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- this is a rectangle . and yes , this is a rectangle . let 's measure the green line below using both rectangles and a centimeter ruler . so , we have this green line and we 're going to measure it in terms of rectangles and we 're going to measure it on this ruler . and you immediately see the green line is equal to ...
now , in terms of centimeters , it is four , four centimeters long . four centimeters long . the length of each rectangle is blank than a centimeter .
at 10 ; 17 , how is it 8 centimeters ?
- this is a rectangle . and yes , this is a rectangle . let 's measure the green line below using both rectangles and a centimeter ruler . so , we have this green line and we 're going to measure it in terms of rectangles and we 're going to measure it on this ruler . and you immediately see the green line is equal to ...
four centimeters long . the length of each rectangle is blank than a centimeter . well , each rectangle is more than a centimeter .
why do people use inch , centimeter or length ?
- this is a rectangle . and yes , this is a rectangle . let 's measure the green line below using both rectangles and a centimeter ruler . so , we have this green line and we 're going to measure it in terms of rectangles and we 're going to measure it on this ruler . and you immediately see the green line is equal to ...
you see , each rectangle is actually two centimeters . so , it 's longer than a centimeter . so it takes blank rectangles than centimeters to measure the line .
why do people use inch , centimeter , of lenght ?
- this is a rectangle . and yes , this is a rectangle . let 's measure the green line below using both rectangles and a centimeter ruler . so , we have this green line and we 're going to measure it in terms of rectangles and we 're going to measure it on this ruler . and you immediately see the green line is equal to ...
alright , this is a rectangle . let 's measure the green line below . same idea .
what is the most lengths you can measure with different units at once ?
- this is a rectangle . and yes , this is a rectangle . let 's measure the green line below using both rectangles and a centimeter ruler . so , we have this green line and we 're going to measure it in terms of rectangles and we 're going to measure it on this ruler . and you immediately see the green line is equal to ...
now , in terms of centimeters , it is four , four centimeters long . four centimeters long . the length of each rectangle is blank than a centimeter .
how many centimeters are in a inch ?
- this is a rectangle . and yes , this is a rectangle . let 's measure the green line below using both rectangles and a centimeter ruler . so , we have this green line and we 're going to measure it in terms of rectangles and we 're going to measure it on this ruler . and you immediately see the green line is equal to ...
- this is a rectangle . and yes , this is a rectangle .
how many different measuring systems are there ?
- this is a rectangle . and yes , this is a rectangle . let 's measure the green line below using both rectangles and a centimeter ruler . so , we have this green line and we 're going to measure it in terms of rectangles and we 're going to measure it on this ruler . and you immediately see the green line is equal to ...
let 's see . let 's do one more of these . these are a lot of fun .
how many sqare meter in one brase ?
so here i 'm gon na talk about the gradient . and in this video , i 'm only gon na describe how you compute the gradient , and in the next couple ones i 'm gon na give the geometric interpretation . and i hate doing this , i hate showing the computation before the geometric intuition since usually it should go the oth...
as far as x is concerned , the derivative of x is 2x so we see that this will be 2x times that constant sine of y , sine of y . whereas the partial derivative with respect to y . now we look up here and we say x is considered a constant so x-squared is also considered a constant so this is just a constant times sine of...
5 , when we take the derivative of f in respect to x , therefore take y = sin ( y ) as a constant , why does n't it disappear in the derivative ?
so here i 'm gon na talk about the gradient . and in this video , i 'm only gon na describe how you compute the gradient , and in the next couple ones i 'm gon na give the geometric interpretation . and i hate doing this , i hate showing the computation before the geometric intuition since usually it should go the oth...
so here i 'm gon na talk about the gradient . and in this video , i 'm only gon na describe how you compute the gradient , and in the next couple ones i 'm gon na give the geometric interpretation .
so the output of the gradient is mutlidimensional ?
so here i 'm gon na talk about the gradient . and in this video , i 'm only gon na describe how you compute the gradient , and in the next couple ones i 'm gon na give the geometric interpretation . and i hate doing this , i hate showing the computation before the geometric intuition since usually it should go the oth...
so here i 'm gon na talk about the gradient . and in this video , i 'm only gon na describe how you compute the gradient , and in the next couple ones i 'm gon na give the geometric interpretation .
what is the class code ?
so here i 'm gon na talk about the gradient . and in this video , i 'm only gon na describe how you compute the gradient , and in the next couple ones i 'm gon na give the geometric interpretation . and i hate doing this , i hate showing the computation before the geometric intuition since usually it should go the oth...
so you give this guy the function f and it gives you this expression , this multi-variable function as a result . so the nabla symbol is this vector full of different partial derivative operators . and in this case it might just be two of them , and this is kind of a weird thing because it 's like what , this is a vect...
how would you describe the way the total derivative works versus the full ( del operator ) derivative ?
so here i 'm gon na talk about the gradient . and in this video , i 'm only gon na describe how you compute the gradient , and in the next couple ones i 'm gon na give the geometric interpretation . and i hate doing this , i hate showing the computation before the geometric intuition since usually it should go the oth...
and i 'm just gon na make it a two-variable function . and let 's say it 's f of x , y , equals x-squared sine of y . the gradient is a way of packing together all the partial derivative information of a function .
how the result was square of x multply cosy , it should be siny , shouldnt it ?
so here i 'm gon na talk about the gradient . and in this video , i 'm only gon na describe how you compute the gradient , and in the next couple ones i 'm gon na give the geometric interpretation . and i hate doing this , i hate showing the computation before the geometric intuition since usually it should go the oth...
so here i 'm gon na talk about the gradient . and in this video , i 'm only gon na describe how you compute the gradient , and in the next couple ones i 'm gon na give the geometric interpretation .
please explain : why is area the opposite of gradient in calculus ?
so here i 'm gon na talk about the gradient . and in this video , i 'm only gon na describe how you compute the gradient , and in the next couple ones i 'm gon na give the geometric interpretation . and i hate doing this , i hate showing the computation before the geometric intuition since usually it should go the oth...
so the first one is the partial derivative with respect to x , to x times sine of y . and the bottom one , partial derivative with respect to y x-squared cosine of y . and notice , maybe i should emphasize , this is actually a vector-valued function .
especially when diferentiating requires one value and and intergation requires 2values ?
construct a regular hexagon inscribed inside the circle . so what i 'm going to do , first , i 'm going to draw a diameter of the circle . and actually , i 'm going to go beyond the diameter of the circle . i 'm just going to draw a line that goes through the center of the circle and just keeps on going . and i 'm goin...
radius , radius , radius . another equilateral triangle . i 've just got to do this , i have to do this four more times .
how can a polygon be equilateral and not equiangular ?
construct a regular hexagon inscribed inside the circle . so what i 'm going to do , first , i 'm going to draw a diameter of the circle . and actually , i 'm going to go beyond the diameter of the circle . i 'm just going to draw a line that goes through the center of the circle and just keeps on going . and i 'm goin...
construct a regular hexagon inscribed inside the circle . so what i 'm going to do , first , i 'm going to draw a diameter of the circle .
is there any way to construct a regular octagon inscribed in a circle ?
construct a regular hexagon inscribed inside the circle . so what i 'm going to do , first , i 'm going to draw a diameter of the circle . and actually , i 'm going to go beyond the diameter of the circle . i 'm just going to draw a line that goes through the center of the circle and just keeps on going . and i 'm goin...
construct a regular hexagon inscribed inside the circle . so what i 'm going to do , first , i 'm going to draw a diameter of the circle .
why would we even need to construct inscribed figures in real world problems ?
construct a regular hexagon inscribed inside the circle . so what i 'm going to do , first , i 'm going to draw a diameter of the circle . and actually , i 'm going to go beyond the diameter of the circle . i 'm just going to draw a line that goes through the center of the circle and just keeps on going . and i 'm goin...
so i have another equilateral triangle . radius , radius , radius . another equilateral triangle .
if you 're given the radius of the circle is there an easy formula to find the area of the hexagon without using trig ?
construct a regular hexagon inscribed inside the circle . so what i 'm going to do , first , i 'm going to draw a diameter of the circle . and actually , i 'm going to go beyond the diameter of the circle . i 'm just going to draw a line that goes through the center of the circle and just keeps on going . and i 'm goin...
but we know that these are all the lengths of the radius anyway . actually , i 'm not even having to change the length there . then , i have to just connect one more right down here .
if the length of ed is 12 , what is the length of fg ?
construct a regular hexagon inscribed inside the circle . so what i 'm going to do , first , i 'm going to draw a diameter of the circle . and actually , i 'm going to go beyond the diameter of the circle . i 'm just going to draw a line that goes through the center of the circle and just keeps on going . and i 'm goin...
construct a regular hexagon inscribed inside the circle . so what i 'm going to do , first , i 'm going to draw a diameter of the circle .
is there any other ways to draw a circle-inscribed regular hexagon ?
construct a regular hexagon inscribed inside the circle . so what i 'm going to do , first , i 'm going to draw a diameter of the circle . and actually , i 'm going to go beyond the diameter of the circle . i 'm just going to draw a line that goes through the center of the circle and just keeps on going . and i 'm goin...
construct a regular hexagon inscribed inside the circle . so what i 'm going to do , first , i 'm going to draw a diameter of the circle .
why is der no loci ( of angles ) on khan academy ?
construct a regular hexagon inscribed inside the circle . so what i 'm going to do , first , i 'm going to draw a diameter of the circle . and actually , i 'm going to go beyond the diameter of the circle . i 'm just going to draw a line that goes through the center of the circle and just keeps on going . and i 'm goin...
construct a regular hexagon inscribed inside the circle . so what i 'm going to do , first , i 'm going to draw a diameter of the circle .
what steps are different from an inscribed square ?
construct a regular hexagon inscribed inside the circle . so what i 'm going to do , first , i 'm going to draw a diameter of the circle . and actually , i 'm going to go beyond the diameter of the circle . i 'm just going to draw a line that goes through the center of the circle and just keeps on going . and i 'm goin...
construct a regular hexagon inscribed inside the circle . so what i 'm going to do , first , i 'm going to draw a diameter of the circle .
if a circle is inscribed in an hexagon , which of the following must be true ?
construct a regular hexagon inscribed inside the circle . so what i 'm going to do , first , i 'm going to draw a diameter of the circle . and actually , i 'm going to go beyond the diameter of the circle . i 'm just going to draw a line that goes through the center of the circle and just keeps on going . and i 'm goin...
and these circles are the same size . so notice , this center intersects the old circle . and the new circle itself intersects the center of the old circle . now , the reason why this is interesting , we already know that this distance , the distance between these two centers , this is equal to a radius .
can you tell me the derivation of the chord of contact of a circle ?
construct a regular hexagon inscribed inside the circle . so what i 'm going to do , first , i 'm going to draw a diameter of the circle . and actually , i 'm going to go beyond the diameter of the circle . i 'm just going to draw a line that goes through the center of the circle and just keeps on going . and i 'm goin...
construct a regular hexagon inscribed inside the circle . so what i 'm going to do , first , i 'm going to draw a diameter of the circle .
how can i use a straightedge and compass to construct a regular pentagon ?
construct a regular hexagon inscribed inside the circle . so what i 'm going to do , first , i 'm going to draw a diameter of the circle . and actually , i 'm going to go beyond the diameter of the circle . i 'm just going to draw a line that goes through the center of the circle and just keeps on going . and i 'm goin...
construct a regular hexagon inscribed inside the circle . so what i 'm going to do , first , i 'm going to draw a diameter of the circle .
how to construct a regular pentagon inscribed in a circle ?
so in this video we 're going to install the switch you see in the lower center of the screen . that 's the on off switch for bit-zee . and the first thing we need to do is just take the switch and push it through the hole that we drilled out and marked in a previous video . so we 're going to push the switch through ....
so that is the wire that came directly from our switch . and there 's our tightening down the terminal block there . the screw in the terminal block . so we have our negative wire , which has come directly from the battery .
is there an electrical reason for putting the wires in specific holes in the terminal block ?
so in this video we 're going to install the switch you see in the lower center of the screen . that 's the on off switch for bit-zee . and the first thing we need to do is just take the switch and push it through the hole that we drilled out and marked in a previous video . so we 're going to push the switch through ....
so in this video we 're going to install the switch you see in the lower center of the screen . that 's the on off switch for bit-zee .
what was the tool and ?
so how do we take our products here that we 've taken apart -- except for the bottle , which is just a recycled good -- and we want to see if we can create value by building something new out of the parts that we 've taken out of all these different components here . so what we 've done is we 've designed a new product...
and that sends a signal right here to the ir sensor . and then that communicates with the arduino board and tells the arduino board that it just got a signal . and the arduino can turn on and off different functions , so we can make bit-zee do a little dance , make its lights come on .
is the arduino board mentioned at :and the l-298 chip described reusable ?
so how do we take our products here that we 've taken apart -- except for the bottle , which is just a recycled good -- and we want to see if we can create value by building something new out of the parts that we 've taken out of all these different components here . so what we 've done is we 've designed a new product...
the resistors limit current flow , and the transistors are functioning as switches , so they allow us to control different devices , again , with our arduino here . so this is bit-zee , and bit-zee has got a personality . you can see bit-zee lights up and does different things when it gets its bumper pressed or when it...
ie once you make the bit-zee bot can you take it apart and use these components to create something else ?
so how do we take our products here that we 've taken apart -- except for the bottle , which is just a recycled good -- and we want to see if we can create value by building something new out of the parts that we 've taken out of all these different components here . so what we 've done is we 've designed a new product...
and bit-zee has a couple of switches here . there 's a switch here and a switch here , and those came out of the radio . and then you can that bit-zee 's nose came from a bottle cap , and its eyes came from a bottle cap .
what was the radio used for ?
so how do we take our products here that we 've taken apart -- except for the bottle , which is just a recycled good -- and we want to see if we can create value by building something new out of the parts that we 've taken out of all these different components here . so what we 've done is we 've designed a new product...
you can control bit-zee with a universal remote control -- the one that we took apart , actually . and that sends a signal right here to the ir sensor . and then that communicates with the arduino board and tells the arduino board that it just got a signal .
what is an ir sensor , and what does it do ?
so how do we take our products here that we 've taken apart -- except for the bottle , which is just a recycled good -- and we want to see if we can create value by building something new out of the parts that we 've taken out of all these different components here . so what we 've done is we 've designed a new product...
the resistors limit current flow , and the transistors are functioning as switches , so they allow us to control different devices , again , with our arduino here . so this is bit-zee , and bit-zee has got a personality . you can see bit-zee lights up and does different things when it gets its bumper pressed or when it...
hi , how would you view the pictures you take with the camera mounted to bit-zee ?
so how do we take our products here that we 've taken apart -- except for the bottle , which is just a recycled good -- and we want to see if we can create value by building something new out of the parts that we 've taken out of all these different components here . so what we 've done is we 've designed a new product...
the resistors limit current flow , and the transistors are functioning as switches , so they allow us to control different devices , again , with our arduino here . so this is bit-zee , and bit-zee has got a personality . you can see bit-zee lights up and does different things when it gets its bumper pressed or when it...
will they ever make another bit-zee bot like a friend for bit-zee bot ?
so how do we take our products here that we 've taken apart -- except for the bottle , which is just a recycled good -- and we want to see if we can create value by building something new out of the parts that we 've taken out of all these different components here . so what we 've done is we 've designed a new product...
the resistors limit current flow , and the transistors are functioning as switches , so they allow us to control different devices , again , with our arduino here . so this is bit-zee , and bit-zee has got a personality . you can see bit-zee lights up and does different things when it gets its bumper pressed or when it...
i 'm just wondering why did n't the people that made bit-zee but a cover over all of the wires ?
so how do we take our products here that we 've taken apart -- except for the bottle , which is just a recycled good -- and we want to see if we can create value by building something new out of the parts that we 've taken out of all these different components here . so what we 've done is we 've designed a new product...
the camera that we took apart , we mounted to the board here , and that came out of this camera . and you can use that to take photos of things . and again , the arduino controls that , and we control the arduino with the remote control .
is there a simpler robot that can do all the same things ?
so how do we take our products here that we 've taken apart -- except for the bottle , which is just a recycled good -- and we want to see if we can create value by building something new out of the parts that we 've taken out of all these different components here . so what we 've done is we 've designed a new product...
the motor controller will let us drive motors around , and then this guy will help us to record and play back sound . and we 're going to use some of the parts from these products to make something cool . so after three weeks of development , we 've come up with bit-zee bot .
what are key parts to the robot ?
so how do we take our products here that we 've taken apart -- except for the bottle , which is just a recycled good -- and we want to see if we can create value by building something new out of the parts that we 've taken out of all these different components here . so what we 've done is we 've designed a new product...
so after three weeks of development , we 've come up with bit-zee bot . bit-zee is a little programmable robot that drives around and has a little personality . you can control bit-zee with a universal remote control -- the one that we took apart , actually .
what are the principles of spider robot science kit ?
so how do we take our products here that we 've taken apart -- except for the bottle , which is just a recycled good -- and we want to see if we can create value by building something new out of the parts that we 've taken out of all these different components here . so what we 've done is we 've designed a new product...
so what we 've done is we 've designed a new product that 's kind of designed to get kids excited about math and science , and in order for all these products to work for us , we need to incorporate some electronics . so we have an arduino . it 's a basically programmable chip that you can easily wire to other componen...
where is the code for the arduino ?
so how do we take our products here that we 've taken apart -- except for the bottle , which is just a recycled good -- and we want to see if we can create value by building something new out of the parts that we 've taken out of all these different components here . so what we 've done is we 've designed a new product...
so how do we take our products here that we 've taken apart -- except for the bottle , which is just a recycled good -- and we want to see if we can create value by building something new out of the parts that we 've taken out of all these different components here . so what we 've done is we 've designed a new product...
9 , what is the spelling of that item ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
why attack 2-methyl pent-2-ene with hydronium instead of water ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so let 's think about how we can , how this actually happens in the presence of our hydronium . so let me redraw this molecule right over here . so we copy and paste it , so that 's not exactly it yet , that is just with the single bond .
just to clarify , the first molecule could 've been calleded z-2-methylpent-2-ene as well right ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
because the higher order of carbon , the more stable it will be if it forms some type of cation . so if you look at this carbon right over here , our number two carbon , let me circle it , our number two carbon is bonded to one , two , three carbons . so this is a tertiary carbon .
so what makes the pi bond between the two carbons less stable/prone to elicit these reactions ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so let me draw , woops , wrong tool . let me draw the double bond there . and now let me put it in the presence of some hydronium .
is a pi bond easier to break than a sigma bond ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so the water molecules are all equivalent , but let me draw another water molecule here . and you can imagine , if they just pump into each other in just the right way , this is , water is a polar molecule , it has a partially negative end near the oxygen because the oxygen likes to hog the electrons , and then you hav...
why does n't attack oh- the carbocation at 05 ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
you have another water molecule , let 's say , let me pick a color . so let 's say these electrons right over here , maybe they form a bond with that hydrogen proton , and then these , the electrons in that bond can go back to form a lone pair on that oxygen , and then what are we left with ? and this really is the hom...
i mean in the end of the theory sal tells us there is a free proton left and this will bind to the oh- anyway , right ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so if you look at this carbon right over here , our number two carbon , let me circle it , our number two carbon is bonded to one , two , three carbons . so this is a tertiary carbon . this one right over here , this carbon on the other side of the double bond is only bonded to one , two carbons . so this is a secondar...
isnt one of the carbons a tertiary and the other one a secondary carbon ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so we are in equilibrium with , so let me draw my five carbons , so let 's see , i have ... h3c , carbon , carbon , ch2 , ch3 , i have a ch3 , i say h3c instead of ch3 , i wrote it that way just so it 's clear that the carbons are bonded to the carbons , you have the original hydrogen right over there , you have the on...
as in why is the hydrogen moved to another water molecule to form hydronium ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so we are in equilibrium with , so let me draw my five carbons , so let 's see , i have ... h3c , carbon , carbon , ch2 , ch3 , i have a ch3 , i say h3c instead of ch3 , i wrote it that way just so it 's clear that the carbons are bonded to the carbons , you have the original hydrogen right over there , you have the on...
why does the name of the 1st molecule have 2 before the ene ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
and now let me put it in the presence of some hydronium . alright , so we have an oxygen bonded , two . so this would just be water , as oxygen has two lone pairs , but hydronium is a situation where oxygen is sharing one of those lone pairs with a hydrogen proton , thus making the entire molecule positive , because th...
why does oxygen have a positive charge , with 1 lone pair left should n't it have a negative charge ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
let me draw the double bond there . and now let me put it in the presence of some hydronium . alright , so we have an oxygen bonded , two . so this would just be water , as oxygen has two lone pairs , but hydronium is a situation where oxygen is sharing one of those lone pairs with a hydrogen proton , thus making the e...
why does sal not put the positive charge on the oxygen atom ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so it would be more likely to lose the electrons in one of these , in one of these bonds , and so the way that we can think about this mechanism , and it might be a little bit clearer when we form the carbocation , is let 's have , going to do this in blue . let 's have these two electrons that form this bond , well no...
if two oxygen electrons are shared , then why is n't a double bond formed ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so one way to think about this is , in the presence of an acid , it 's acid-catalyzed , we have gained two hydrogens and an oxygen , which is what we 've gained , what could be used to make a water . and this is actually called an acid-catalyzed addition of water . the water is n't sitting on one part of the molecule ,...
what 's the name of the final product of the addition ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
it now , it now forms an actual bond . and we 're really close to our final product , we have our hydrogen on the number three carbon , we have more than we want on our number two carbon , we just want a hydroxyl group , now we have a whole water bonded to the carbon . so somehow we have to get one of these other hydro...
one of the methyl groups was an ether ) , would we expect that carbon to be r or s once the hydrogen leaves the water group forming the final product ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so this would just be water , as oxygen has two lone pairs , but hydronium is a situation where oxygen is sharing one of those lone pairs with a hydrogen proton , thus making the entire molecule positive , because the hydrogen proton is positive . so there you go , this now has a positive charge . and this can be prett...
a carboncation is formed with a +1 charge , but should n't it have a +2 charge ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so it would be more likely to lose the electrons in one of these , in one of these bonds , and so the way that we can think about this mechanism , and it might be a little bit clearer when we form the carbocation , is let 's have , going to do this in blue . let 's have these two electrons that form this bond , well no...
in this video , sal draws the molecule of water with two pairs of free electrons and two more electrons bonded to two hydrogen atoms , but should n't there be another pair of electrons because oxygen has 6 electrons in it 's last shell and needs two more to complete an octet ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so let 's think about how we can , how this actually happens in the presence of our hydronium . so let me redraw this molecule right over here . so we copy and paste it , so that 's not exactly it yet , that is just with the single bond .
so that means the new h should bind to the right c. but here sal says that the c-c bonding is what 's important ... can someone explain this to me please ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
because the higher order of carbon , the more stable it will be if it forms some type of cation . so if you look at this carbon right over here , our number two carbon , let me circle it , our number two carbon is bonded to one , two , three carbons . so this is a tertiary carbon . this one right over here , this carbo...
so the carbocation will always be the most `` substituted '' carbon ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
with that hydrogen , just like this , and so since it got the hydrogen proton it 's giving its , sharing its electrons now , now this has a positive , this has a positive charge , just like that . i have to be very careful , in the last step i forgot to draw the positive charge ! we always wan na make sure that your ch...
would the rate determining step of this reaction be the first step of pi bond attacking hydronium ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so we are in equilibrium with , so let me draw my five carbons , so let 's see , i have ... h3c , carbon , carbon , ch2 , ch3 , i have a ch3 , i say h3c instead of ch3 , i wrote it that way just so it 's clear that the carbons are bonded to the carbons , you have the original hydrogen right over there , you have the on...
why do the h and oh attach onto the same side of the molecule ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
because the higher order of carbon , the more stable it will be if it forms some type of cation . so if you look at this carbon right over here , our number two carbon , let me circle it , our number two carbon is bonded to one , two , three carbons . so this is a tertiary carbon .
how do we apply markavnikov 's rule if both carbons are bonded to same number of carbons or functional groups ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
is there a difference between having the h2o on top of the arrow or bottom of the arrow ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
what is the name of the resulting compound ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
because the higher order of carbon , the more stable it will be if it forms some type of cation . so if you look at this carbon right over here , our number two carbon , let me circle it , our number two carbon is bonded to one , two , three carbons . so this is a tertiary carbon .
if you have two molecules that are both 2-butene , one is z-isomer and the other is e-isomer , which is is more reactive ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so let 's think about how we can , how this actually happens in the presence of our hydronium . so let me redraw this molecule right over here . so we copy and paste it , so that 's not exactly it yet , that is just with the single bond .
also , if a molecule has more hydrogens , it is more stable than those with less right ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
and this is actually called an acid-catalyzed addition of water . the water is n't sitting on one part of the molecule , but if you take the hydrogen we added , and the hydroxyl we added , if you combine them , that 's what you need to make a water . so let 's think about how we can , how this actually happens in the p...
will the catalizer always be the first part of a mechanism ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so one way to think about this is , in the presence of an acid , it 's acid-catalyzed , we have gained two hydrogens and an oxygen , which is what we 've gained , what could be used to make a water . and this is actually called an acid-catalyzed addition of water . the water is n't sitting on one part of the molecule ,...
would the final product be called 1-butanol ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
and you can imagine , if they just pump into each other in just the right way , this is , water is a polar molecule , it has a partially negative end near the oxygen because the oxygen likes to hog the electrons , and then you have a partial positive end near the hydrogens 'cause they get their electrons hogged , so yo...
what were we trying to obtain as the final result ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so one way to think about this is , in the presence of an acid , it 's acid-catalyzed , we have gained two hydrogens and an oxygen , which is what we 've gained , what could be used to make a water . and this is actually called an acid-catalyzed addition of water . the water is n't sitting on one part of the molecule ,...
is this mechanism syn addition or trans addition ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
because the higher order of carbon , the more stable it will be if it forms some type of cation . so if you look at this carbon right over here , our number two carbon , let me circle it , our number two carbon is bonded to one , two , three carbons . so this is a tertiary carbon . this one right over here , this carbo...
why the oh^ ( -1 ) is not just bonds to the positively charged carbon ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
we have our oxygen bonded to the two hydrogens , it had one of those lone pairs , and now the electrons in this bond are now going to form another lone pair . so it took back an electron , or you can think of it , it gave away a hydrogen proton . and so this is now just neutral water , and we see that we have a conserv...
at 2.52 sal states that in the h3o+ , the o wants the electron back from hydrogen , but why ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so it would be more likely to lose the electrons in one of these , in one of these bonds , and so the way that we can think about this mechanism , and it might be a little bit clearer when we form the carbocation , is let 's have , going to do this in blue . let 's have these two electrons that form this bond , well no...
why does n't it take the electrons from the other hydrogens as well then ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
well what if one of these carbons , especially the ones that have the double bonds , what if some of the electrons from this double bond could be used to snab , to take that hydrogen proton , and then oxygen can hog its electrons again . and you might say , `` oh that 's reasonable , but which of these carbons would ac...
what is the significance of the h-oh above the reaction arrow in the original equation , since the h3o is what is reacting ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
now we need to think about , well how do we get a hydroxyl group added right over here ? well we have all this water , we have all this water floating around , let me , i could use this water molecule but the odds of it being the exact same water molecule , we do n't know . but there 's all sorts of water molecules , w...
i understand that there is a newly formed carbocation that is reactive because it is positively charged and thus is in search of an electron , but the water molecule does n't make a good electron donor , right ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
because the higher order of carbon , the more stable it will be if it forms some type of cation . so if you look at this carbon right over here , our number two carbon , let me circle it , our number two carbon is bonded to one , two , three carbons . so this is a tertiary carbon . this one right over here , this carbo...
sal , we only talk about situations in which the carbon becomes a carboncation , are there any moments in which it becomes a carbon anion ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
this carbon , our number two carbon , has lost an electron , it 's no longer sharing this bond . and so now it is going to have a positive charge , it is a carbocation and once again is a tertiary carbocation , it is bonded to one , two , three carbons . that is stable , more stable than if we did it the other way arou...
since when h2o attacks the carbocation attack from both sides is equally hindered..so why is the cis product shown in particular ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
and now let me put it in the presence of some hydronium . alright , so we have an oxygen bonded , two . so this would just be water , as oxygen has two lone pairs , but hydronium is a situation where oxygen is sharing one of those lone pairs with a hydrogen proton , thus making the entire molecule positive , because th...
if oxygen is electronegative in nature then why would oxygen will give its electron to hydrogen in the formation of h3o+ ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
let me draw the double bond there . and now let me put it in the presence of some hydronium . alright , so we have an oxygen bonded , two . so this would just be water , as oxygen has two lone pairs , but hydronium is a situation where oxygen is sharing one of those lone pairs with a hydrogen proton , thus making the e...
shouldn '' t sal have put a positive charge on the oxygen atom ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
well what if one of these carbons , especially the ones that have the double bonds , what if some of the electrons from this double bond could be used to snab , to take that hydrogen proton , and then oxygen can hog its electrons again . and you might say , `` oh that 's reasonable , but which of these carbons would ac...
how would you usse this in reverse to determine the starting product ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
why is 2-methyl pent-2-ene and not 2 bimethyl hex 2 ene ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so one way to think about this is , in the presence of an acid , it 's acid-catalyzed , we have gained two hydrogens and an oxygen , which is what we 've gained , what could be used to make a water . and this is actually called an acid-catalyzed addition of water . the water is n't sitting on one part of the molecule ,...
does markovnikov 's rule work for all addition reactions apart for free radical addition ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so let me draw that , so this is now , oxygen , hydrogen , had one lone pair that did n't react , and it had one lone pair that i put in blue that is reacting with this hydrogen proton . with that hydrogen , just like this , and so since it got the hydrogen proton it 's giving its , sharing its electrons now , now this...
i did n't get why that oxygen has positive charge ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
but there 's all sorts of water molecules , we 're in an aqueous solution , so let me draw another water molecule here . so the water molecules are all equivalent , but let me draw another water molecule here . and you can imagine , if they just pump into each other in just the right way , this is , water is a polar mo...
so is water the solvent or the reagent ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
but there 's all sorts of water molecules , we 're in an aqueous solution , so let me draw another water molecule here . so the water molecules are all equivalent , but let me draw another water molecule here . and you can imagine , if they just pump into each other in just the right way , this is , water is a polar mo...
would this type of similar mechanism be used to do for example : reaction of ethylene with water to produce ethanol ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so once this happens , we have this carbon , the number three carbon , now , woops i keep using the wrong tool . the number three carbon now forms a bond with this hydrogen just like that . this carbon , our number two carbon , has lost an electron , it 's no longer sharing this bond .
why isnt there hydrogen bonding between oxygen of oh and the hydrogen attached to the other carbon ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so once this happens , we have this carbon , the number three carbon , now , woops i keep using the wrong tool . the number three carbon now forms a bond with this hydrogen just like that . this carbon , our number two carbon , has lost an electron , it 's no longer sharing this bond .
why isnt there hydrogen bonding between oxygen of oh and the hydrogen attached to the other carbon ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
and to think about which of those carbons would do it , we have to turn to markovnikov 's rule . markovnikov 's rule tells us that , look , if you have a reaction like this , and alkene reaction , the carbon that already has , that 's already attached to more hydrogens is more likely to gain more hydrogens , the carbon...
can this reaction also be named hydration ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
what is the name of the newly formed compound ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
well what if one of these carbons , especially the ones that have the double bonds , what if some of the electrons from this double bond could be used to snab , to take that hydrogen proton , and then oxygen can hog its electrons again . and you might say , `` oh that 's reasonable , but which of these carbons would ac...
would this be considered a hydration reaction ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
because the higher order of carbon , the more stable it will be if it forms some type of cation . so if you look at this carbon right over here , our number two carbon , let me circle it , our number two carbon is bonded to one , two , three carbons . so this is a tertiary carbon .
the carbon is acting as a base and taking the hydrogen away from hydronium , right ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so there you go , this now has a positive charge . and this can be pretty reactive , 'cause we know that oxygen is quite electronegative , it lives to keep its electrons . so what is there was a way , what if there 's a way for the oxygen to take back the electrons in this bond right over here , the two electrons in th...
how can we know that the following catalyst is better for a specific reaction ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so once this happens , we have this carbon , the number three carbon , now , woops i keep using the wrong tool . the number three carbon now forms a bond with this hydrogen just like that . this carbon , our number two carbon , has lost an electron , it 's no longer sharing this bond . and so now it is going to have a ...
do you have to draw the arrow coming from the lone electron of the carbon atom to the hydrogen ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so there you go , this now has a positive charge . and this can be pretty reactive , 'cause we know that oxygen is quite electronegative , it lives to keep its electrons . so what is there was a way , what if there 's a way for the oxygen to take back the electrons in this bond right over here , the two electrons in th...
how do we know that a particular equation is in equilibrium ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
let 's have these two electrons that form this bond , well now they form a bond with that hydrogen , and now the oxygen can take back these two electrons , and what are we going , what is going to result ? and i 'm drawing it in equilibrium , remember all of these things are going back and forth depending on how things...
how can we generalize the idea of equilibrium while solving such problems ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so let me draw , woops , wrong tool . let me draw the double bond there . and now let me put it in the presence of some hydronium . alright , so we have an oxygen bonded , two . so this would just be water , as oxygen has two lone pairs , but hydronium is a situation where oxygen is sharing one of those lone pairs with...
for the last part of the mechanism , is n't it supposed to be that the h-o-h bonded to another h should be a positive charge ( making it a hydronium ion ) since the o lost one of its electrons which it shared with the h coming from the h-o-h bond from the entire pentene molecule ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
but there 's all sorts of water molecules , we 're in an aqueous solution , so let me draw another water molecule here . so the water molecules are all equivalent , but let me draw another water molecule here . and you can imagine , if they just pump into each other in just the right way , this is , water is a polar mo...
it has a complete octate ) , so how can the carbocation ( formed above ) attack and extract an electon from the water molecule ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
so there you go , this now has a positive charge . and this can be pretty reactive , 'cause we know that oxygen is quite electronegative , it lives to keep its electrons . so what is there was a way , what if there 's a way for the oxygen to take back the electrons in this bond right over here , the two electrons in th...
and is n't oxygen the second most electonegative element in the periodic table , so wo n't it attract the bond electrons towards itself ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
and now let me put it in the presence of some hydronium . alright , so we have an oxygen bonded , two . so this would just be water , as oxygen has two lone pairs , but hydronium is a situation where oxygen is sharing one of those lone pairs with a hydrogen proton , thus making the entire molecule positive , because th...
why does the oxygen in the substituent group have a positive charge ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
let 's see what it looks like now . we have our oxygen bonded to the two hydrogens , it had one of those lone pairs , and now the electrons in this bond are now going to form another lone pair . so it took back an electron , or you can think of it , it gave away a hydrogen proton .
oxygen already has 8 valence electrons , 1 lone pair and 3 pairs sharing , so should n't the charge be neutral ?
anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let ...
well we have all this water , we have all this water floating around , let me , i could use this water molecule but the odds of it being the exact same water molecule , we do n't know . but there 's all sorts of water molecules , we 're in an aqueous solution , so let me draw another water molecule here . so the water ...
is the solution always aqueous ?