oxygen , so let 's highlight our electrons in magenta , these electrons took this proton to form this bond , and now we have water as a leaving group , let me just fix this hydrogen here really fast , and these electrons can come off onto our oxygen , so that gives us water as our leaving group , and let me go ahead and draw in the water molecule here , and let me highlight electrons , the electrons in light blue , in this bond , came off onto the oxygen , which forms water , and we know water is a good leaving group . we took a bond away from this carbon in red , so that carbon would now be a carbocation , so let me draw in our carbocation here , so the carbon in red is now positively charged , so let me draw in a plus-one formal charge on that carbon , the next step of our mechanism , we know a weak base comes along and takes a proton , one of the protons on one of the beta carbons over here , so let 's just say it 's this one , and i 'm just gon na draw in a generic base , so a generic base right here , which is gon na take this proton , and then these electrons are gon na move in to form our product , so let me draw our product in here , and let me highlight those electrons . so the electrons in , let 's use green this time , the electrons in green moved in here to form our double bond , to form our alkene . so i just put a generic base , let me go ahead and talk about the base for a second here . i just put in a generic base , sometimes you might see water acting as a base , sometimes you might see hso4- , right , the conjugate base to sulfuric acid acting as the base , different textbooks give you different things , i do n't think it really matters , but one of those acting as a weak base , it 's probably water , takes this proton to form your alkene . sometimes this reaction is called a dehydration reaction since we lost water in the process .
|
and that would form water as your leaving group , and water is a much better leaving group than the hydroxide anion , and again , we know that by pka values . water is the conjugate base to the hydronium ion , h3o+ , which is much better at donating a proton , the pka value is much , much lower . and that means that water is stable , so the first step , the first step when you are doing an e1 mechanism with an alcohol is to protonate the oh group .
|
what happens to the sulphate ion ?
|
let 's look at the mechanism for an e1 elimination reaction , and we 'll start with our substrate , so on the left . let 's say we 're dealing with alkyl halide . so the carbon that 's bonded to our halogen would be the alpha carbon , and the carbon next to that carbon would be the beta carbon , so we need a beta hydrogen for this reaction . the first step of an e1 elimination mechanism is loss of our leaving group , so loss of leaving group , let me just write that in here really quickly , and in this case , the electrons would come off onto our leaving group in the first step of the mechanism . so we 're taking a bond away from this carbon , the one that i 've circled in red here , so that carbon is going from being sp3 hybridized to being sp2 hybridized . so now we have a carbocation , and we know that carbocations , sp2 hybridized carbons have planar geometry around them , so i 've attempted to show the planar geometry around this carbocation . so that 's the first step , loss of the leaving group to form a carbocation . in the second step , our base comes along and takes this proton , which leaves these electrons behind , and those electrons move in to form our alkene , so this is the second step of the mechanism , which is the base takes , or abstracts , a proton , so base takes a proton to form our alkene . and let me go ahead and highlight those electrons , so these electrons here in magenta moved in to form our double bond , and we form our product , we form our alkene . so the first step of the mechanism , the loss of the leaving group , this turns out to be the rate determining step , so this is the slowest step of the mechanism . so if you 're writing a rate law , the rate of this reaction would be equal to the rate constant k times the concentration of your substrate , so that 's what studies have shown , that these mechanisms depend on the concentration of only your substrate , this over here on the left , so it 's first order with respect to the substrate . and that 's because of this rate determining step . the loss of the leaving group is the rate determining step , and so the concentration of your substrate , your starting material , that 's what matters . your base ca n't do anything until you lose your leaving group . and so , since the base does not participate in the rate determining step , it participates in the second step , the concentration of the base has no effect on the rate of the reaction , so it 's the concentration of the substrate only , and since it 's only dependent on the concentration of the substrate , that 's where the one comes from in e1 , so i 'm gon na go ahead and write this out here , so in e1 mechanism , the one comes from the fact this is a unimolecular , a unimolecular rate law here , and the e comes from the fact that this is an elimination reaction , so when you see e1 , that 's what you 're thinking about , it 's an elimination reaction , and it 's unimolecular , the overall rate of the reaction only depends on the concentration of your substrate , so if you increase , let 's say you have , let 's say this was your substrate right here , and you increase the concentration of your substrate , let me just write this down , so if you increase the concentration of your substrate by a factor of two , you would also increase the rate of reaction by a factor of two , so it 's first order with respect to the substrate , so this is some general chemistry here . if you increase the concentration of your base by a factor of two , you would have no effect on the overall rate of the reaction . so let 's talk about one more point here in the mechanism , and that is the formation of this carbocation . since we have a carbocation in this mechanism , we need to think about the possibility of rearrangements in the mechanism , and you need to think what would form , what substrate would form a stable carbocation , so something like a tertiary substrate forming a tertiary carbocation would be favorable for an e1 mechanism . here we have a tertiary alkyl halides , and let 's say this tertiary alkyl halide undergoes an e1 elimination reaction . so the carbon that 's bonded to the iodine must be our alpha carbon , and then we would have three beta carbons , so that 's a beta carbon , that 's a beta carbon , and that 's a beta carbon . so the first step in an e1 mechanism is loss of our leaving group , so if i draw the lone pairs of electrons in here on iodine , i know that these electrons in this bond would come off onto iodine to form the iodide anion , so let me draw that in here , so we would make the iodide anion , and let me highlight our electron , so the electrons in this bond come off onto the iodine to form the iodide anion . and this is an excellent leaving group . iodide is an excellent leaving group , and you know that by looking at pka values . the iodide anion is the conjugate base of a very strong acid , hi , with a approximate pka value of negative 11 , so hi is very good at donating a proton , which must mean that the conjugate base is very stable , so the iodide anion is an excellent leaving group . so if we lose the iodide anion , that means we 're gon na have a carbocation , so we lost a bond to this carbon in red , so we 're gon na form a carbocation , let me go ahead and draw that in , so this is a planar carbocation , and so the carbon , let me go ahead and highlight it here , the carbon in red has a plus one formal charge , it lost a bond . so that 's the first step of an e1 elimination mechanism . the second step of an e1 elimination mechanism is the base comes along , and it takes a proton from a beta carbon , so our base in this case would be ethanol , so let me go ahead and draw in lone pairs of electrons on the oxygen , so notice we 're also heating this reaction , so the ethanol is gon na function as a base , so ethanol 's not a strong base , but it can take a proton , so let me go ahead and draw in a proton right here , and a lone pair of electrons on the oxygen is going to take this proton , and the electrons would move into here to form our alkene , so let me go ahead and draw our product , let me put that in here , and let me highlight some electrons , so the electrons in blue moved in here to form our double bond . so a couple of points about this reaction , one point is , when you 're looking at sn1 mechanisms , the first step is loss of a leaving group to form your carbocation , so when you get to this carbocation , you might think , well , why is ethanol acting as a base here ? why could n't it act as a nucleophile ? and the answer is , the ethanol certainly can act as a nucleophile , and it would attack the positively-charged carbon , and you would definitely get a substitution product for this reaction as well , so if ethanol acts as a nucleophile , you 're gon na get a substitution reaction , an sn1 mechanism . if the ethanol acts as a base , you 're gon na get an e1 elimination mechanism , so here , we 're just gon na focus on the elimination product , and we wo n't worry about the substitution product , but we will talk about this stuff in a later video , 'cause that would definitely happen . alright , something else i wan na talk about is we had three beta carbons over here , and if i look at these three beta carbons , and i just picked one of them , i just said that this carbon right here , let me highlight it , i just took a proton from this carbon , but it does n't matter which of those carbons that we take a proton off because of symmetry , let me go ahead and draw this in over here , so this is my carbocation , let 's say , and let 's say we took a proton from this carbon , so our weak base comes along , and takes a proton from here , and these electrons have moved into here , that would give us the same product , right ? so this would be , let me go and highlight those electrons , so these electrons in dark blue would move in to form our double bond , but this is the same as that product . alcohols can also react via an e1 mechanism . the carbon that 's bonded to the oh would be the alpha carbon , and the carbon next to that would be the beta carbon , so reacting an alcohol with sulfuric acid and heating up your reaction mixture will give you an alkene , and sometimes , phosphoric acid is used instead of sulfuric acid . so we saw the first step of an e1 mechanism was loss of a leaving group , but if that happens here , if these electrons come off onto the oxygen , that would form hydroxide as your leaving group , and the hydroxide anion is a poor leaving group , and we know that by looking at pka values . down here is the hydroxide anion , it is the conjugate base to water , but water is not a great asset , and we know that from the pka value here , so water is not great at donating a proton , which means that the hydroxide anion is not that stable , and since the hydroxide anion is not that stable , it 's not a great leaving group . so let 's go ahead and take off this arrow here , because the first step is not loss of a leaving group , the first step is a proton transfer . we have a strong acid here , sulfuric acid , and the alcohol will act as a base and take a proton from sulfuric acid . and that would form water as your leaving group , and water is a much better leaving group than the hydroxide anion , and again , we know that by pka values . water is the conjugate base to the hydronium ion , h3o+ , which is much better at donating a proton , the pka value is much , much lower . and that means that water is stable , so the first step , the first step when you are doing an e1 mechanism with an alcohol is to protonate the oh group . so here 's our alcohol , and the carbon bonded to the oh is our alpha carbon , and then these carbons next to the alpha carbon would all be beta carbons . we just saw the first step is a proton transfer , a lone pair of electrons on the oxygen take a proton from sulfuric acid , so we transfer a proton , and let 's go ahead and draw in what we would have now , so there 'd be a plus-one formal charge on the oxygen , so let 's highlight our electrons in magenta , these electrons took this proton to form this bond , and now we have water as a leaving group , let me just fix this hydrogen here really fast , and these electrons can come off onto our oxygen , so that gives us water as our leaving group , and let me go ahead and draw in the water molecule here , and let me highlight electrons , the electrons in light blue , in this bond , came off onto the oxygen , which forms water , and we know water is a good leaving group . we took a bond away from this carbon in red , so that carbon would now be a carbocation , so let me draw in our carbocation here , so the carbon in red is now positively charged , so let me draw in a plus-one formal charge on that carbon , the next step of our mechanism , we know a weak base comes along and takes a proton , one of the protons on one of the beta carbons over here , so let 's just say it 's this one , and i 'm just gon na draw in a generic base , so a generic base right here , which is gon na take this proton , and then these electrons are gon na move in to form our product , so let me draw our product in here , and let me highlight those electrons . so the electrons in , let 's use green this time , the electrons in green moved in here to form our double bond , to form our alkene . so i just put a generic base , let me go ahead and talk about the base for a second here . i just put in a generic base , sometimes you might see water acting as a base , sometimes you might see hso4- , right , the conjugate base to sulfuric acid acting as the base , different textbooks give you different things , i do n't think it really matters , but one of those acting as a weak base , it 's probably water , takes this proton to form your alkene . sometimes this reaction is called a dehydration reaction since we lost water in the process .
|
so let 's go ahead and take off this arrow here , because the first step is not loss of a leaving group , the first step is a proton transfer . we have a strong acid here , sulfuric acid , and the alcohol will act as a base and take a proton from sulfuric acid . and that would form water as your leaving group , and water is a much better leaving group than the hydroxide anion , and again , we know that by pka values .
|
how is it an e1 reaction if the concentration of both cyclohexanol and sulfuric acid determine the rate of this step ?
|
let 's look at the mechanism for an e1 elimination reaction , and we 'll start with our substrate , so on the left . let 's say we 're dealing with alkyl halide . so the carbon that 's bonded to our halogen would be the alpha carbon , and the carbon next to that carbon would be the beta carbon , so we need a beta hydrogen for this reaction . the first step of an e1 elimination mechanism is loss of our leaving group , so loss of leaving group , let me just write that in here really quickly , and in this case , the electrons would come off onto our leaving group in the first step of the mechanism . so we 're taking a bond away from this carbon , the one that i 've circled in red here , so that carbon is going from being sp3 hybridized to being sp2 hybridized . so now we have a carbocation , and we know that carbocations , sp2 hybridized carbons have planar geometry around them , so i 've attempted to show the planar geometry around this carbocation . so that 's the first step , loss of the leaving group to form a carbocation . in the second step , our base comes along and takes this proton , which leaves these electrons behind , and those electrons move in to form our alkene , so this is the second step of the mechanism , which is the base takes , or abstracts , a proton , so base takes a proton to form our alkene . and let me go ahead and highlight those electrons , so these electrons here in magenta moved in to form our double bond , and we form our product , we form our alkene . so the first step of the mechanism , the loss of the leaving group , this turns out to be the rate determining step , so this is the slowest step of the mechanism . so if you 're writing a rate law , the rate of this reaction would be equal to the rate constant k times the concentration of your substrate , so that 's what studies have shown , that these mechanisms depend on the concentration of only your substrate , this over here on the left , so it 's first order with respect to the substrate . and that 's because of this rate determining step . the loss of the leaving group is the rate determining step , and so the concentration of your substrate , your starting material , that 's what matters . your base ca n't do anything until you lose your leaving group . and so , since the base does not participate in the rate determining step , it participates in the second step , the concentration of the base has no effect on the rate of the reaction , so it 's the concentration of the substrate only , and since it 's only dependent on the concentration of the substrate , that 's where the one comes from in e1 , so i 'm gon na go ahead and write this out here , so in e1 mechanism , the one comes from the fact this is a unimolecular , a unimolecular rate law here , and the e comes from the fact that this is an elimination reaction , so when you see e1 , that 's what you 're thinking about , it 's an elimination reaction , and it 's unimolecular , the overall rate of the reaction only depends on the concentration of your substrate , so if you increase , let 's say you have , let 's say this was your substrate right here , and you increase the concentration of your substrate , let me just write this down , so if you increase the concentration of your substrate by a factor of two , you would also increase the rate of reaction by a factor of two , so it 's first order with respect to the substrate , so this is some general chemistry here . if you increase the concentration of your base by a factor of two , you would have no effect on the overall rate of the reaction . so let 's talk about one more point here in the mechanism , and that is the formation of this carbocation . since we have a carbocation in this mechanism , we need to think about the possibility of rearrangements in the mechanism , and you need to think what would form , what substrate would form a stable carbocation , so something like a tertiary substrate forming a tertiary carbocation would be favorable for an e1 mechanism . here we have a tertiary alkyl halides , and let 's say this tertiary alkyl halide undergoes an e1 elimination reaction . so the carbon that 's bonded to the iodine must be our alpha carbon , and then we would have three beta carbons , so that 's a beta carbon , that 's a beta carbon , and that 's a beta carbon . so the first step in an e1 mechanism is loss of our leaving group , so if i draw the lone pairs of electrons in here on iodine , i know that these electrons in this bond would come off onto iodine to form the iodide anion , so let me draw that in here , so we would make the iodide anion , and let me highlight our electron , so the electrons in this bond come off onto the iodine to form the iodide anion . and this is an excellent leaving group . iodide is an excellent leaving group , and you know that by looking at pka values . the iodide anion is the conjugate base of a very strong acid , hi , with a approximate pka value of negative 11 , so hi is very good at donating a proton , which must mean that the conjugate base is very stable , so the iodide anion is an excellent leaving group . so if we lose the iodide anion , that means we 're gon na have a carbocation , so we lost a bond to this carbon in red , so we 're gon na form a carbocation , let me go ahead and draw that in , so this is a planar carbocation , and so the carbon , let me go ahead and highlight it here , the carbon in red has a plus one formal charge , it lost a bond . so that 's the first step of an e1 elimination mechanism . the second step of an e1 elimination mechanism is the base comes along , and it takes a proton from a beta carbon , so our base in this case would be ethanol , so let me go ahead and draw in lone pairs of electrons on the oxygen , so notice we 're also heating this reaction , so the ethanol is gon na function as a base , so ethanol 's not a strong base , but it can take a proton , so let me go ahead and draw in a proton right here , and a lone pair of electrons on the oxygen is going to take this proton , and the electrons would move into here to form our alkene , so let me go ahead and draw our product , let me put that in here , and let me highlight some electrons , so the electrons in blue moved in here to form our double bond . so a couple of points about this reaction , one point is , when you 're looking at sn1 mechanisms , the first step is loss of a leaving group to form your carbocation , so when you get to this carbocation , you might think , well , why is ethanol acting as a base here ? why could n't it act as a nucleophile ? and the answer is , the ethanol certainly can act as a nucleophile , and it would attack the positively-charged carbon , and you would definitely get a substitution product for this reaction as well , so if ethanol acts as a nucleophile , you 're gon na get a substitution reaction , an sn1 mechanism . if the ethanol acts as a base , you 're gon na get an e1 elimination mechanism , so here , we 're just gon na focus on the elimination product , and we wo n't worry about the substitution product , but we will talk about this stuff in a later video , 'cause that would definitely happen . alright , something else i wan na talk about is we had three beta carbons over here , and if i look at these three beta carbons , and i just picked one of them , i just said that this carbon right here , let me highlight it , i just took a proton from this carbon , but it does n't matter which of those carbons that we take a proton off because of symmetry , let me go ahead and draw this in over here , so this is my carbocation , let 's say , and let 's say we took a proton from this carbon , so our weak base comes along , and takes a proton from here , and these electrons have moved into here , that would give us the same product , right ? so this would be , let me go and highlight those electrons , so these electrons in dark blue would move in to form our double bond , but this is the same as that product . alcohols can also react via an e1 mechanism . the carbon that 's bonded to the oh would be the alpha carbon , and the carbon next to that would be the beta carbon , so reacting an alcohol with sulfuric acid and heating up your reaction mixture will give you an alkene , and sometimes , phosphoric acid is used instead of sulfuric acid . so we saw the first step of an e1 mechanism was loss of a leaving group , but if that happens here , if these electrons come off onto the oxygen , that would form hydroxide as your leaving group , and the hydroxide anion is a poor leaving group , and we know that by looking at pka values . down here is the hydroxide anion , it is the conjugate base to water , but water is not a great asset , and we know that from the pka value here , so water is not great at donating a proton , which means that the hydroxide anion is not that stable , and since the hydroxide anion is not that stable , it 's not a great leaving group . so let 's go ahead and take off this arrow here , because the first step is not loss of a leaving group , the first step is a proton transfer . we have a strong acid here , sulfuric acid , and the alcohol will act as a base and take a proton from sulfuric acid . and that would form water as your leaving group , and water is a much better leaving group than the hydroxide anion , and again , we know that by pka values . water is the conjugate base to the hydronium ion , h3o+ , which is much better at donating a proton , the pka value is much , much lower . and that means that water is stable , so the first step , the first step when you are doing an e1 mechanism with an alcohol is to protonate the oh group . so here 's our alcohol , and the carbon bonded to the oh is our alpha carbon , and then these carbons next to the alpha carbon would all be beta carbons . we just saw the first step is a proton transfer , a lone pair of electrons on the oxygen take a proton from sulfuric acid , so we transfer a proton , and let 's go ahead and draw in what we would have now , so there 'd be a plus-one formal charge on the oxygen , so let 's highlight our electrons in magenta , these electrons took this proton to form this bond , and now we have water as a leaving group , let me just fix this hydrogen here really fast , and these electrons can come off onto our oxygen , so that gives us water as our leaving group , and let me go ahead and draw in the water molecule here , and let me highlight electrons , the electrons in light blue , in this bond , came off onto the oxygen , which forms water , and we know water is a good leaving group . we took a bond away from this carbon in red , so that carbon would now be a carbocation , so let me draw in our carbocation here , so the carbon in red is now positively charged , so let me draw in a plus-one formal charge on that carbon , the next step of our mechanism , we know a weak base comes along and takes a proton , one of the protons on one of the beta carbons over here , so let 's just say it 's this one , and i 'm just gon na draw in a generic base , so a generic base right here , which is gon na take this proton , and then these electrons are gon na move in to form our product , so let me draw our product in here , and let me highlight those electrons . so the electrons in , let 's use green this time , the electrons in green moved in here to form our double bond , to form our alkene . so i just put a generic base , let me go ahead and talk about the base for a second here . i just put in a generic base , sometimes you might see water acting as a base , sometimes you might see hso4- , right , the conjugate base to sulfuric acid acting as the base , different textbooks give you different things , i do n't think it really matters , but one of those acting as a weak base , it 's probably water , takes this proton to form your alkene . sometimes this reaction is called a dehydration reaction since we lost water in the process .
|
let 's say we 're dealing with alkyl halide . so the carbon that 's bonded to our halogen would be the alpha carbon , and the carbon next to that carbon would be the beta carbon , so we need a beta hydrogen for this reaction . the first step of an e1 elimination mechanism is loss of our leaving group , so loss of leaving group , let me just write that in here really quickly , and in this case , the electrons would come off onto our leaving group in the first step of the mechanism .
|
0 the guy says that the water will take the the proton from hydrogen attached to the beta carbon ... why would the water behave in such a way ?
|
let 's look at the mechanism for an e1 elimination reaction , and we 'll start with our substrate , so on the left . let 's say we 're dealing with alkyl halide . so the carbon that 's bonded to our halogen would be the alpha carbon , and the carbon next to that carbon would be the beta carbon , so we need a beta hydrogen for this reaction . the first step of an e1 elimination mechanism is loss of our leaving group , so loss of leaving group , let me just write that in here really quickly , and in this case , the electrons would come off onto our leaving group in the first step of the mechanism . so we 're taking a bond away from this carbon , the one that i 've circled in red here , so that carbon is going from being sp3 hybridized to being sp2 hybridized . so now we have a carbocation , and we know that carbocations , sp2 hybridized carbons have planar geometry around them , so i 've attempted to show the planar geometry around this carbocation . so that 's the first step , loss of the leaving group to form a carbocation . in the second step , our base comes along and takes this proton , which leaves these electrons behind , and those electrons move in to form our alkene , so this is the second step of the mechanism , which is the base takes , or abstracts , a proton , so base takes a proton to form our alkene . and let me go ahead and highlight those electrons , so these electrons here in magenta moved in to form our double bond , and we form our product , we form our alkene . so the first step of the mechanism , the loss of the leaving group , this turns out to be the rate determining step , so this is the slowest step of the mechanism . so if you 're writing a rate law , the rate of this reaction would be equal to the rate constant k times the concentration of your substrate , so that 's what studies have shown , that these mechanisms depend on the concentration of only your substrate , this over here on the left , so it 's first order with respect to the substrate . and that 's because of this rate determining step . the loss of the leaving group is the rate determining step , and so the concentration of your substrate , your starting material , that 's what matters . your base ca n't do anything until you lose your leaving group . and so , since the base does not participate in the rate determining step , it participates in the second step , the concentration of the base has no effect on the rate of the reaction , so it 's the concentration of the substrate only , and since it 's only dependent on the concentration of the substrate , that 's where the one comes from in e1 , so i 'm gon na go ahead and write this out here , so in e1 mechanism , the one comes from the fact this is a unimolecular , a unimolecular rate law here , and the e comes from the fact that this is an elimination reaction , so when you see e1 , that 's what you 're thinking about , it 's an elimination reaction , and it 's unimolecular , the overall rate of the reaction only depends on the concentration of your substrate , so if you increase , let 's say you have , let 's say this was your substrate right here , and you increase the concentration of your substrate , let me just write this down , so if you increase the concentration of your substrate by a factor of two , you would also increase the rate of reaction by a factor of two , so it 's first order with respect to the substrate , so this is some general chemistry here . if you increase the concentration of your base by a factor of two , you would have no effect on the overall rate of the reaction . so let 's talk about one more point here in the mechanism , and that is the formation of this carbocation . since we have a carbocation in this mechanism , we need to think about the possibility of rearrangements in the mechanism , and you need to think what would form , what substrate would form a stable carbocation , so something like a tertiary substrate forming a tertiary carbocation would be favorable for an e1 mechanism . here we have a tertiary alkyl halides , and let 's say this tertiary alkyl halide undergoes an e1 elimination reaction . so the carbon that 's bonded to the iodine must be our alpha carbon , and then we would have three beta carbons , so that 's a beta carbon , that 's a beta carbon , and that 's a beta carbon . so the first step in an e1 mechanism is loss of our leaving group , so if i draw the lone pairs of electrons in here on iodine , i know that these electrons in this bond would come off onto iodine to form the iodide anion , so let me draw that in here , so we would make the iodide anion , and let me highlight our electron , so the electrons in this bond come off onto the iodine to form the iodide anion . and this is an excellent leaving group . iodide is an excellent leaving group , and you know that by looking at pka values . the iodide anion is the conjugate base of a very strong acid , hi , with a approximate pka value of negative 11 , so hi is very good at donating a proton , which must mean that the conjugate base is very stable , so the iodide anion is an excellent leaving group . so if we lose the iodide anion , that means we 're gon na have a carbocation , so we lost a bond to this carbon in red , so we 're gon na form a carbocation , let me go ahead and draw that in , so this is a planar carbocation , and so the carbon , let me go ahead and highlight it here , the carbon in red has a plus one formal charge , it lost a bond . so that 's the first step of an e1 elimination mechanism . the second step of an e1 elimination mechanism is the base comes along , and it takes a proton from a beta carbon , so our base in this case would be ethanol , so let me go ahead and draw in lone pairs of electrons on the oxygen , so notice we 're also heating this reaction , so the ethanol is gon na function as a base , so ethanol 's not a strong base , but it can take a proton , so let me go ahead and draw in a proton right here , and a lone pair of electrons on the oxygen is going to take this proton , and the electrons would move into here to form our alkene , so let me go ahead and draw our product , let me put that in here , and let me highlight some electrons , so the electrons in blue moved in here to form our double bond . so a couple of points about this reaction , one point is , when you 're looking at sn1 mechanisms , the first step is loss of a leaving group to form your carbocation , so when you get to this carbocation , you might think , well , why is ethanol acting as a base here ? why could n't it act as a nucleophile ? and the answer is , the ethanol certainly can act as a nucleophile , and it would attack the positively-charged carbon , and you would definitely get a substitution product for this reaction as well , so if ethanol acts as a nucleophile , you 're gon na get a substitution reaction , an sn1 mechanism . if the ethanol acts as a base , you 're gon na get an e1 elimination mechanism , so here , we 're just gon na focus on the elimination product , and we wo n't worry about the substitution product , but we will talk about this stuff in a later video , 'cause that would definitely happen . alright , something else i wan na talk about is we had three beta carbons over here , and if i look at these three beta carbons , and i just picked one of them , i just said that this carbon right here , let me highlight it , i just took a proton from this carbon , but it does n't matter which of those carbons that we take a proton off because of symmetry , let me go ahead and draw this in over here , so this is my carbocation , let 's say , and let 's say we took a proton from this carbon , so our weak base comes along , and takes a proton from here , and these electrons have moved into here , that would give us the same product , right ? so this would be , let me go and highlight those electrons , so these electrons in dark blue would move in to form our double bond , but this is the same as that product . alcohols can also react via an e1 mechanism . the carbon that 's bonded to the oh would be the alpha carbon , and the carbon next to that would be the beta carbon , so reacting an alcohol with sulfuric acid and heating up your reaction mixture will give you an alkene , and sometimes , phosphoric acid is used instead of sulfuric acid . so we saw the first step of an e1 mechanism was loss of a leaving group , but if that happens here , if these electrons come off onto the oxygen , that would form hydroxide as your leaving group , and the hydroxide anion is a poor leaving group , and we know that by looking at pka values . down here is the hydroxide anion , it is the conjugate base to water , but water is not a great asset , and we know that from the pka value here , so water is not great at donating a proton , which means that the hydroxide anion is not that stable , and since the hydroxide anion is not that stable , it 's not a great leaving group . so let 's go ahead and take off this arrow here , because the first step is not loss of a leaving group , the first step is a proton transfer . we have a strong acid here , sulfuric acid , and the alcohol will act as a base and take a proton from sulfuric acid . and that would form water as your leaving group , and water is a much better leaving group than the hydroxide anion , and again , we know that by pka values . water is the conjugate base to the hydronium ion , h3o+ , which is much better at donating a proton , the pka value is much , much lower . and that means that water is stable , so the first step , the first step when you are doing an e1 mechanism with an alcohol is to protonate the oh group . so here 's our alcohol , and the carbon bonded to the oh is our alpha carbon , and then these carbons next to the alpha carbon would all be beta carbons . we just saw the first step is a proton transfer , a lone pair of electrons on the oxygen take a proton from sulfuric acid , so we transfer a proton , and let 's go ahead and draw in what we would have now , so there 'd be a plus-one formal charge on the oxygen , so let 's highlight our electrons in magenta , these electrons took this proton to form this bond , and now we have water as a leaving group , let me just fix this hydrogen here really fast , and these electrons can come off onto our oxygen , so that gives us water as our leaving group , and let me go ahead and draw in the water molecule here , and let me highlight electrons , the electrons in light blue , in this bond , came off onto the oxygen , which forms water , and we know water is a good leaving group . we took a bond away from this carbon in red , so that carbon would now be a carbocation , so let me draw in our carbocation here , so the carbon in red is now positively charged , so let me draw in a plus-one formal charge on that carbon , the next step of our mechanism , we know a weak base comes along and takes a proton , one of the protons on one of the beta carbons over here , so let 's just say it 's this one , and i 'm just gon na draw in a generic base , so a generic base right here , which is gon na take this proton , and then these electrons are gon na move in to form our product , so let me draw our product in here , and let me highlight those electrons . so the electrons in , let 's use green this time , the electrons in green moved in here to form our double bond , to form our alkene . so i just put a generic base , let me go ahead and talk about the base for a second here . i just put in a generic base , sometimes you might see water acting as a base , sometimes you might see hso4- , right , the conjugate base to sulfuric acid acting as the base , different textbooks give you different things , i do n't think it really matters , but one of those acting as a weak base , it 's probably water , takes this proton to form your alkene . sometimes this reaction is called a dehydration reaction since we lost water in the process .
|
here we have a tertiary alkyl halides , and let 's say this tertiary alkyl halide undergoes an e1 elimination reaction . so the carbon that 's bonded to the iodine must be our alpha carbon , and then we would have three beta carbons , so that 's a beta carbon , that 's a beta carbon , and that 's a beta carbon . so the first step in an e1 mechanism is loss of our leaving group , so if i draw the lone pairs of electrons in here on iodine , i know that these electrons in this bond would come off onto iodine to form the iodide anion , so let me draw that in here , so we would make the iodide anion , and let me highlight our electron , so the electrons in this bond come off onto the iodine to form the iodide anion .
|
will this stable structure be able to pull of the beta-hydrogne as well or is it too stable ?
|
let 's look at the mechanism for an e1 elimination reaction , and we 'll start with our substrate , so on the left . let 's say we 're dealing with alkyl halide . so the carbon that 's bonded to our halogen would be the alpha carbon , and the carbon next to that carbon would be the beta carbon , so we need a beta hydrogen for this reaction . the first step of an e1 elimination mechanism is loss of our leaving group , so loss of leaving group , let me just write that in here really quickly , and in this case , the electrons would come off onto our leaving group in the first step of the mechanism . so we 're taking a bond away from this carbon , the one that i 've circled in red here , so that carbon is going from being sp3 hybridized to being sp2 hybridized . so now we have a carbocation , and we know that carbocations , sp2 hybridized carbons have planar geometry around them , so i 've attempted to show the planar geometry around this carbocation . so that 's the first step , loss of the leaving group to form a carbocation . in the second step , our base comes along and takes this proton , which leaves these electrons behind , and those electrons move in to form our alkene , so this is the second step of the mechanism , which is the base takes , or abstracts , a proton , so base takes a proton to form our alkene . and let me go ahead and highlight those electrons , so these electrons here in magenta moved in to form our double bond , and we form our product , we form our alkene . so the first step of the mechanism , the loss of the leaving group , this turns out to be the rate determining step , so this is the slowest step of the mechanism . so if you 're writing a rate law , the rate of this reaction would be equal to the rate constant k times the concentration of your substrate , so that 's what studies have shown , that these mechanisms depend on the concentration of only your substrate , this over here on the left , so it 's first order with respect to the substrate . and that 's because of this rate determining step . the loss of the leaving group is the rate determining step , and so the concentration of your substrate , your starting material , that 's what matters . your base ca n't do anything until you lose your leaving group . and so , since the base does not participate in the rate determining step , it participates in the second step , the concentration of the base has no effect on the rate of the reaction , so it 's the concentration of the substrate only , and since it 's only dependent on the concentration of the substrate , that 's where the one comes from in e1 , so i 'm gon na go ahead and write this out here , so in e1 mechanism , the one comes from the fact this is a unimolecular , a unimolecular rate law here , and the e comes from the fact that this is an elimination reaction , so when you see e1 , that 's what you 're thinking about , it 's an elimination reaction , and it 's unimolecular , the overall rate of the reaction only depends on the concentration of your substrate , so if you increase , let 's say you have , let 's say this was your substrate right here , and you increase the concentration of your substrate , let me just write this down , so if you increase the concentration of your substrate by a factor of two , you would also increase the rate of reaction by a factor of two , so it 's first order with respect to the substrate , so this is some general chemistry here . if you increase the concentration of your base by a factor of two , you would have no effect on the overall rate of the reaction . so let 's talk about one more point here in the mechanism , and that is the formation of this carbocation . since we have a carbocation in this mechanism , we need to think about the possibility of rearrangements in the mechanism , and you need to think what would form , what substrate would form a stable carbocation , so something like a tertiary substrate forming a tertiary carbocation would be favorable for an e1 mechanism . here we have a tertiary alkyl halides , and let 's say this tertiary alkyl halide undergoes an e1 elimination reaction . so the carbon that 's bonded to the iodine must be our alpha carbon , and then we would have three beta carbons , so that 's a beta carbon , that 's a beta carbon , and that 's a beta carbon . so the first step in an e1 mechanism is loss of our leaving group , so if i draw the lone pairs of electrons in here on iodine , i know that these electrons in this bond would come off onto iodine to form the iodide anion , so let me draw that in here , so we would make the iodide anion , and let me highlight our electron , so the electrons in this bond come off onto the iodine to form the iodide anion . and this is an excellent leaving group . iodide is an excellent leaving group , and you know that by looking at pka values . the iodide anion is the conjugate base of a very strong acid , hi , with a approximate pka value of negative 11 , so hi is very good at donating a proton , which must mean that the conjugate base is very stable , so the iodide anion is an excellent leaving group . so if we lose the iodide anion , that means we 're gon na have a carbocation , so we lost a bond to this carbon in red , so we 're gon na form a carbocation , let me go ahead and draw that in , so this is a planar carbocation , and so the carbon , let me go ahead and highlight it here , the carbon in red has a plus one formal charge , it lost a bond . so that 's the first step of an e1 elimination mechanism . the second step of an e1 elimination mechanism is the base comes along , and it takes a proton from a beta carbon , so our base in this case would be ethanol , so let me go ahead and draw in lone pairs of electrons on the oxygen , so notice we 're also heating this reaction , so the ethanol is gon na function as a base , so ethanol 's not a strong base , but it can take a proton , so let me go ahead and draw in a proton right here , and a lone pair of electrons on the oxygen is going to take this proton , and the electrons would move into here to form our alkene , so let me go ahead and draw our product , let me put that in here , and let me highlight some electrons , so the electrons in blue moved in here to form our double bond . so a couple of points about this reaction , one point is , when you 're looking at sn1 mechanisms , the first step is loss of a leaving group to form your carbocation , so when you get to this carbocation , you might think , well , why is ethanol acting as a base here ? why could n't it act as a nucleophile ? and the answer is , the ethanol certainly can act as a nucleophile , and it would attack the positively-charged carbon , and you would definitely get a substitution product for this reaction as well , so if ethanol acts as a nucleophile , you 're gon na get a substitution reaction , an sn1 mechanism . if the ethanol acts as a base , you 're gon na get an e1 elimination mechanism , so here , we 're just gon na focus on the elimination product , and we wo n't worry about the substitution product , but we will talk about this stuff in a later video , 'cause that would definitely happen . alright , something else i wan na talk about is we had three beta carbons over here , and if i look at these three beta carbons , and i just picked one of them , i just said that this carbon right here , let me highlight it , i just took a proton from this carbon , but it does n't matter which of those carbons that we take a proton off because of symmetry , let me go ahead and draw this in over here , so this is my carbocation , let 's say , and let 's say we took a proton from this carbon , so our weak base comes along , and takes a proton from here , and these electrons have moved into here , that would give us the same product , right ? so this would be , let me go and highlight those electrons , so these electrons in dark blue would move in to form our double bond , but this is the same as that product . alcohols can also react via an e1 mechanism . the carbon that 's bonded to the oh would be the alpha carbon , and the carbon next to that would be the beta carbon , so reacting an alcohol with sulfuric acid and heating up your reaction mixture will give you an alkene , and sometimes , phosphoric acid is used instead of sulfuric acid . so we saw the first step of an e1 mechanism was loss of a leaving group , but if that happens here , if these electrons come off onto the oxygen , that would form hydroxide as your leaving group , and the hydroxide anion is a poor leaving group , and we know that by looking at pka values . down here is the hydroxide anion , it is the conjugate base to water , but water is not a great asset , and we know that from the pka value here , so water is not great at donating a proton , which means that the hydroxide anion is not that stable , and since the hydroxide anion is not that stable , it 's not a great leaving group . so let 's go ahead and take off this arrow here , because the first step is not loss of a leaving group , the first step is a proton transfer . we have a strong acid here , sulfuric acid , and the alcohol will act as a base and take a proton from sulfuric acid . and that would form water as your leaving group , and water is a much better leaving group than the hydroxide anion , and again , we know that by pka values . water is the conjugate base to the hydronium ion , h3o+ , which is much better at donating a proton , the pka value is much , much lower . and that means that water is stable , so the first step , the first step when you are doing an e1 mechanism with an alcohol is to protonate the oh group . so here 's our alcohol , and the carbon bonded to the oh is our alpha carbon , and then these carbons next to the alpha carbon would all be beta carbons . we just saw the first step is a proton transfer , a lone pair of electrons on the oxygen take a proton from sulfuric acid , so we transfer a proton , and let 's go ahead and draw in what we would have now , so there 'd be a plus-one formal charge on the oxygen , so let 's highlight our electrons in magenta , these electrons took this proton to form this bond , and now we have water as a leaving group , let me just fix this hydrogen here really fast , and these electrons can come off onto our oxygen , so that gives us water as our leaving group , and let me go ahead and draw in the water molecule here , and let me highlight electrons , the electrons in light blue , in this bond , came off onto the oxygen , which forms water , and we know water is a good leaving group . we took a bond away from this carbon in red , so that carbon would now be a carbocation , so let me draw in our carbocation here , so the carbon in red is now positively charged , so let me draw in a plus-one formal charge on that carbon , the next step of our mechanism , we know a weak base comes along and takes a proton , one of the protons on one of the beta carbons over here , so let 's just say it 's this one , and i 'm just gon na draw in a generic base , so a generic base right here , which is gon na take this proton , and then these electrons are gon na move in to form our product , so let me draw our product in here , and let me highlight those electrons . so the electrons in , let 's use green this time , the electrons in green moved in here to form our double bond , to form our alkene . so i just put a generic base , let me go ahead and talk about the base for a second here . i just put in a generic base , sometimes you might see water acting as a base , sometimes you might see hso4- , right , the conjugate base to sulfuric acid acting as the base , different textbooks give you different things , i do n't think it really matters , but one of those acting as a weak base , it 's probably water , takes this proton to form your alkene . sometimes this reaction is called a dehydration reaction since we lost water in the process .
|
here we have a tertiary alkyl halides , and let 's say this tertiary alkyl halide undergoes an e1 elimination reaction . so the carbon that 's bonded to the iodine must be our alpha carbon , and then we would have three beta carbons , so that 's a beta carbon , that 's a beta carbon , and that 's a beta carbon . so the first step in an e1 mechanism is loss of our leaving group , so if i draw the lone pairs of electrons in here on iodine , i know that these electrons in this bond would come off onto iodine to form the iodide anion , so let me draw that in here , so we would make the iodide anion , and let me highlight our electron , so the electrons in this bond come off onto the iodine to form the iodide anion .
|
what is an alpha and beta carbon ?
|
let 's look at the mechanism for an e1 elimination reaction , and we 'll start with our substrate , so on the left . let 's say we 're dealing with alkyl halide . so the carbon that 's bonded to our halogen would be the alpha carbon , and the carbon next to that carbon would be the beta carbon , so we need a beta hydrogen for this reaction . the first step of an e1 elimination mechanism is loss of our leaving group , so loss of leaving group , let me just write that in here really quickly , and in this case , the electrons would come off onto our leaving group in the first step of the mechanism . so we 're taking a bond away from this carbon , the one that i 've circled in red here , so that carbon is going from being sp3 hybridized to being sp2 hybridized . so now we have a carbocation , and we know that carbocations , sp2 hybridized carbons have planar geometry around them , so i 've attempted to show the planar geometry around this carbocation . so that 's the first step , loss of the leaving group to form a carbocation . in the second step , our base comes along and takes this proton , which leaves these electrons behind , and those electrons move in to form our alkene , so this is the second step of the mechanism , which is the base takes , or abstracts , a proton , so base takes a proton to form our alkene . and let me go ahead and highlight those electrons , so these electrons here in magenta moved in to form our double bond , and we form our product , we form our alkene . so the first step of the mechanism , the loss of the leaving group , this turns out to be the rate determining step , so this is the slowest step of the mechanism . so if you 're writing a rate law , the rate of this reaction would be equal to the rate constant k times the concentration of your substrate , so that 's what studies have shown , that these mechanisms depend on the concentration of only your substrate , this over here on the left , so it 's first order with respect to the substrate . and that 's because of this rate determining step . the loss of the leaving group is the rate determining step , and so the concentration of your substrate , your starting material , that 's what matters . your base ca n't do anything until you lose your leaving group . and so , since the base does not participate in the rate determining step , it participates in the second step , the concentration of the base has no effect on the rate of the reaction , so it 's the concentration of the substrate only , and since it 's only dependent on the concentration of the substrate , that 's where the one comes from in e1 , so i 'm gon na go ahead and write this out here , so in e1 mechanism , the one comes from the fact this is a unimolecular , a unimolecular rate law here , and the e comes from the fact that this is an elimination reaction , so when you see e1 , that 's what you 're thinking about , it 's an elimination reaction , and it 's unimolecular , the overall rate of the reaction only depends on the concentration of your substrate , so if you increase , let 's say you have , let 's say this was your substrate right here , and you increase the concentration of your substrate , let me just write this down , so if you increase the concentration of your substrate by a factor of two , you would also increase the rate of reaction by a factor of two , so it 's first order with respect to the substrate , so this is some general chemistry here . if you increase the concentration of your base by a factor of two , you would have no effect on the overall rate of the reaction . so let 's talk about one more point here in the mechanism , and that is the formation of this carbocation . since we have a carbocation in this mechanism , we need to think about the possibility of rearrangements in the mechanism , and you need to think what would form , what substrate would form a stable carbocation , so something like a tertiary substrate forming a tertiary carbocation would be favorable for an e1 mechanism . here we have a tertiary alkyl halides , and let 's say this tertiary alkyl halide undergoes an e1 elimination reaction . so the carbon that 's bonded to the iodine must be our alpha carbon , and then we would have three beta carbons , so that 's a beta carbon , that 's a beta carbon , and that 's a beta carbon . so the first step in an e1 mechanism is loss of our leaving group , so if i draw the lone pairs of electrons in here on iodine , i know that these electrons in this bond would come off onto iodine to form the iodide anion , so let me draw that in here , so we would make the iodide anion , and let me highlight our electron , so the electrons in this bond come off onto the iodine to form the iodide anion . and this is an excellent leaving group . iodide is an excellent leaving group , and you know that by looking at pka values . the iodide anion is the conjugate base of a very strong acid , hi , with a approximate pka value of negative 11 , so hi is very good at donating a proton , which must mean that the conjugate base is very stable , so the iodide anion is an excellent leaving group . so if we lose the iodide anion , that means we 're gon na have a carbocation , so we lost a bond to this carbon in red , so we 're gon na form a carbocation , let me go ahead and draw that in , so this is a planar carbocation , and so the carbon , let me go ahead and highlight it here , the carbon in red has a plus one formal charge , it lost a bond . so that 's the first step of an e1 elimination mechanism . the second step of an e1 elimination mechanism is the base comes along , and it takes a proton from a beta carbon , so our base in this case would be ethanol , so let me go ahead and draw in lone pairs of electrons on the oxygen , so notice we 're also heating this reaction , so the ethanol is gon na function as a base , so ethanol 's not a strong base , but it can take a proton , so let me go ahead and draw in a proton right here , and a lone pair of electrons on the oxygen is going to take this proton , and the electrons would move into here to form our alkene , so let me go ahead and draw our product , let me put that in here , and let me highlight some electrons , so the electrons in blue moved in here to form our double bond . so a couple of points about this reaction , one point is , when you 're looking at sn1 mechanisms , the first step is loss of a leaving group to form your carbocation , so when you get to this carbocation , you might think , well , why is ethanol acting as a base here ? why could n't it act as a nucleophile ? and the answer is , the ethanol certainly can act as a nucleophile , and it would attack the positively-charged carbon , and you would definitely get a substitution product for this reaction as well , so if ethanol acts as a nucleophile , you 're gon na get a substitution reaction , an sn1 mechanism . if the ethanol acts as a base , you 're gon na get an e1 elimination mechanism , so here , we 're just gon na focus on the elimination product , and we wo n't worry about the substitution product , but we will talk about this stuff in a later video , 'cause that would definitely happen . alright , something else i wan na talk about is we had three beta carbons over here , and if i look at these three beta carbons , and i just picked one of them , i just said that this carbon right here , let me highlight it , i just took a proton from this carbon , but it does n't matter which of those carbons that we take a proton off because of symmetry , let me go ahead and draw this in over here , so this is my carbocation , let 's say , and let 's say we took a proton from this carbon , so our weak base comes along , and takes a proton from here , and these electrons have moved into here , that would give us the same product , right ? so this would be , let me go and highlight those electrons , so these electrons in dark blue would move in to form our double bond , but this is the same as that product . alcohols can also react via an e1 mechanism . the carbon that 's bonded to the oh would be the alpha carbon , and the carbon next to that would be the beta carbon , so reacting an alcohol with sulfuric acid and heating up your reaction mixture will give you an alkene , and sometimes , phosphoric acid is used instead of sulfuric acid . so we saw the first step of an e1 mechanism was loss of a leaving group , but if that happens here , if these electrons come off onto the oxygen , that would form hydroxide as your leaving group , and the hydroxide anion is a poor leaving group , and we know that by looking at pka values . down here is the hydroxide anion , it is the conjugate base to water , but water is not a great asset , and we know that from the pka value here , so water is not great at donating a proton , which means that the hydroxide anion is not that stable , and since the hydroxide anion is not that stable , it 's not a great leaving group . so let 's go ahead and take off this arrow here , because the first step is not loss of a leaving group , the first step is a proton transfer . we have a strong acid here , sulfuric acid , and the alcohol will act as a base and take a proton from sulfuric acid . and that would form water as your leaving group , and water is a much better leaving group than the hydroxide anion , and again , we know that by pka values . water is the conjugate base to the hydronium ion , h3o+ , which is much better at donating a proton , the pka value is much , much lower . and that means that water is stable , so the first step , the first step when you are doing an e1 mechanism with an alcohol is to protonate the oh group . so here 's our alcohol , and the carbon bonded to the oh is our alpha carbon , and then these carbons next to the alpha carbon would all be beta carbons . we just saw the first step is a proton transfer , a lone pair of electrons on the oxygen take a proton from sulfuric acid , so we transfer a proton , and let 's go ahead and draw in what we would have now , so there 'd be a plus-one formal charge on the oxygen , so let 's highlight our electrons in magenta , these electrons took this proton to form this bond , and now we have water as a leaving group , let me just fix this hydrogen here really fast , and these electrons can come off onto our oxygen , so that gives us water as our leaving group , and let me go ahead and draw in the water molecule here , and let me highlight electrons , the electrons in light blue , in this bond , came off onto the oxygen , which forms water , and we know water is a good leaving group . we took a bond away from this carbon in red , so that carbon would now be a carbocation , so let me draw in our carbocation here , so the carbon in red is now positively charged , so let me draw in a plus-one formal charge on that carbon , the next step of our mechanism , we know a weak base comes along and takes a proton , one of the protons on one of the beta carbons over here , so let 's just say it 's this one , and i 'm just gon na draw in a generic base , so a generic base right here , which is gon na take this proton , and then these electrons are gon na move in to form our product , so let me draw our product in here , and let me highlight those electrons . so the electrons in , let 's use green this time , the electrons in green moved in here to form our double bond , to form our alkene . so i just put a generic base , let me go ahead and talk about the base for a second here . i just put in a generic base , sometimes you might see water acting as a base , sometimes you might see hso4- , right , the conjugate base to sulfuric acid acting as the base , different textbooks give you different things , i do n't think it really matters , but one of those acting as a weak base , it 's probably water , takes this proton to form your alkene . sometimes this reaction is called a dehydration reaction since we lost water in the process .
|
so here 's our alcohol , and the carbon bonded to the oh is our alpha carbon , and then these carbons next to the alpha carbon would all be beta carbons . we just saw the first step is a proton transfer , a lone pair of electrons on the oxygen take a proton from sulfuric acid , so we transfer a proton , and let 's go ahead and draw in what we would have now , so there 'd be a plus-one formal charge on the oxygen , so let 's highlight our electrons in magenta , these electrons took this proton to form this bond , and now we have water as a leaving group , let me just fix this hydrogen here really fast , and these electrons can come off onto our oxygen , so that gives us water as our leaving group , and let me go ahead and draw in the water molecule here , and let me highlight electrons , the electrons in light blue , in this bond , came off onto the oxygen , which forms water , and we know water is a good leaving group . we took a bond away from this carbon in red , so that carbon would now be a carbocation , so let me draw in our carbocation here , so the carbon in red is now positively charged , so let me draw in a plus-one formal charge on that carbon , the next step of our mechanism , we know a weak base comes along and takes a proton , one of the protons on one of the beta carbons over here , so let 's just say it 's this one , and i 'm just gon na draw in a generic base , so a generic base right here , which is gon na take this proton , and then these electrons are gon na move in to form our product , so let me draw our product in here , and let me highlight those electrons .
|
how can we predict that a neutral molecule such as ethanol or water molecule would act as a base as shown ?
|
let 's look at the mechanism for an e1 elimination reaction , and we 'll start with our substrate , so on the left . let 's say we 're dealing with alkyl halide . so the carbon that 's bonded to our halogen would be the alpha carbon , and the carbon next to that carbon would be the beta carbon , so we need a beta hydrogen for this reaction . the first step of an e1 elimination mechanism is loss of our leaving group , so loss of leaving group , let me just write that in here really quickly , and in this case , the electrons would come off onto our leaving group in the first step of the mechanism . so we 're taking a bond away from this carbon , the one that i 've circled in red here , so that carbon is going from being sp3 hybridized to being sp2 hybridized . so now we have a carbocation , and we know that carbocations , sp2 hybridized carbons have planar geometry around them , so i 've attempted to show the planar geometry around this carbocation . so that 's the first step , loss of the leaving group to form a carbocation . in the second step , our base comes along and takes this proton , which leaves these electrons behind , and those electrons move in to form our alkene , so this is the second step of the mechanism , which is the base takes , or abstracts , a proton , so base takes a proton to form our alkene . and let me go ahead and highlight those electrons , so these electrons here in magenta moved in to form our double bond , and we form our product , we form our alkene . so the first step of the mechanism , the loss of the leaving group , this turns out to be the rate determining step , so this is the slowest step of the mechanism . so if you 're writing a rate law , the rate of this reaction would be equal to the rate constant k times the concentration of your substrate , so that 's what studies have shown , that these mechanisms depend on the concentration of only your substrate , this over here on the left , so it 's first order with respect to the substrate . and that 's because of this rate determining step . the loss of the leaving group is the rate determining step , and so the concentration of your substrate , your starting material , that 's what matters . your base ca n't do anything until you lose your leaving group . and so , since the base does not participate in the rate determining step , it participates in the second step , the concentration of the base has no effect on the rate of the reaction , so it 's the concentration of the substrate only , and since it 's only dependent on the concentration of the substrate , that 's where the one comes from in e1 , so i 'm gon na go ahead and write this out here , so in e1 mechanism , the one comes from the fact this is a unimolecular , a unimolecular rate law here , and the e comes from the fact that this is an elimination reaction , so when you see e1 , that 's what you 're thinking about , it 's an elimination reaction , and it 's unimolecular , the overall rate of the reaction only depends on the concentration of your substrate , so if you increase , let 's say you have , let 's say this was your substrate right here , and you increase the concentration of your substrate , let me just write this down , so if you increase the concentration of your substrate by a factor of two , you would also increase the rate of reaction by a factor of two , so it 's first order with respect to the substrate , so this is some general chemistry here . if you increase the concentration of your base by a factor of two , you would have no effect on the overall rate of the reaction . so let 's talk about one more point here in the mechanism , and that is the formation of this carbocation . since we have a carbocation in this mechanism , we need to think about the possibility of rearrangements in the mechanism , and you need to think what would form , what substrate would form a stable carbocation , so something like a tertiary substrate forming a tertiary carbocation would be favorable for an e1 mechanism . here we have a tertiary alkyl halides , and let 's say this tertiary alkyl halide undergoes an e1 elimination reaction . so the carbon that 's bonded to the iodine must be our alpha carbon , and then we would have three beta carbons , so that 's a beta carbon , that 's a beta carbon , and that 's a beta carbon . so the first step in an e1 mechanism is loss of our leaving group , so if i draw the lone pairs of electrons in here on iodine , i know that these electrons in this bond would come off onto iodine to form the iodide anion , so let me draw that in here , so we would make the iodide anion , and let me highlight our electron , so the electrons in this bond come off onto the iodine to form the iodide anion . and this is an excellent leaving group . iodide is an excellent leaving group , and you know that by looking at pka values . the iodide anion is the conjugate base of a very strong acid , hi , with a approximate pka value of negative 11 , so hi is very good at donating a proton , which must mean that the conjugate base is very stable , so the iodide anion is an excellent leaving group . so if we lose the iodide anion , that means we 're gon na have a carbocation , so we lost a bond to this carbon in red , so we 're gon na form a carbocation , let me go ahead and draw that in , so this is a planar carbocation , and so the carbon , let me go ahead and highlight it here , the carbon in red has a plus one formal charge , it lost a bond . so that 's the first step of an e1 elimination mechanism . the second step of an e1 elimination mechanism is the base comes along , and it takes a proton from a beta carbon , so our base in this case would be ethanol , so let me go ahead and draw in lone pairs of electrons on the oxygen , so notice we 're also heating this reaction , so the ethanol is gon na function as a base , so ethanol 's not a strong base , but it can take a proton , so let me go ahead and draw in a proton right here , and a lone pair of electrons on the oxygen is going to take this proton , and the electrons would move into here to form our alkene , so let me go ahead and draw our product , let me put that in here , and let me highlight some electrons , so the electrons in blue moved in here to form our double bond . so a couple of points about this reaction , one point is , when you 're looking at sn1 mechanisms , the first step is loss of a leaving group to form your carbocation , so when you get to this carbocation , you might think , well , why is ethanol acting as a base here ? why could n't it act as a nucleophile ? and the answer is , the ethanol certainly can act as a nucleophile , and it would attack the positively-charged carbon , and you would definitely get a substitution product for this reaction as well , so if ethanol acts as a nucleophile , you 're gon na get a substitution reaction , an sn1 mechanism . if the ethanol acts as a base , you 're gon na get an e1 elimination mechanism , so here , we 're just gon na focus on the elimination product , and we wo n't worry about the substitution product , but we will talk about this stuff in a later video , 'cause that would definitely happen . alright , something else i wan na talk about is we had three beta carbons over here , and if i look at these three beta carbons , and i just picked one of them , i just said that this carbon right here , let me highlight it , i just took a proton from this carbon , but it does n't matter which of those carbons that we take a proton off because of symmetry , let me go ahead and draw this in over here , so this is my carbocation , let 's say , and let 's say we took a proton from this carbon , so our weak base comes along , and takes a proton from here , and these electrons have moved into here , that would give us the same product , right ? so this would be , let me go and highlight those electrons , so these electrons in dark blue would move in to form our double bond , but this is the same as that product . alcohols can also react via an e1 mechanism . the carbon that 's bonded to the oh would be the alpha carbon , and the carbon next to that would be the beta carbon , so reacting an alcohol with sulfuric acid and heating up your reaction mixture will give you an alkene , and sometimes , phosphoric acid is used instead of sulfuric acid . so we saw the first step of an e1 mechanism was loss of a leaving group , but if that happens here , if these electrons come off onto the oxygen , that would form hydroxide as your leaving group , and the hydroxide anion is a poor leaving group , and we know that by looking at pka values . down here is the hydroxide anion , it is the conjugate base to water , but water is not a great asset , and we know that from the pka value here , so water is not great at donating a proton , which means that the hydroxide anion is not that stable , and since the hydroxide anion is not that stable , it 's not a great leaving group . so let 's go ahead and take off this arrow here , because the first step is not loss of a leaving group , the first step is a proton transfer . we have a strong acid here , sulfuric acid , and the alcohol will act as a base and take a proton from sulfuric acid . and that would form water as your leaving group , and water is a much better leaving group than the hydroxide anion , and again , we know that by pka values . water is the conjugate base to the hydronium ion , h3o+ , which is much better at donating a proton , the pka value is much , much lower . and that means that water is stable , so the first step , the first step when you are doing an e1 mechanism with an alcohol is to protonate the oh group . so here 's our alcohol , and the carbon bonded to the oh is our alpha carbon , and then these carbons next to the alpha carbon would all be beta carbons . we just saw the first step is a proton transfer , a lone pair of electrons on the oxygen take a proton from sulfuric acid , so we transfer a proton , and let 's go ahead and draw in what we would have now , so there 'd be a plus-one formal charge on the oxygen , so let 's highlight our electrons in magenta , these electrons took this proton to form this bond , and now we have water as a leaving group , let me just fix this hydrogen here really fast , and these electrons can come off onto our oxygen , so that gives us water as our leaving group , and let me go ahead and draw in the water molecule here , and let me highlight electrons , the electrons in light blue , in this bond , came off onto the oxygen , which forms water , and we know water is a good leaving group . we took a bond away from this carbon in red , so that carbon would now be a carbocation , so let me draw in our carbocation here , so the carbon in red is now positively charged , so let me draw in a plus-one formal charge on that carbon , the next step of our mechanism , we know a weak base comes along and takes a proton , one of the protons on one of the beta carbons over here , so let 's just say it 's this one , and i 'm just gon na draw in a generic base , so a generic base right here , which is gon na take this proton , and then these electrons are gon na move in to form our product , so let me draw our product in here , and let me highlight those electrons . so the electrons in , let 's use green this time , the electrons in green moved in here to form our double bond , to form our alkene . so i just put a generic base , let me go ahead and talk about the base for a second here . i just put in a generic base , sometimes you might see water acting as a base , sometimes you might see hso4- , right , the conjugate base to sulfuric acid acting as the base , different textbooks give you different things , i do n't think it really matters , but one of those acting as a weak base , it 's probably water , takes this proton to form your alkene . sometimes this reaction is called a dehydration reaction since we lost water in the process .
|
i just put in a generic base , sometimes you might see water acting as a base , sometimes you might see hso4- , right , the conjugate base to sulfuric acid acting as the base , different textbooks give you different things , i do n't think it really matters , but one of those acting as a weak base , it 's probably water , takes this proton to form your alkene . sometimes this reaction is called a dehydration reaction since we lost water in the process .
|
what does the triangle mean on the reaction arrow ?
|
let 's look at the mechanism for an e1 elimination reaction , and we 'll start with our substrate , so on the left . let 's say we 're dealing with alkyl halide . so the carbon that 's bonded to our halogen would be the alpha carbon , and the carbon next to that carbon would be the beta carbon , so we need a beta hydrogen for this reaction . the first step of an e1 elimination mechanism is loss of our leaving group , so loss of leaving group , let me just write that in here really quickly , and in this case , the electrons would come off onto our leaving group in the first step of the mechanism . so we 're taking a bond away from this carbon , the one that i 've circled in red here , so that carbon is going from being sp3 hybridized to being sp2 hybridized . so now we have a carbocation , and we know that carbocations , sp2 hybridized carbons have planar geometry around them , so i 've attempted to show the planar geometry around this carbocation . so that 's the first step , loss of the leaving group to form a carbocation . in the second step , our base comes along and takes this proton , which leaves these electrons behind , and those electrons move in to form our alkene , so this is the second step of the mechanism , which is the base takes , or abstracts , a proton , so base takes a proton to form our alkene . and let me go ahead and highlight those electrons , so these electrons here in magenta moved in to form our double bond , and we form our product , we form our alkene . so the first step of the mechanism , the loss of the leaving group , this turns out to be the rate determining step , so this is the slowest step of the mechanism . so if you 're writing a rate law , the rate of this reaction would be equal to the rate constant k times the concentration of your substrate , so that 's what studies have shown , that these mechanisms depend on the concentration of only your substrate , this over here on the left , so it 's first order with respect to the substrate . and that 's because of this rate determining step . the loss of the leaving group is the rate determining step , and so the concentration of your substrate , your starting material , that 's what matters . your base ca n't do anything until you lose your leaving group . and so , since the base does not participate in the rate determining step , it participates in the second step , the concentration of the base has no effect on the rate of the reaction , so it 's the concentration of the substrate only , and since it 's only dependent on the concentration of the substrate , that 's where the one comes from in e1 , so i 'm gon na go ahead and write this out here , so in e1 mechanism , the one comes from the fact this is a unimolecular , a unimolecular rate law here , and the e comes from the fact that this is an elimination reaction , so when you see e1 , that 's what you 're thinking about , it 's an elimination reaction , and it 's unimolecular , the overall rate of the reaction only depends on the concentration of your substrate , so if you increase , let 's say you have , let 's say this was your substrate right here , and you increase the concentration of your substrate , let me just write this down , so if you increase the concentration of your substrate by a factor of two , you would also increase the rate of reaction by a factor of two , so it 's first order with respect to the substrate , so this is some general chemistry here . if you increase the concentration of your base by a factor of two , you would have no effect on the overall rate of the reaction . so let 's talk about one more point here in the mechanism , and that is the formation of this carbocation . since we have a carbocation in this mechanism , we need to think about the possibility of rearrangements in the mechanism , and you need to think what would form , what substrate would form a stable carbocation , so something like a tertiary substrate forming a tertiary carbocation would be favorable for an e1 mechanism . here we have a tertiary alkyl halides , and let 's say this tertiary alkyl halide undergoes an e1 elimination reaction . so the carbon that 's bonded to the iodine must be our alpha carbon , and then we would have three beta carbons , so that 's a beta carbon , that 's a beta carbon , and that 's a beta carbon . so the first step in an e1 mechanism is loss of our leaving group , so if i draw the lone pairs of electrons in here on iodine , i know that these electrons in this bond would come off onto iodine to form the iodide anion , so let me draw that in here , so we would make the iodide anion , and let me highlight our electron , so the electrons in this bond come off onto the iodine to form the iodide anion . and this is an excellent leaving group . iodide is an excellent leaving group , and you know that by looking at pka values . the iodide anion is the conjugate base of a very strong acid , hi , with a approximate pka value of negative 11 , so hi is very good at donating a proton , which must mean that the conjugate base is very stable , so the iodide anion is an excellent leaving group . so if we lose the iodide anion , that means we 're gon na have a carbocation , so we lost a bond to this carbon in red , so we 're gon na form a carbocation , let me go ahead and draw that in , so this is a planar carbocation , and so the carbon , let me go ahead and highlight it here , the carbon in red has a plus one formal charge , it lost a bond . so that 's the first step of an e1 elimination mechanism . the second step of an e1 elimination mechanism is the base comes along , and it takes a proton from a beta carbon , so our base in this case would be ethanol , so let me go ahead and draw in lone pairs of electrons on the oxygen , so notice we 're also heating this reaction , so the ethanol is gon na function as a base , so ethanol 's not a strong base , but it can take a proton , so let me go ahead and draw in a proton right here , and a lone pair of electrons on the oxygen is going to take this proton , and the electrons would move into here to form our alkene , so let me go ahead and draw our product , let me put that in here , and let me highlight some electrons , so the electrons in blue moved in here to form our double bond . so a couple of points about this reaction , one point is , when you 're looking at sn1 mechanisms , the first step is loss of a leaving group to form your carbocation , so when you get to this carbocation , you might think , well , why is ethanol acting as a base here ? why could n't it act as a nucleophile ? and the answer is , the ethanol certainly can act as a nucleophile , and it would attack the positively-charged carbon , and you would definitely get a substitution product for this reaction as well , so if ethanol acts as a nucleophile , you 're gon na get a substitution reaction , an sn1 mechanism . if the ethanol acts as a base , you 're gon na get an e1 elimination mechanism , so here , we 're just gon na focus on the elimination product , and we wo n't worry about the substitution product , but we will talk about this stuff in a later video , 'cause that would definitely happen . alright , something else i wan na talk about is we had three beta carbons over here , and if i look at these three beta carbons , and i just picked one of them , i just said that this carbon right here , let me highlight it , i just took a proton from this carbon , but it does n't matter which of those carbons that we take a proton off because of symmetry , let me go ahead and draw this in over here , so this is my carbocation , let 's say , and let 's say we took a proton from this carbon , so our weak base comes along , and takes a proton from here , and these electrons have moved into here , that would give us the same product , right ? so this would be , let me go and highlight those electrons , so these electrons in dark blue would move in to form our double bond , but this is the same as that product . alcohols can also react via an e1 mechanism . the carbon that 's bonded to the oh would be the alpha carbon , and the carbon next to that would be the beta carbon , so reacting an alcohol with sulfuric acid and heating up your reaction mixture will give you an alkene , and sometimes , phosphoric acid is used instead of sulfuric acid . so we saw the first step of an e1 mechanism was loss of a leaving group , but if that happens here , if these electrons come off onto the oxygen , that would form hydroxide as your leaving group , and the hydroxide anion is a poor leaving group , and we know that by looking at pka values . down here is the hydroxide anion , it is the conjugate base to water , but water is not a great asset , and we know that from the pka value here , so water is not great at donating a proton , which means that the hydroxide anion is not that stable , and since the hydroxide anion is not that stable , it 's not a great leaving group . so let 's go ahead and take off this arrow here , because the first step is not loss of a leaving group , the first step is a proton transfer . we have a strong acid here , sulfuric acid , and the alcohol will act as a base and take a proton from sulfuric acid . and that would form water as your leaving group , and water is a much better leaving group than the hydroxide anion , and again , we know that by pka values . water is the conjugate base to the hydronium ion , h3o+ , which is much better at donating a proton , the pka value is much , much lower . and that means that water is stable , so the first step , the first step when you are doing an e1 mechanism with an alcohol is to protonate the oh group . so here 's our alcohol , and the carbon bonded to the oh is our alpha carbon , and then these carbons next to the alpha carbon would all be beta carbons . we just saw the first step is a proton transfer , a lone pair of electrons on the oxygen take a proton from sulfuric acid , so we transfer a proton , and let 's go ahead and draw in what we would have now , so there 'd be a plus-one formal charge on the oxygen , so let 's highlight our electrons in magenta , these electrons took this proton to form this bond , and now we have water as a leaving group , let me just fix this hydrogen here really fast , and these electrons can come off onto our oxygen , so that gives us water as our leaving group , and let me go ahead and draw in the water molecule here , and let me highlight electrons , the electrons in light blue , in this bond , came off onto the oxygen , which forms water , and we know water is a good leaving group . we took a bond away from this carbon in red , so that carbon would now be a carbocation , so let me draw in our carbocation here , so the carbon in red is now positively charged , so let me draw in a plus-one formal charge on that carbon , the next step of our mechanism , we know a weak base comes along and takes a proton , one of the protons on one of the beta carbons over here , so let 's just say it 's this one , and i 'm just gon na draw in a generic base , so a generic base right here , which is gon na take this proton , and then these electrons are gon na move in to form our product , so let me draw our product in here , and let me highlight those electrons . so the electrons in , let 's use green this time , the electrons in green moved in here to form our double bond , to form our alkene . so i just put a generic base , let me go ahead and talk about the base for a second here . i just put in a generic base , sometimes you might see water acting as a base , sometimes you might see hso4- , right , the conjugate base to sulfuric acid acting as the base , different textbooks give you different things , i do n't think it really matters , but one of those acting as a weak base , it 's probably water , takes this proton to form your alkene . sometimes this reaction is called a dehydration reaction since we lost water in the process .
|
here we have a tertiary alkyl halides , and let 's say this tertiary alkyl halide undergoes an e1 elimination reaction . so the carbon that 's bonded to the iodine must be our alpha carbon , and then we would have three beta carbons , so that 's a beta carbon , that 's a beta carbon , and that 's a beta carbon . so the first step in an e1 mechanism is loss of our leaving group , so if i draw the lone pairs of electrons in here on iodine , i know that these electrons in this bond would come off onto iodine to form the iodide anion , so let me draw that in here , so we would make the iodide anion , and let me highlight our electron , so the electrons in this bond come off onto the iodine to form the iodide anion .
|
cant we view the mechanism to start with the base plucking a proton from beta carbon ?
|
let 's look at the mechanism for an e1 elimination reaction , and we 'll start with our substrate , so on the left . let 's say we 're dealing with alkyl halide . so the carbon that 's bonded to our halogen would be the alpha carbon , and the carbon next to that carbon would be the beta carbon , so we need a beta hydrogen for this reaction . the first step of an e1 elimination mechanism is loss of our leaving group , so loss of leaving group , let me just write that in here really quickly , and in this case , the electrons would come off onto our leaving group in the first step of the mechanism . so we 're taking a bond away from this carbon , the one that i 've circled in red here , so that carbon is going from being sp3 hybridized to being sp2 hybridized . so now we have a carbocation , and we know that carbocations , sp2 hybridized carbons have planar geometry around them , so i 've attempted to show the planar geometry around this carbocation . so that 's the first step , loss of the leaving group to form a carbocation . in the second step , our base comes along and takes this proton , which leaves these electrons behind , and those electrons move in to form our alkene , so this is the second step of the mechanism , which is the base takes , or abstracts , a proton , so base takes a proton to form our alkene . and let me go ahead and highlight those electrons , so these electrons here in magenta moved in to form our double bond , and we form our product , we form our alkene . so the first step of the mechanism , the loss of the leaving group , this turns out to be the rate determining step , so this is the slowest step of the mechanism . so if you 're writing a rate law , the rate of this reaction would be equal to the rate constant k times the concentration of your substrate , so that 's what studies have shown , that these mechanisms depend on the concentration of only your substrate , this over here on the left , so it 's first order with respect to the substrate . and that 's because of this rate determining step . the loss of the leaving group is the rate determining step , and so the concentration of your substrate , your starting material , that 's what matters . your base ca n't do anything until you lose your leaving group . and so , since the base does not participate in the rate determining step , it participates in the second step , the concentration of the base has no effect on the rate of the reaction , so it 's the concentration of the substrate only , and since it 's only dependent on the concentration of the substrate , that 's where the one comes from in e1 , so i 'm gon na go ahead and write this out here , so in e1 mechanism , the one comes from the fact this is a unimolecular , a unimolecular rate law here , and the e comes from the fact that this is an elimination reaction , so when you see e1 , that 's what you 're thinking about , it 's an elimination reaction , and it 's unimolecular , the overall rate of the reaction only depends on the concentration of your substrate , so if you increase , let 's say you have , let 's say this was your substrate right here , and you increase the concentration of your substrate , let me just write this down , so if you increase the concentration of your substrate by a factor of two , you would also increase the rate of reaction by a factor of two , so it 's first order with respect to the substrate , so this is some general chemistry here . if you increase the concentration of your base by a factor of two , you would have no effect on the overall rate of the reaction . so let 's talk about one more point here in the mechanism , and that is the formation of this carbocation . since we have a carbocation in this mechanism , we need to think about the possibility of rearrangements in the mechanism , and you need to think what would form , what substrate would form a stable carbocation , so something like a tertiary substrate forming a tertiary carbocation would be favorable for an e1 mechanism . here we have a tertiary alkyl halides , and let 's say this tertiary alkyl halide undergoes an e1 elimination reaction . so the carbon that 's bonded to the iodine must be our alpha carbon , and then we would have three beta carbons , so that 's a beta carbon , that 's a beta carbon , and that 's a beta carbon . so the first step in an e1 mechanism is loss of our leaving group , so if i draw the lone pairs of electrons in here on iodine , i know that these electrons in this bond would come off onto iodine to form the iodide anion , so let me draw that in here , so we would make the iodide anion , and let me highlight our electron , so the electrons in this bond come off onto the iodine to form the iodide anion . and this is an excellent leaving group . iodide is an excellent leaving group , and you know that by looking at pka values . the iodide anion is the conjugate base of a very strong acid , hi , with a approximate pka value of negative 11 , so hi is very good at donating a proton , which must mean that the conjugate base is very stable , so the iodide anion is an excellent leaving group . so if we lose the iodide anion , that means we 're gon na have a carbocation , so we lost a bond to this carbon in red , so we 're gon na form a carbocation , let me go ahead and draw that in , so this is a planar carbocation , and so the carbon , let me go ahead and highlight it here , the carbon in red has a plus one formal charge , it lost a bond . so that 's the first step of an e1 elimination mechanism . the second step of an e1 elimination mechanism is the base comes along , and it takes a proton from a beta carbon , so our base in this case would be ethanol , so let me go ahead and draw in lone pairs of electrons on the oxygen , so notice we 're also heating this reaction , so the ethanol is gon na function as a base , so ethanol 's not a strong base , but it can take a proton , so let me go ahead and draw in a proton right here , and a lone pair of electrons on the oxygen is going to take this proton , and the electrons would move into here to form our alkene , so let me go ahead and draw our product , let me put that in here , and let me highlight some electrons , so the electrons in blue moved in here to form our double bond . so a couple of points about this reaction , one point is , when you 're looking at sn1 mechanisms , the first step is loss of a leaving group to form your carbocation , so when you get to this carbocation , you might think , well , why is ethanol acting as a base here ? why could n't it act as a nucleophile ? and the answer is , the ethanol certainly can act as a nucleophile , and it would attack the positively-charged carbon , and you would definitely get a substitution product for this reaction as well , so if ethanol acts as a nucleophile , you 're gon na get a substitution reaction , an sn1 mechanism . if the ethanol acts as a base , you 're gon na get an e1 elimination mechanism , so here , we 're just gon na focus on the elimination product , and we wo n't worry about the substitution product , but we will talk about this stuff in a later video , 'cause that would definitely happen . alright , something else i wan na talk about is we had three beta carbons over here , and if i look at these three beta carbons , and i just picked one of them , i just said that this carbon right here , let me highlight it , i just took a proton from this carbon , but it does n't matter which of those carbons that we take a proton off because of symmetry , let me go ahead and draw this in over here , so this is my carbocation , let 's say , and let 's say we took a proton from this carbon , so our weak base comes along , and takes a proton from here , and these electrons have moved into here , that would give us the same product , right ? so this would be , let me go and highlight those electrons , so these electrons in dark blue would move in to form our double bond , but this is the same as that product . alcohols can also react via an e1 mechanism . the carbon that 's bonded to the oh would be the alpha carbon , and the carbon next to that would be the beta carbon , so reacting an alcohol with sulfuric acid and heating up your reaction mixture will give you an alkene , and sometimes , phosphoric acid is used instead of sulfuric acid . so we saw the first step of an e1 mechanism was loss of a leaving group , but if that happens here , if these electrons come off onto the oxygen , that would form hydroxide as your leaving group , and the hydroxide anion is a poor leaving group , and we know that by looking at pka values . down here is the hydroxide anion , it is the conjugate base to water , but water is not a great asset , and we know that from the pka value here , so water is not great at donating a proton , which means that the hydroxide anion is not that stable , and since the hydroxide anion is not that stable , it 's not a great leaving group . so let 's go ahead and take off this arrow here , because the first step is not loss of a leaving group , the first step is a proton transfer . we have a strong acid here , sulfuric acid , and the alcohol will act as a base and take a proton from sulfuric acid . and that would form water as your leaving group , and water is a much better leaving group than the hydroxide anion , and again , we know that by pka values . water is the conjugate base to the hydronium ion , h3o+ , which is much better at donating a proton , the pka value is much , much lower . and that means that water is stable , so the first step , the first step when you are doing an e1 mechanism with an alcohol is to protonate the oh group . so here 's our alcohol , and the carbon bonded to the oh is our alpha carbon , and then these carbons next to the alpha carbon would all be beta carbons . we just saw the first step is a proton transfer , a lone pair of electrons on the oxygen take a proton from sulfuric acid , so we transfer a proton , and let 's go ahead and draw in what we would have now , so there 'd be a plus-one formal charge on the oxygen , so let 's highlight our electrons in magenta , these electrons took this proton to form this bond , and now we have water as a leaving group , let me just fix this hydrogen here really fast , and these electrons can come off onto our oxygen , so that gives us water as our leaving group , and let me go ahead and draw in the water molecule here , and let me highlight electrons , the electrons in light blue , in this bond , came off onto the oxygen , which forms water , and we know water is a good leaving group . we took a bond away from this carbon in red , so that carbon would now be a carbocation , so let me draw in our carbocation here , so the carbon in red is now positively charged , so let me draw in a plus-one formal charge on that carbon , the next step of our mechanism , we know a weak base comes along and takes a proton , one of the protons on one of the beta carbons over here , so let 's just say it 's this one , and i 'm just gon na draw in a generic base , so a generic base right here , which is gon na take this proton , and then these electrons are gon na move in to form our product , so let me draw our product in here , and let me highlight those electrons . so the electrons in , let 's use green this time , the electrons in green moved in here to form our double bond , to form our alkene . so i just put a generic base , let me go ahead and talk about the base for a second here . i just put in a generic base , sometimes you might see water acting as a base , sometimes you might see hso4- , right , the conjugate base to sulfuric acid acting as the base , different textbooks give you different things , i do n't think it really matters , but one of those acting as a weak base , it 's probably water , takes this proton to form your alkene . sometimes this reaction is called a dehydration reaction since we lost water in the process .
|
iodide is an excellent leaving group , and you know that by looking at pka values . the iodide anion is the conjugate base of a very strong acid , hi , with a approximate pka value of negative 11 , so hi is very good at donating a proton , which must mean that the conjugate base is very stable , so the iodide anion is an excellent leaving group . so if we lose the iodide anion , that means we 're gon na have a carbocation , so we lost a bond to this carbon in red , so we 're gon na form a carbocation , let me go ahead and draw that in , so this is a planar carbocation , and so the carbon , let me go ahead and highlight it here , the carbon in red has a plus one formal charge , it lost a bond .
|
does this mean there is a small amount of ethylene in a cocktail drink with lemon juice ?
|
let 's look at the mechanism for an e1 elimination reaction , and we 'll start with our substrate , so on the left . let 's say we 're dealing with alkyl halide . so the carbon that 's bonded to our halogen would be the alpha carbon , and the carbon next to that carbon would be the beta carbon , so we need a beta hydrogen for this reaction . the first step of an e1 elimination mechanism is loss of our leaving group , so loss of leaving group , let me just write that in here really quickly , and in this case , the electrons would come off onto our leaving group in the first step of the mechanism . so we 're taking a bond away from this carbon , the one that i 've circled in red here , so that carbon is going from being sp3 hybridized to being sp2 hybridized . so now we have a carbocation , and we know that carbocations , sp2 hybridized carbons have planar geometry around them , so i 've attempted to show the planar geometry around this carbocation . so that 's the first step , loss of the leaving group to form a carbocation . in the second step , our base comes along and takes this proton , which leaves these electrons behind , and those electrons move in to form our alkene , so this is the second step of the mechanism , which is the base takes , or abstracts , a proton , so base takes a proton to form our alkene . and let me go ahead and highlight those electrons , so these electrons here in magenta moved in to form our double bond , and we form our product , we form our alkene . so the first step of the mechanism , the loss of the leaving group , this turns out to be the rate determining step , so this is the slowest step of the mechanism . so if you 're writing a rate law , the rate of this reaction would be equal to the rate constant k times the concentration of your substrate , so that 's what studies have shown , that these mechanisms depend on the concentration of only your substrate , this over here on the left , so it 's first order with respect to the substrate . and that 's because of this rate determining step . the loss of the leaving group is the rate determining step , and so the concentration of your substrate , your starting material , that 's what matters . your base ca n't do anything until you lose your leaving group . and so , since the base does not participate in the rate determining step , it participates in the second step , the concentration of the base has no effect on the rate of the reaction , so it 's the concentration of the substrate only , and since it 's only dependent on the concentration of the substrate , that 's where the one comes from in e1 , so i 'm gon na go ahead and write this out here , so in e1 mechanism , the one comes from the fact this is a unimolecular , a unimolecular rate law here , and the e comes from the fact that this is an elimination reaction , so when you see e1 , that 's what you 're thinking about , it 's an elimination reaction , and it 's unimolecular , the overall rate of the reaction only depends on the concentration of your substrate , so if you increase , let 's say you have , let 's say this was your substrate right here , and you increase the concentration of your substrate , let me just write this down , so if you increase the concentration of your substrate by a factor of two , you would also increase the rate of reaction by a factor of two , so it 's first order with respect to the substrate , so this is some general chemistry here . if you increase the concentration of your base by a factor of two , you would have no effect on the overall rate of the reaction . so let 's talk about one more point here in the mechanism , and that is the formation of this carbocation . since we have a carbocation in this mechanism , we need to think about the possibility of rearrangements in the mechanism , and you need to think what would form , what substrate would form a stable carbocation , so something like a tertiary substrate forming a tertiary carbocation would be favorable for an e1 mechanism . here we have a tertiary alkyl halides , and let 's say this tertiary alkyl halide undergoes an e1 elimination reaction . so the carbon that 's bonded to the iodine must be our alpha carbon , and then we would have three beta carbons , so that 's a beta carbon , that 's a beta carbon , and that 's a beta carbon . so the first step in an e1 mechanism is loss of our leaving group , so if i draw the lone pairs of electrons in here on iodine , i know that these electrons in this bond would come off onto iodine to form the iodide anion , so let me draw that in here , so we would make the iodide anion , and let me highlight our electron , so the electrons in this bond come off onto the iodine to form the iodide anion . and this is an excellent leaving group . iodide is an excellent leaving group , and you know that by looking at pka values . the iodide anion is the conjugate base of a very strong acid , hi , with a approximate pka value of negative 11 , so hi is very good at donating a proton , which must mean that the conjugate base is very stable , so the iodide anion is an excellent leaving group . so if we lose the iodide anion , that means we 're gon na have a carbocation , so we lost a bond to this carbon in red , so we 're gon na form a carbocation , let me go ahead and draw that in , so this is a planar carbocation , and so the carbon , let me go ahead and highlight it here , the carbon in red has a plus one formal charge , it lost a bond . so that 's the first step of an e1 elimination mechanism . the second step of an e1 elimination mechanism is the base comes along , and it takes a proton from a beta carbon , so our base in this case would be ethanol , so let me go ahead and draw in lone pairs of electrons on the oxygen , so notice we 're also heating this reaction , so the ethanol is gon na function as a base , so ethanol 's not a strong base , but it can take a proton , so let me go ahead and draw in a proton right here , and a lone pair of electrons on the oxygen is going to take this proton , and the electrons would move into here to form our alkene , so let me go ahead and draw our product , let me put that in here , and let me highlight some electrons , so the electrons in blue moved in here to form our double bond . so a couple of points about this reaction , one point is , when you 're looking at sn1 mechanisms , the first step is loss of a leaving group to form your carbocation , so when you get to this carbocation , you might think , well , why is ethanol acting as a base here ? why could n't it act as a nucleophile ? and the answer is , the ethanol certainly can act as a nucleophile , and it would attack the positively-charged carbon , and you would definitely get a substitution product for this reaction as well , so if ethanol acts as a nucleophile , you 're gon na get a substitution reaction , an sn1 mechanism . if the ethanol acts as a base , you 're gon na get an e1 elimination mechanism , so here , we 're just gon na focus on the elimination product , and we wo n't worry about the substitution product , but we will talk about this stuff in a later video , 'cause that would definitely happen . alright , something else i wan na talk about is we had three beta carbons over here , and if i look at these three beta carbons , and i just picked one of them , i just said that this carbon right here , let me highlight it , i just took a proton from this carbon , but it does n't matter which of those carbons that we take a proton off because of symmetry , let me go ahead and draw this in over here , so this is my carbocation , let 's say , and let 's say we took a proton from this carbon , so our weak base comes along , and takes a proton from here , and these electrons have moved into here , that would give us the same product , right ? so this would be , let me go and highlight those electrons , so these electrons in dark blue would move in to form our double bond , but this is the same as that product . alcohols can also react via an e1 mechanism . the carbon that 's bonded to the oh would be the alpha carbon , and the carbon next to that would be the beta carbon , so reacting an alcohol with sulfuric acid and heating up your reaction mixture will give you an alkene , and sometimes , phosphoric acid is used instead of sulfuric acid . so we saw the first step of an e1 mechanism was loss of a leaving group , but if that happens here , if these electrons come off onto the oxygen , that would form hydroxide as your leaving group , and the hydroxide anion is a poor leaving group , and we know that by looking at pka values . down here is the hydroxide anion , it is the conjugate base to water , but water is not a great asset , and we know that from the pka value here , so water is not great at donating a proton , which means that the hydroxide anion is not that stable , and since the hydroxide anion is not that stable , it 's not a great leaving group . so let 's go ahead and take off this arrow here , because the first step is not loss of a leaving group , the first step is a proton transfer . we have a strong acid here , sulfuric acid , and the alcohol will act as a base and take a proton from sulfuric acid . and that would form water as your leaving group , and water is a much better leaving group than the hydroxide anion , and again , we know that by pka values . water is the conjugate base to the hydronium ion , h3o+ , which is much better at donating a proton , the pka value is much , much lower . and that means that water is stable , so the first step , the first step when you are doing an e1 mechanism with an alcohol is to protonate the oh group . so here 's our alcohol , and the carbon bonded to the oh is our alpha carbon , and then these carbons next to the alpha carbon would all be beta carbons . we just saw the first step is a proton transfer , a lone pair of electrons on the oxygen take a proton from sulfuric acid , so we transfer a proton , and let 's go ahead and draw in what we would have now , so there 'd be a plus-one formal charge on the oxygen , so let 's highlight our electrons in magenta , these electrons took this proton to form this bond , and now we have water as a leaving group , let me just fix this hydrogen here really fast , and these electrons can come off onto our oxygen , so that gives us water as our leaving group , and let me go ahead and draw in the water molecule here , and let me highlight electrons , the electrons in light blue , in this bond , came off onto the oxygen , which forms water , and we know water is a good leaving group . we took a bond away from this carbon in red , so that carbon would now be a carbocation , so let me draw in our carbocation here , so the carbon in red is now positively charged , so let me draw in a plus-one formal charge on that carbon , the next step of our mechanism , we know a weak base comes along and takes a proton , one of the protons on one of the beta carbons over here , so let 's just say it 's this one , and i 'm just gon na draw in a generic base , so a generic base right here , which is gon na take this proton , and then these electrons are gon na move in to form our product , so let me draw our product in here , and let me highlight those electrons . so the electrons in , let 's use green this time , the electrons in green moved in here to form our double bond , to form our alkene . so i just put a generic base , let me go ahead and talk about the base for a second here . i just put in a generic base , sometimes you might see water acting as a base , sometimes you might see hso4- , right , the conjugate base to sulfuric acid acting as the base , different textbooks give you different things , i do n't think it really matters , but one of those acting as a weak base , it 's probably water , takes this proton to form your alkene . sometimes this reaction is called a dehydration reaction since we lost water in the process .
|
so a couple of points about this reaction , one point is , when you 're looking at sn1 mechanisms , the first step is loss of a leaving group to form your carbocation , so when you get to this carbocation , you might think , well , why is ethanol acting as a base here ? why could n't it act as a nucleophile ? and the answer is , the ethanol certainly can act as a nucleophile , and it would attack the positively-charged carbon , and you would definitely get a substitution product for this reaction as well , so if ethanol acts as a nucleophile , you 're gon na get a substitution reaction , an sn1 mechanism .
|
i know ethanol could n't form really stable carbocations as it only has primary carbons , but could the protons from the citric acid carboxyl groups knock off the oh ?
|
let 's look at the mechanism for an e1 elimination reaction , and we 'll start with our substrate , so on the left . let 's say we 're dealing with alkyl halide . so the carbon that 's bonded to our halogen would be the alpha carbon , and the carbon next to that carbon would be the beta carbon , so we need a beta hydrogen for this reaction . the first step of an e1 elimination mechanism is loss of our leaving group , so loss of leaving group , let me just write that in here really quickly , and in this case , the electrons would come off onto our leaving group in the first step of the mechanism . so we 're taking a bond away from this carbon , the one that i 've circled in red here , so that carbon is going from being sp3 hybridized to being sp2 hybridized . so now we have a carbocation , and we know that carbocations , sp2 hybridized carbons have planar geometry around them , so i 've attempted to show the planar geometry around this carbocation . so that 's the first step , loss of the leaving group to form a carbocation . in the second step , our base comes along and takes this proton , which leaves these electrons behind , and those electrons move in to form our alkene , so this is the second step of the mechanism , which is the base takes , or abstracts , a proton , so base takes a proton to form our alkene . and let me go ahead and highlight those electrons , so these electrons here in magenta moved in to form our double bond , and we form our product , we form our alkene . so the first step of the mechanism , the loss of the leaving group , this turns out to be the rate determining step , so this is the slowest step of the mechanism . so if you 're writing a rate law , the rate of this reaction would be equal to the rate constant k times the concentration of your substrate , so that 's what studies have shown , that these mechanisms depend on the concentration of only your substrate , this over here on the left , so it 's first order with respect to the substrate . and that 's because of this rate determining step . the loss of the leaving group is the rate determining step , and so the concentration of your substrate , your starting material , that 's what matters . your base ca n't do anything until you lose your leaving group . and so , since the base does not participate in the rate determining step , it participates in the second step , the concentration of the base has no effect on the rate of the reaction , so it 's the concentration of the substrate only , and since it 's only dependent on the concentration of the substrate , that 's where the one comes from in e1 , so i 'm gon na go ahead and write this out here , so in e1 mechanism , the one comes from the fact this is a unimolecular , a unimolecular rate law here , and the e comes from the fact that this is an elimination reaction , so when you see e1 , that 's what you 're thinking about , it 's an elimination reaction , and it 's unimolecular , the overall rate of the reaction only depends on the concentration of your substrate , so if you increase , let 's say you have , let 's say this was your substrate right here , and you increase the concentration of your substrate , let me just write this down , so if you increase the concentration of your substrate by a factor of two , you would also increase the rate of reaction by a factor of two , so it 's first order with respect to the substrate , so this is some general chemistry here . if you increase the concentration of your base by a factor of two , you would have no effect on the overall rate of the reaction . so let 's talk about one more point here in the mechanism , and that is the formation of this carbocation . since we have a carbocation in this mechanism , we need to think about the possibility of rearrangements in the mechanism , and you need to think what would form , what substrate would form a stable carbocation , so something like a tertiary substrate forming a tertiary carbocation would be favorable for an e1 mechanism . here we have a tertiary alkyl halides , and let 's say this tertiary alkyl halide undergoes an e1 elimination reaction . so the carbon that 's bonded to the iodine must be our alpha carbon , and then we would have three beta carbons , so that 's a beta carbon , that 's a beta carbon , and that 's a beta carbon . so the first step in an e1 mechanism is loss of our leaving group , so if i draw the lone pairs of electrons in here on iodine , i know that these electrons in this bond would come off onto iodine to form the iodide anion , so let me draw that in here , so we would make the iodide anion , and let me highlight our electron , so the electrons in this bond come off onto the iodine to form the iodide anion . and this is an excellent leaving group . iodide is an excellent leaving group , and you know that by looking at pka values . the iodide anion is the conjugate base of a very strong acid , hi , with a approximate pka value of negative 11 , so hi is very good at donating a proton , which must mean that the conjugate base is very stable , so the iodide anion is an excellent leaving group . so if we lose the iodide anion , that means we 're gon na have a carbocation , so we lost a bond to this carbon in red , so we 're gon na form a carbocation , let me go ahead and draw that in , so this is a planar carbocation , and so the carbon , let me go ahead and highlight it here , the carbon in red has a plus one formal charge , it lost a bond . so that 's the first step of an e1 elimination mechanism . the second step of an e1 elimination mechanism is the base comes along , and it takes a proton from a beta carbon , so our base in this case would be ethanol , so let me go ahead and draw in lone pairs of electrons on the oxygen , so notice we 're also heating this reaction , so the ethanol is gon na function as a base , so ethanol 's not a strong base , but it can take a proton , so let me go ahead and draw in a proton right here , and a lone pair of electrons on the oxygen is going to take this proton , and the electrons would move into here to form our alkene , so let me go ahead and draw our product , let me put that in here , and let me highlight some electrons , so the electrons in blue moved in here to form our double bond . so a couple of points about this reaction , one point is , when you 're looking at sn1 mechanisms , the first step is loss of a leaving group to form your carbocation , so when you get to this carbocation , you might think , well , why is ethanol acting as a base here ? why could n't it act as a nucleophile ? and the answer is , the ethanol certainly can act as a nucleophile , and it would attack the positively-charged carbon , and you would definitely get a substitution product for this reaction as well , so if ethanol acts as a nucleophile , you 're gon na get a substitution reaction , an sn1 mechanism . if the ethanol acts as a base , you 're gon na get an e1 elimination mechanism , so here , we 're just gon na focus on the elimination product , and we wo n't worry about the substitution product , but we will talk about this stuff in a later video , 'cause that would definitely happen . alright , something else i wan na talk about is we had three beta carbons over here , and if i look at these three beta carbons , and i just picked one of them , i just said that this carbon right here , let me highlight it , i just took a proton from this carbon , but it does n't matter which of those carbons that we take a proton off because of symmetry , let me go ahead and draw this in over here , so this is my carbocation , let 's say , and let 's say we took a proton from this carbon , so our weak base comes along , and takes a proton from here , and these electrons have moved into here , that would give us the same product , right ? so this would be , let me go and highlight those electrons , so these electrons in dark blue would move in to form our double bond , but this is the same as that product . alcohols can also react via an e1 mechanism . the carbon that 's bonded to the oh would be the alpha carbon , and the carbon next to that would be the beta carbon , so reacting an alcohol with sulfuric acid and heating up your reaction mixture will give you an alkene , and sometimes , phosphoric acid is used instead of sulfuric acid . so we saw the first step of an e1 mechanism was loss of a leaving group , but if that happens here , if these electrons come off onto the oxygen , that would form hydroxide as your leaving group , and the hydroxide anion is a poor leaving group , and we know that by looking at pka values . down here is the hydroxide anion , it is the conjugate base to water , but water is not a great asset , and we know that from the pka value here , so water is not great at donating a proton , which means that the hydroxide anion is not that stable , and since the hydroxide anion is not that stable , it 's not a great leaving group . so let 's go ahead and take off this arrow here , because the first step is not loss of a leaving group , the first step is a proton transfer . we have a strong acid here , sulfuric acid , and the alcohol will act as a base and take a proton from sulfuric acid . and that would form water as your leaving group , and water is a much better leaving group than the hydroxide anion , and again , we know that by pka values . water is the conjugate base to the hydronium ion , h3o+ , which is much better at donating a proton , the pka value is much , much lower . and that means that water is stable , so the first step , the first step when you are doing an e1 mechanism with an alcohol is to protonate the oh group . so here 's our alcohol , and the carbon bonded to the oh is our alpha carbon , and then these carbons next to the alpha carbon would all be beta carbons . we just saw the first step is a proton transfer , a lone pair of electrons on the oxygen take a proton from sulfuric acid , so we transfer a proton , and let 's go ahead and draw in what we would have now , so there 'd be a plus-one formal charge on the oxygen , so let 's highlight our electrons in magenta , these electrons took this proton to form this bond , and now we have water as a leaving group , let me just fix this hydrogen here really fast , and these electrons can come off onto our oxygen , so that gives us water as our leaving group , and let me go ahead and draw in the water molecule here , and let me highlight electrons , the electrons in light blue , in this bond , came off onto the oxygen , which forms water , and we know water is a good leaving group . we took a bond away from this carbon in red , so that carbon would now be a carbocation , so let me draw in our carbocation here , so the carbon in red is now positively charged , so let me draw in a plus-one formal charge on that carbon , the next step of our mechanism , we know a weak base comes along and takes a proton , one of the protons on one of the beta carbons over here , so let 's just say it 's this one , and i 'm just gon na draw in a generic base , so a generic base right here , which is gon na take this proton , and then these electrons are gon na move in to form our product , so let me draw our product in here , and let me highlight those electrons . so the electrons in , let 's use green this time , the electrons in green moved in here to form our double bond , to form our alkene . so i just put a generic base , let me go ahead and talk about the base for a second here . i just put in a generic base , sometimes you might see water acting as a base , sometimes you might see hso4- , right , the conjugate base to sulfuric acid acting as the base , different textbooks give you different things , i do n't think it really matters , but one of those acting as a weak base , it 's probably water , takes this proton to form your alkene . sometimes this reaction is called a dehydration reaction since we lost water in the process .
|
so a couple of points about this reaction , one point is , when you 're looking at sn1 mechanisms , the first step is loss of a leaving group to form your carbocation , so when you get to this carbocation , you might think , well , why is ethanol acting as a base here ? why could n't it act as a nucleophile ? and the answer is , the ethanol certainly can act as a nucleophile , and it would attack the positively-charged carbon , and you would definitely get a substitution product for this reaction as well , so if ethanol acts as a nucleophile , you 're gon na get a substitution reaction , an sn1 mechanism .
|
could n't an sn1 reaction occur ?
|
let 's look at the mechanism for an e1 elimination reaction , and we 'll start with our substrate , so on the left . let 's say we 're dealing with alkyl halide . so the carbon that 's bonded to our halogen would be the alpha carbon , and the carbon next to that carbon would be the beta carbon , so we need a beta hydrogen for this reaction . the first step of an e1 elimination mechanism is loss of our leaving group , so loss of leaving group , let me just write that in here really quickly , and in this case , the electrons would come off onto our leaving group in the first step of the mechanism . so we 're taking a bond away from this carbon , the one that i 've circled in red here , so that carbon is going from being sp3 hybridized to being sp2 hybridized . so now we have a carbocation , and we know that carbocations , sp2 hybridized carbons have planar geometry around them , so i 've attempted to show the planar geometry around this carbocation . so that 's the first step , loss of the leaving group to form a carbocation . in the second step , our base comes along and takes this proton , which leaves these electrons behind , and those electrons move in to form our alkene , so this is the second step of the mechanism , which is the base takes , or abstracts , a proton , so base takes a proton to form our alkene . and let me go ahead and highlight those electrons , so these electrons here in magenta moved in to form our double bond , and we form our product , we form our alkene . so the first step of the mechanism , the loss of the leaving group , this turns out to be the rate determining step , so this is the slowest step of the mechanism . so if you 're writing a rate law , the rate of this reaction would be equal to the rate constant k times the concentration of your substrate , so that 's what studies have shown , that these mechanisms depend on the concentration of only your substrate , this over here on the left , so it 's first order with respect to the substrate . and that 's because of this rate determining step . the loss of the leaving group is the rate determining step , and so the concentration of your substrate , your starting material , that 's what matters . your base ca n't do anything until you lose your leaving group . and so , since the base does not participate in the rate determining step , it participates in the second step , the concentration of the base has no effect on the rate of the reaction , so it 's the concentration of the substrate only , and since it 's only dependent on the concentration of the substrate , that 's where the one comes from in e1 , so i 'm gon na go ahead and write this out here , so in e1 mechanism , the one comes from the fact this is a unimolecular , a unimolecular rate law here , and the e comes from the fact that this is an elimination reaction , so when you see e1 , that 's what you 're thinking about , it 's an elimination reaction , and it 's unimolecular , the overall rate of the reaction only depends on the concentration of your substrate , so if you increase , let 's say you have , let 's say this was your substrate right here , and you increase the concentration of your substrate , let me just write this down , so if you increase the concentration of your substrate by a factor of two , you would also increase the rate of reaction by a factor of two , so it 's first order with respect to the substrate , so this is some general chemistry here . if you increase the concentration of your base by a factor of two , you would have no effect on the overall rate of the reaction . so let 's talk about one more point here in the mechanism , and that is the formation of this carbocation . since we have a carbocation in this mechanism , we need to think about the possibility of rearrangements in the mechanism , and you need to think what would form , what substrate would form a stable carbocation , so something like a tertiary substrate forming a tertiary carbocation would be favorable for an e1 mechanism . here we have a tertiary alkyl halides , and let 's say this tertiary alkyl halide undergoes an e1 elimination reaction . so the carbon that 's bonded to the iodine must be our alpha carbon , and then we would have three beta carbons , so that 's a beta carbon , that 's a beta carbon , and that 's a beta carbon . so the first step in an e1 mechanism is loss of our leaving group , so if i draw the lone pairs of electrons in here on iodine , i know that these electrons in this bond would come off onto iodine to form the iodide anion , so let me draw that in here , so we would make the iodide anion , and let me highlight our electron , so the electrons in this bond come off onto the iodine to form the iodide anion . and this is an excellent leaving group . iodide is an excellent leaving group , and you know that by looking at pka values . the iodide anion is the conjugate base of a very strong acid , hi , with a approximate pka value of negative 11 , so hi is very good at donating a proton , which must mean that the conjugate base is very stable , so the iodide anion is an excellent leaving group . so if we lose the iodide anion , that means we 're gon na have a carbocation , so we lost a bond to this carbon in red , so we 're gon na form a carbocation , let me go ahead and draw that in , so this is a planar carbocation , and so the carbon , let me go ahead and highlight it here , the carbon in red has a plus one formal charge , it lost a bond . so that 's the first step of an e1 elimination mechanism . the second step of an e1 elimination mechanism is the base comes along , and it takes a proton from a beta carbon , so our base in this case would be ethanol , so let me go ahead and draw in lone pairs of electrons on the oxygen , so notice we 're also heating this reaction , so the ethanol is gon na function as a base , so ethanol 's not a strong base , but it can take a proton , so let me go ahead and draw in a proton right here , and a lone pair of electrons on the oxygen is going to take this proton , and the electrons would move into here to form our alkene , so let me go ahead and draw our product , let me put that in here , and let me highlight some electrons , so the electrons in blue moved in here to form our double bond . so a couple of points about this reaction , one point is , when you 're looking at sn1 mechanisms , the first step is loss of a leaving group to form your carbocation , so when you get to this carbocation , you might think , well , why is ethanol acting as a base here ? why could n't it act as a nucleophile ? and the answer is , the ethanol certainly can act as a nucleophile , and it would attack the positively-charged carbon , and you would definitely get a substitution product for this reaction as well , so if ethanol acts as a nucleophile , you 're gon na get a substitution reaction , an sn1 mechanism . if the ethanol acts as a base , you 're gon na get an e1 elimination mechanism , so here , we 're just gon na focus on the elimination product , and we wo n't worry about the substitution product , but we will talk about this stuff in a later video , 'cause that would definitely happen . alright , something else i wan na talk about is we had three beta carbons over here , and if i look at these three beta carbons , and i just picked one of them , i just said that this carbon right here , let me highlight it , i just took a proton from this carbon , but it does n't matter which of those carbons that we take a proton off because of symmetry , let me go ahead and draw this in over here , so this is my carbocation , let 's say , and let 's say we took a proton from this carbon , so our weak base comes along , and takes a proton from here , and these electrons have moved into here , that would give us the same product , right ? so this would be , let me go and highlight those electrons , so these electrons in dark blue would move in to form our double bond , but this is the same as that product . alcohols can also react via an e1 mechanism . the carbon that 's bonded to the oh would be the alpha carbon , and the carbon next to that would be the beta carbon , so reacting an alcohol with sulfuric acid and heating up your reaction mixture will give you an alkene , and sometimes , phosphoric acid is used instead of sulfuric acid . so we saw the first step of an e1 mechanism was loss of a leaving group , but if that happens here , if these electrons come off onto the oxygen , that would form hydroxide as your leaving group , and the hydroxide anion is a poor leaving group , and we know that by looking at pka values . down here is the hydroxide anion , it is the conjugate base to water , but water is not a great asset , and we know that from the pka value here , so water is not great at donating a proton , which means that the hydroxide anion is not that stable , and since the hydroxide anion is not that stable , it 's not a great leaving group . so let 's go ahead and take off this arrow here , because the first step is not loss of a leaving group , the first step is a proton transfer . we have a strong acid here , sulfuric acid , and the alcohol will act as a base and take a proton from sulfuric acid . and that would form water as your leaving group , and water is a much better leaving group than the hydroxide anion , and again , we know that by pka values . water is the conjugate base to the hydronium ion , h3o+ , which is much better at donating a proton , the pka value is much , much lower . and that means that water is stable , so the first step , the first step when you are doing an e1 mechanism with an alcohol is to protonate the oh group . so here 's our alcohol , and the carbon bonded to the oh is our alpha carbon , and then these carbons next to the alpha carbon would all be beta carbons . we just saw the first step is a proton transfer , a lone pair of electrons on the oxygen take a proton from sulfuric acid , so we transfer a proton , and let 's go ahead and draw in what we would have now , so there 'd be a plus-one formal charge on the oxygen , so let 's highlight our electrons in magenta , these electrons took this proton to form this bond , and now we have water as a leaving group , let me just fix this hydrogen here really fast , and these electrons can come off onto our oxygen , so that gives us water as our leaving group , and let me go ahead and draw in the water molecule here , and let me highlight electrons , the electrons in light blue , in this bond , came off onto the oxygen , which forms water , and we know water is a good leaving group . we took a bond away from this carbon in red , so that carbon would now be a carbocation , so let me draw in our carbocation here , so the carbon in red is now positively charged , so let me draw in a plus-one formal charge on that carbon , the next step of our mechanism , we know a weak base comes along and takes a proton , one of the protons on one of the beta carbons over here , so let 's just say it 's this one , and i 'm just gon na draw in a generic base , so a generic base right here , which is gon na take this proton , and then these electrons are gon na move in to form our product , so let me draw our product in here , and let me highlight those electrons . so the electrons in , let 's use green this time , the electrons in green moved in here to form our double bond , to form our alkene . so i just put a generic base , let me go ahead and talk about the base for a second here . i just put in a generic base , sometimes you might see water acting as a base , sometimes you might see hso4- , right , the conjugate base to sulfuric acid acting as the base , different textbooks give you different things , i do n't think it really matters , but one of those acting as a weak base , it 's probably water , takes this proton to form your alkene . sometimes this reaction is called a dehydration reaction since we lost water in the process .
|
in the second step , our base comes along and takes this proton , which leaves these electrons behind , and those electrons move in to form our alkene , so this is the second step of the mechanism , which is the base takes , or abstracts , a proton , so base takes a proton to form our alkene . and let me go ahead and highlight those electrons , so these electrons here in magenta moved in to form our double bond , and we form our product , we form our alkene . so the first step of the mechanism , the loss of the leaving group , this turns out to be the rate determining step , so this is the slowest step of the mechanism .
|
how is it that we determine that an alkene will form instead of 1-methyl 1-ethoxycyclohexane ?
|
let 's look at the mechanism for an e1 elimination reaction , and we 'll start with our substrate , so on the left . let 's say we 're dealing with alkyl halide . so the carbon that 's bonded to our halogen would be the alpha carbon , and the carbon next to that carbon would be the beta carbon , so we need a beta hydrogen for this reaction . the first step of an e1 elimination mechanism is loss of our leaving group , so loss of leaving group , let me just write that in here really quickly , and in this case , the electrons would come off onto our leaving group in the first step of the mechanism . so we 're taking a bond away from this carbon , the one that i 've circled in red here , so that carbon is going from being sp3 hybridized to being sp2 hybridized . so now we have a carbocation , and we know that carbocations , sp2 hybridized carbons have planar geometry around them , so i 've attempted to show the planar geometry around this carbocation . so that 's the first step , loss of the leaving group to form a carbocation . in the second step , our base comes along and takes this proton , which leaves these electrons behind , and those electrons move in to form our alkene , so this is the second step of the mechanism , which is the base takes , or abstracts , a proton , so base takes a proton to form our alkene . and let me go ahead and highlight those electrons , so these electrons here in magenta moved in to form our double bond , and we form our product , we form our alkene . so the first step of the mechanism , the loss of the leaving group , this turns out to be the rate determining step , so this is the slowest step of the mechanism . so if you 're writing a rate law , the rate of this reaction would be equal to the rate constant k times the concentration of your substrate , so that 's what studies have shown , that these mechanisms depend on the concentration of only your substrate , this over here on the left , so it 's first order with respect to the substrate . and that 's because of this rate determining step . the loss of the leaving group is the rate determining step , and so the concentration of your substrate , your starting material , that 's what matters . your base ca n't do anything until you lose your leaving group . and so , since the base does not participate in the rate determining step , it participates in the second step , the concentration of the base has no effect on the rate of the reaction , so it 's the concentration of the substrate only , and since it 's only dependent on the concentration of the substrate , that 's where the one comes from in e1 , so i 'm gon na go ahead and write this out here , so in e1 mechanism , the one comes from the fact this is a unimolecular , a unimolecular rate law here , and the e comes from the fact that this is an elimination reaction , so when you see e1 , that 's what you 're thinking about , it 's an elimination reaction , and it 's unimolecular , the overall rate of the reaction only depends on the concentration of your substrate , so if you increase , let 's say you have , let 's say this was your substrate right here , and you increase the concentration of your substrate , let me just write this down , so if you increase the concentration of your substrate by a factor of two , you would also increase the rate of reaction by a factor of two , so it 's first order with respect to the substrate , so this is some general chemistry here . if you increase the concentration of your base by a factor of two , you would have no effect on the overall rate of the reaction . so let 's talk about one more point here in the mechanism , and that is the formation of this carbocation . since we have a carbocation in this mechanism , we need to think about the possibility of rearrangements in the mechanism , and you need to think what would form , what substrate would form a stable carbocation , so something like a tertiary substrate forming a tertiary carbocation would be favorable for an e1 mechanism . here we have a tertiary alkyl halides , and let 's say this tertiary alkyl halide undergoes an e1 elimination reaction . so the carbon that 's bonded to the iodine must be our alpha carbon , and then we would have three beta carbons , so that 's a beta carbon , that 's a beta carbon , and that 's a beta carbon . so the first step in an e1 mechanism is loss of our leaving group , so if i draw the lone pairs of electrons in here on iodine , i know that these electrons in this bond would come off onto iodine to form the iodide anion , so let me draw that in here , so we would make the iodide anion , and let me highlight our electron , so the electrons in this bond come off onto the iodine to form the iodide anion . and this is an excellent leaving group . iodide is an excellent leaving group , and you know that by looking at pka values . the iodide anion is the conjugate base of a very strong acid , hi , with a approximate pka value of negative 11 , so hi is very good at donating a proton , which must mean that the conjugate base is very stable , so the iodide anion is an excellent leaving group . so if we lose the iodide anion , that means we 're gon na have a carbocation , so we lost a bond to this carbon in red , so we 're gon na form a carbocation , let me go ahead and draw that in , so this is a planar carbocation , and so the carbon , let me go ahead and highlight it here , the carbon in red has a plus one formal charge , it lost a bond . so that 's the first step of an e1 elimination mechanism . the second step of an e1 elimination mechanism is the base comes along , and it takes a proton from a beta carbon , so our base in this case would be ethanol , so let me go ahead and draw in lone pairs of electrons on the oxygen , so notice we 're also heating this reaction , so the ethanol is gon na function as a base , so ethanol 's not a strong base , but it can take a proton , so let me go ahead and draw in a proton right here , and a lone pair of electrons on the oxygen is going to take this proton , and the electrons would move into here to form our alkene , so let me go ahead and draw our product , let me put that in here , and let me highlight some electrons , so the electrons in blue moved in here to form our double bond . so a couple of points about this reaction , one point is , when you 're looking at sn1 mechanisms , the first step is loss of a leaving group to form your carbocation , so when you get to this carbocation , you might think , well , why is ethanol acting as a base here ? why could n't it act as a nucleophile ? and the answer is , the ethanol certainly can act as a nucleophile , and it would attack the positively-charged carbon , and you would definitely get a substitution product for this reaction as well , so if ethanol acts as a nucleophile , you 're gon na get a substitution reaction , an sn1 mechanism . if the ethanol acts as a base , you 're gon na get an e1 elimination mechanism , so here , we 're just gon na focus on the elimination product , and we wo n't worry about the substitution product , but we will talk about this stuff in a later video , 'cause that would definitely happen . alright , something else i wan na talk about is we had three beta carbons over here , and if i look at these three beta carbons , and i just picked one of them , i just said that this carbon right here , let me highlight it , i just took a proton from this carbon , but it does n't matter which of those carbons that we take a proton off because of symmetry , let me go ahead and draw this in over here , so this is my carbocation , let 's say , and let 's say we took a proton from this carbon , so our weak base comes along , and takes a proton from here , and these electrons have moved into here , that would give us the same product , right ? so this would be , let me go and highlight those electrons , so these electrons in dark blue would move in to form our double bond , but this is the same as that product . alcohols can also react via an e1 mechanism . the carbon that 's bonded to the oh would be the alpha carbon , and the carbon next to that would be the beta carbon , so reacting an alcohol with sulfuric acid and heating up your reaction mixture will give you an alkene , and sometimes , phosphoric acid is used instead of sulfuric acid . so we saw the first step of an e1 mechanism was loss of a leaving group , but if that happens here , if these electrons come off onto the oxygen , that would form hydroxide as your leaving group , and the hydroxide anion is a poor leaving group , and we know that by looking at pka values . down here is the hydroxide anion , it is the conjugate base to water , but water is not a great asset , and we know that from the pka value here , so water is not great at donating a proton , which means that the hydroxide anion is not that stable , and since the hydroxide anion is not that stable , it 's not a great leaving group . so let 's go ahead and take off this arrow here , because the first step is not loss of a leaving group , the first step is a proton transfer . we have a strong acid here , sulfuric acid , and the alcohol will act as a base and take a proton from sulfuric acid . and that would form water as your leaving group , and water is a much better leaving group than the hydroxide anion , and again , we know that by pka values . water is the conjugate base to the hydronium ion , h3o+ , which is much better at donating a proton , the pka value is much , much lower . and that means that water is stable , so the first step , the first step when you are doing an e1 mechanism with an alcohol is to protonate the oh group . so here 's our alcohol , and the carbon bonded to the oh is our alpha carbon , and then these carbons next to the alpha carbon would all be beta carbons . we just saw the first step is a proton transfer , a lone pair of electrons on the oxygen take a proton from sulfuric acid , so we transfer a proton , and let 's go ahead and draw in what we would have now , so there 'd be a plus-one formal charge on the oxygen , so let 's highlight our electrons in magenta , these electrons took this proton to form this bond , and now we have water as a leaving group , let me just fix this hydrogen here really fast , and these electrons can come off onto our oxygen , so that gives us water as our leaving group , and let me go ahead and draw in the water molecule here , and let me highlight electrons , the electrons in light blue , in this bond , came off onto the oxygen , which forms water , and we know water is a good leaving group . we took a bond away from this carbon in red , so that carbon would now be a carbocation , so let me draw in our carbocation here , so the carbon in red is now positively charged , so let me draw in a plus-one formal charge on that carbon , the next step of our mechanism , we know a weak base comes along and takes a proton , one of the protons on one of the beta carbons over here , so let 's just say it 's this one , and i 'm just gon na draw in a generic base , so a generic base right here , which is gon na take this proton , and then these electrons are gon na move in to form our product , so let me draw our product in here , and let me highlight those electrons . so the electrons in , let 's use green this time , the electrons in green moved in here to form our double bond , to form our alkene . so i just put a generic base , let me go ahead and talk about the base for a second here . i just put in a generic base , sometimes you might see water acting as a base , sometimes you might see hso4- , right , the conjugate base to sulfuric acid acting as the base , different textbooks give you different things , i do n't think it really matters , but one of those acting as a weak base , it 's probably water , takes this proton to form your alkene . sometimes this reaction is called a dehydration reaction since we lost water in the process .
|
so a couple of points about this reaction , one point is , when you 're looking at sn1 mechanisms , the first step is loss of a leaving group to form your carbocation , so when you get to this carbocation , you might think , well , why is ethanol acting as a base here ? why could n't it act as a nucleophile ? and the answer is , the ethanol certainly can act as a nucleophile , and it would attack the positively-charged carbon , and you would definitely get a substitution product for this reaction as well , so if ethanol acts as a nucleophile , you 're gon na get a substitution reaction , an sn1 mechanism . if the ethanol acts as a base , you 're gon na get an e1 elimination mechanism , so here , we 're just gon na focus on the elimination product , and we wo n't worry about the substitution product , but we will talk about this stuff in a later video , 'cause that would definitely happen .
|
or is the solvent not a good nucleophile to cause a substitution reaction ?
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.