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Welcome to Chemistry 2e, an OpenStax resource. This textbook was written to increase student access to high- quality learning materials, maintaining highest standards of academic rigor at little to no cost. About OpenStax OpenStax is a nonprofit based at Rice University, and it’s our mission to improve student access t...
INTRODUCTION Your alarm goes off and, after hitting “snooze” once or twice, you pry yourself out of bed. You make a cup of coffee to help you get going, and then you shower, get dressed, eat breakfast, and check your phone for messages. On your way to school, you stop to fill your car’s gas tank, almost making you late...
Atoms and Molecules An atom is the smallest particle of an element that has the properties of that element and can enter into a chemical combination. Consider the element gold, for example. Imagine cutting a gold nugget in half, then cutting one of the halves in half, and repeating this process until a piece of gold re...
FIGURE 1.15 The decomposition of water is shown at the macroscopic, microscopic, and symbolic levels. The battery provides an electric current (microscopic) that decomposes water. At the macroscopic level, the liquid separates into the gases hydrogen (on the left) and oxygen (on the right). Symbolically, this change is...
Everyday measurement units are often defined as fractions or multiples of other units. Milk is commonly packaged in containers of 1 gallon (4 quarts), 1 quart (0.25 gallon), and one pint (0.5 quart). This same approach is used with SI units, but these fractions or multiples are always powers of 10. Fractional or multip...
SI Base Units The initial units of the metric system, which eventually evolved into the SI system, were established in France during the French Revolution. The original standards for the meter and the kilogram were adopted there in 1799 and eventually by other countries. This section introduces four of the SI base unit...
between these two units and the Fahrenheit scale will be discussed later in this chapter. Time The SI base unit of time is the second (s). Small and large time intervals can be expressed with the appropriate prefixes; for example, 3 microseconds = 0.000003 s = 3 10−6 and 5 megaseconds = 5,000,000 s = 5 106 s. Alternati...
While there are many ways to determine the density of an object, perhaps the most straightforward method involves separately finding the mass and volume of the object, and then dividing the mass of the sample by its volume. In the following example, the mass is found directly by weighing, but the volume is found indire...
Using Displacement of Water to Determine Density This exercise uses a to illustrate an alternative approach to the determination of density that involves measuring the object’s volume via displacement of water. Use the simulator to determine the densities iron and wood. Solution Click the “turn fluid into water” butto...
Remove the iron block from the beaker, change the block material to wood, and then repeat the mass and volume measurements. Unlike iron, the wood block does not sink in the water but instead floats on the water’s surface. To measure its volume, drag it beneath the water’s surface so that it is fully submerged. Note: T...
The leading zeros in this example are not significant. We could use exponential notation (as described in ) and express the number as 8.32407 10−3; then the number 8.32407 contains all of the significant figures, and 10−3 locates the decimal point. The number of significant figures is uncertain in a number that ends wi...
Addition and Subtraction with Significant Figures Rule: When adding or subtracting numbers, round the result to the same number of decimal places as the number with the fewest decimal places (i.e., the least certain value in terms of addition and subtraction). Add 1.0023 g and 4.383 g. Subtract 421.23 g from 486 g. Sol...
Multiplication and Division with Significant Figures Rule: When multiplying or dividing numbers, round the result to the same number of digits as the number with the fewest significant figures (the least certain value in terms of multiplication and division). (a) Multiply 0.6238 cm by 6.6 cm. (b) Divide 421.23 g by 486...
In the midst of all these technicalities, it is important to keep in mind the reason for these rules about significant figures and rounding—to correctly represent the certainty of the values reported and to ensure that a calculated result is not represented as being more certain than the least certain value used in the...
(a) Use these values to determine the density of this piece of rebar. (b) Rebar is mostly iron. Does your result in (a) support this statement? How? Solution The volume of the piece of rebar is equal to the volume of the water displaced:
(rounded to two significant figures, per the rule for multiplication and division) From , the density of iron is 7.9 g/cm3, very close to that of rebar, which lends some support to the fact that rebar is mostly iron. Check Your Learning An irregularly shaped piece of a shiny yellowish material is weighed and then subme...
Considering these results, she will report that dispenser #1 is precise (values all close to one another, within a few tenths of a milliliter) but not accurate (none of the values are close to the target value of 296 mL, each being more than 10 mL too low). Results for dispenser #2 represent improved accuracy (each vol...
Note that this simple arithmetic involves dividing the numbers of each measured quantity to yield the number of the computed quantity (100/10 = 10) and likewise dividing the units of each measured quantity to yield the unit of the computed quantity (m/s = m/s). Now, consider using this same relation to predict the time...
When a quantity (such as distance in inches) is multiplied by an appropriate unit conversion factor, the quantity is converted to an equivalent value with different units (such as distance in centimeters). For example, a basketball player’s vertical jump of 34 inches can be converted to centimeters by: Since this simp...
from the relationship 1 oz = 28.349 g (). Solution Given the conversion factor, the mass in ounces may be derived using an equation similar to the one used for converting length from inches to centimeters.
Beyond simple unit conversions, the factor-label method can be used to solve more complex problems involving computations. Regardless of the details, the basic approach is the same—all the factors involved in the calculation must be appropriately oriented to ensure that their labels (units) will appropriately cancel an...
Computing Quantities from Measurement Results and Known Mathematical Relations While being driven from Philadelphia to Atlanta, a distance of about 1250 km, a 2014 Lamborghini Aventador Roadster uses 213 L gasoline. (a) What (average) fuel economy, in miles per gallon, did the Roadster get during this trip? (b) If gaso...
Check Your Learning A Toyota Prius Hybrid uses 59.7 L gasoline to drive from San Francisco to Seattle, a distance of 1300 km (two significant digits). (a) What (average) fuel economy, in miles per gallon, did the Prius get during this trip? (b) If gasoline costs $3.90 per gallon, what was the fuel cost for this trip?
Conversion of Temperature Units We use the word temperature to refer to the hotness or coldness of a substance. One way we measure a change in temperature is to use the fact that most substances expand when their temperature increases and contract when their temperature decreases. The liquid in a common glass thermomet...
As mentioned earlier in this chapter, the SI unit of temperature is the kelvin (K). Unlike the Celsius and Fahrenheit scales, the kelvin scale is an absolute temperature scale in which 0 (zero) K corresponds to the lowest temperature that can theoretically be achieved. Since the kelvin temperature scale is absolute, a ...
FIGURE 1.28 The Fahrenheit, Celsius, and kelvin temperature scales are compared. Although the kelvin (absolute) temperature scale is the official SI temperature scale, Celsius is commonly used in many scientific contexts and is the scale of choice for nonscience contexts in almost all areas of the world. Very few count...
Conversion from Fahrenheit Baking a ready-made pizza calls for an oven temperature of 450 °F. If you are in Europe, and your oven thermometer uses the Celsius scale, what is the setting? What is the kelvin temperature? Solution
Key Terms accuracy how closely a measurement aligns with a correct value atom smallest particle of an element that can enter into a chemical combination Celsius (°C) unit of temperature; water freezes at 0 °C and boils at 100 °C on this scale chemical change change producing a different kind of matter from the origina...
theory well-substantiated, comprehensive, testable explanation of a particular aspect of nature uncertainty estimate of amount by which measurement differs from true value unit standard of comparison for measurements unit conversion factor ratio of equivalent quantities expressed with different units; used to convert...
Chemistry deals with the composition, structure, and properties of matter, and the ways by which various forms of matter may be interconverted. Thus, it occupies a central place in the study and practice of science and technology. Chemists use the scientific method to perform experiments, pose hypotheses, and formulate...
and an uncertainty. Measurements can be represented in either decimal or scientific notation. Scientists primarily use SI (International System) units such as meters, seconds, and kilograms, as well as derived units, such as liters (for volume) and g/cm3 (for density). In many cases, it is convenient to use prefixes th...
Measurements are made using a variety of units. It is often useful or necessary to convert a measured quantity from one unit into another. These conversions are accomplished using unit conversion factors, which are derived by simple applications of a mathematical approach called the factor-label method or dimensional a...
Is one liter about an ounce, a pint, a quart, or a gallon? Is a meter about an inch, a foot, a yard, or a mile? Indicate the SI base units or derived units that are appropriate for the following measurements: the length of a marathon race (26 miles 385 yards) the mass of an automobile the volume of a swimming pool the ...
Consider the results of the archery contest shown in this figure. Which archer is most precise? Which archer is most accurate? Who is both least precise and least accurate? Classify the following sets of measurements as accurate, precise, both, or neither. Checking for consistency in the weight of chocolate chip cookie...
INTRODUCTION Lung diseases and lung cancers are among the world's most devastating illnesses partly due to delayed detection and diagnosis. Most noninvasive screening procedures aren't reliable, and patients often resist more accurate methods due to discomfort with the procedures or with the potential danger that the p...
It is worth noting that although all samples of a particular compound have the same mass ratio, the converse is not true in general. That is, samples that have the same mass ratio are not necessarily the same substance. For example, there are many compounds other than isooctane that also have a carbon-to-hydrogen mass ...
This supports the law of multiple proportions. This means that A and B are different compounds, with A having one-half as much oxygen per amount of carbon (or twice as much carbon per amount of oxygen) as B. A possible pair of compounds that would fit this relationship would be A = CO and B = CO2. Check Your Learning A...
Evolution of Atomic Theory LEARNING OBJECTIVES By the end of this section, you will be able to: Outline milestones in the development of modern atomic theory Summarize and interpret the results of the experiments of Thomson, Millikan, and Rutherford Describe the three subatomic particles that compose atoms Define isoto...
The number of protons in the nucleus of an atom is its atomic number (Z). This is the defining trait of an element: Its value determines the identity of the atom. For example, any atom that contains six protons is the element carbon and has the atomic number 6, regardless of how many neutrons or electrons it may have. ...
Traditionally, the discoverer (or discoverers) of a new element names the element. However, until the name is recognized by the International Union of Pure and Applied Chemistry (IUPAC), the recommended name of the new element is based on the Latin word(s) for its atomic number. For example, element 106 was called unni...
Atomic Mass Because each proton and each neutron contribute approximately one amu to the mass of an atom, and each electron contributes far less, the atomic mass of a single atom is approximately equal to its mass number (a whole number). However, the average masses of atoms of most elements are not whole numbers becau...
Calculation of Percent Abundance Naturally occurring chlorine consists of 35Cl (mass 34.96885 amu) and 37Cl (mass 36.96590 amu), with an average mass of 35.453 amu. What is the percent composition of Cl in terms of these two isotopes? Solution The average mass of chlorine is the fraction that is 35Cl times the mass of ...
LINK TO LEARNING Visit this to make mixtures of the main isotopes of the first 18 elements, gain experience with average atomic mass, and check naturally occurring isotope ratios using the Isotopes and Atomic Mass simulation. As you will learn, isotopes are important in nature and especially in human understanding o...
Compounds are formed when two or more elements chemically combine, resulting in the formation of bonds. For example, hydrogen and oxygen can react to form water, and sodium and chlorine can react to form table salt. We sometimes describe the composition of these compounds with an empirical formula, which indicates the ...
It is important to be aware that it may be possible for the same atoms to be arranged in different ways: Compounds with the same molecular formula may have different atom-to-atom bonding and therefore different structures. For example, could there be another compound with the same formula as acetic acid, C2H4O2? And if...
3 Per the IUPAC definition, group 12 elements are not transition metals, though they are often referred to as such. Additional details on this group’s elements are provided in a chapter on transition metals and coordination chemistry. calcium sodium sulfur Solution The family names are as follows: halogen alkaline ear...
Composition of Ions An ion found in some compounds used as antiperspirants contains 13 protons and 10 electrons. What is its symbol? Solution Because the number of protons remains unchanged when an atom forms an ion, the atomic number of the element must be 13. Knowing this lets us use the periodic table to identify th...
Note that there is a system for naming some polyatomic ions; -ate and -ite are suffixes designating polyatomic ions containing more or fewer oxygen atoms. Per- (short for “hyper”) and hypo- (meaning “under”) are prefixes meaning more oxygen atoms than -ate and fewer oxygen atoms than -ite, respectively. For example, pe...
FIGURE 2.31 Although pure aluminum oxide is colorless, trace amounts of iron and titanium give blue sapphire its characteristic color. (credit: modification of work by Stanislav Doronenko) Solution Because the ionic compound must be electrically neutral, it must have the same number of positive and negative charges. Tw...
Chemical Nomenclature LEARNING OBJECTIVES By the end of this section, you will be able to: Derive names for common types of inorganic compounds using a systematic approach Nomenclature, a collection of rules for naming things, is important in science and in many other situations. This module describes an approach that ...
Compounds Containing Polyatomic Ions Compounds containing polyatomic ions are named similarly to those containing only monatomic ions, i.e. by naming first the cation and then the anion. Examples are shown in .
Compounds Containing a Metal Ion with a Variable Charge Most of the transition metals and some main group metals can form two or more cations with different charges. Compounds of these metals with nonmetals are named with the same method as compounds in the first category, except the charge of the metal ion is specifie...
Out-of-date nomenclature used the suffixes –ic and –ous to designate metals with higher and lower charges, respectively: Iron(III) chloride, FeCl3, was previously called ferric chloride, and iron(II) chloride, FeCl2, was known as ferrous chloride. Though this naming convention has been largely abandoned by the scientif...
Naming Ionic Compounds Name the following ionic compounds Fe2S3 CuSe GaN MgSO4·7H2O Ti2(SO4)3 Solution The anions in these compounds have a fixed negative charge (S2−, Se2− , N3−, and and the compounds must be neutral. Because the total number of positive charges in each compound must equal the total number of nega...
There are a few common names that you will encounter as you continue your study of chemistry. For example, although NO is often called nitric oxide, its proper name is nitrogen monoxide. Similarly, N2O is known as nitrous oxide even though our rules would specify the name dinitrogen monoxide. (And H2O is usually called...
P4O6 Solution Because these compounds consist solely of nonmetals, we use prefixes to designate the number of atoms of each element: sulfur hexafluoride dinitrogen trioxide dichlorine heptoxide tetraphosphorus hexoxide Check Your Learning Write the formulas for the following compounds: phosphorus pentachloride dinitro...
Many compounds containing three or more elements (such as organic compounds or coordination compounds) are subject to specialized nomenclature rules that you will learn later. However, we will briefly discuss the important compounds known as oxyacids, compounds that contain hydrogen, oxygen, and at least one other elem...
Key Terms actinide inner transition metal in the bottom of the bottom two rows of the periodic table alkali metal element in group 1 alkaline earth metal element in group 2 alpha particle (α particle) positively charged particle consisting of two protons and two neutrons anion negatively charged atom or molecule (con...
atom proton positively charged, subatomic particle located in the nucleus representative element (also, main-group element) element in columns 1, 2, and 12–18 series (also, period) horizontal row of the period table spatial isomers compounds in which the relative orientations of the atoms in space differ structural for...
The ancient Greeks proposed that matter consists of extremely small particles called atoms. Dalton postulated that each element has a characteristic type of atom that differs in properties from atoms of all other elements, and that atoms of different elements can combine in fixed, small, whole- number ratios to form co...
with the same number of electrons as in the preceding noble gas in the periodic table. By this means, a positively charged ion is formed. Similarly, nonmetals (especially those in groups 16 and 17, and, to a lesser extent, those in Group 15) can gain the number of electrons needed to provide atoms with the same number ...
In the following drawing, the green spheres represent atoms of a certain element. The purple spheres represent atoms of another element. If the spheres of different elements touch, they are part of a single unit of a compound. The following chemical change represented by these spheres may violate one of the ideas of Da...
The existence of isotopes violates one of the original ideas of Dalton’s atomic theory. Which one? How are electrons and protons similar? How are they different? How are protons and neutrons similar? How are they different? Predict and test the behavior of α particles fired at a “plum pudding” model atom. Predict the p...
(d) Determine the empirical formulas for the following compounds: caffeine, C8H10N4O2 sucrose, C12H22O11 hydrogen peroxide, H2O2 glucose, C6H12O6 ascorbic acid (vitamin C), C6H8O6 Determine the empirical formulas for the following compounds: acetic acid, C2H4O2 citric acid, C6H8O7 hydrazine, N2H4 nicotine, C10H14N2 but...
Open the and select the “Larger Molecules” tab. Select an appropriate atom’s “Kit” to build a molecule with two carbon and six hydrogen atoms. Drag atoms into the space above the “Kit” to make a molecule. A name will appear when you have made an actual molecule that exists (even if it is not the one you want). You can...
Name the following compounds: CsCl BaO K2S BeCl2 HBr AlF3 Name the following compounds: NaF Rb2O BCl3 H2Se P4O6 ICl3 Write the formulas of the following compounds: rubidium bromide magnesium selenide sodium oxide calcium chloride hydrogen fluoride gallium phosphide aluminum bromide ammonium sulfate Write the fo...
INTRODUCTION Swimming pools have long been a popular means of recreation, exercise, and physical therapy. Since it is impractical to refill large pools with fresh water on a frequent basis, pool water is regularly treated with chemicals to prevent the growth of harmful bacteria and algae. Proper pool maintenance requir...
Computing Molecular Mass for a Covalent Compound Ibuprofen, C13H18O2, is a covalent compound and the active ingredient in several popular nonprescription pain medications, such as Advil and Motrin. What is the molecular mass (amu) for this compound? Solution Molecules of this compound are composed of 13 carbon atoms, 1...
The Mole The identity of a substance is defined not only by the types of atoms or ions it contains, but by the quantity of each type of atom or ion. For example, water, H2O, and hydrogen peroxide, H2O2, are alike in that their respective molecules are composed of hydrogen and oxygen atoms. However, because a hydrogen p...
While atomic mass and molar mass are numerically equivalent, keep in mind that they are vastly different in terms of scale, as represented by the vast difference in the magnitudes of their respective units (amu versus g). To appreciate the enormity of the mole, consider a small drop of water weighing about 0.03 g (see ...
The calculated magnitude (0.12 mol K) is consistent with our ballpark expectation, since it is a bit greater than 0.1 mol. Check Your Learning Beryllium is a light metal used to fabricate transparent X-ray windows for medical imaging instruments. How many moles of Be are in a thin-foil window weighing 3.24 g? Answer: 0...
FIGURE 3.8 Copper wire is composed of many, many atoms of Cu. (credit: Emilian Robert Vicol) Solution The number of Cu atoms in the wire may be conveniently derived from its mass by a two-step computation: first calculating the molar amount of Cu, and then using Avogadro’s number (NA) to convert this molar amount to nu...
Deriving Grams from Moles for a Compound Vitamin C is a covalent compound with the molecular formula C6H8O6. The recommended daily dietary allowance of vitamin C for children aged 4–8 years is 1.42 10−4 mol. What is the mass of this allowance in grams? Solution As for elements, the mass of a compound can be derived fro...
Given that saccharin has a molar mass of 183.18 g/mol, how many saccharin molecules are in a 40.0-mg (0.0400-g) sample of saccharin? How many carbon atoms are in the same sample? Solution The number of molecules in a given mass of compound is computed by first deriving the number of moles, as demonstrated in , and then...
Counting Neurotransmitter Molecules in the Brain The brain is the control center of the central nervous system (). It sends and receives signals to and from muscles and other internal organs to monitor and control their functions; it processes stimuli detected by sensory organs to guide interactions with the external w...
Calculation of Percent Composition Analysis of a 12.04-g sample of a liquid compound composed of carbon, hydrogen, and nitrogen showed it to contain 7.34 g C, 1.85 g H, and 2.85 g N. What is the percent composition of this compound? Solution To calculate percent composition, divide the experimentally derived mass of ea...
Determining Percent Composition from Molecular or Empirical Formulas Percent composition is also useful for evaluating the relative abundance of a given element in different compounds of known formulas. As one example, consider the common nitrogen-containing fertilizers ammonia (NH3), ammonium nitrate (NH4NO3), and ure...
Determining a Compound’s Empirical Formula from the Masses of Its Elements A sample of the black mineral hematite (), an oxide of iron found in many iron ores, contains 34.97 g of iron and 15.03 g of oxygen. What is the empirical formula of hematite?
The ratio is 1.000 mol of iron to 1.500 mol of oxygen (Fe1O1.5). Finally, multiply the ratio by two to get the smallest possible whole number subscripts while still maintaining the correct iron-to-oxygen ratio:
Deriving Empirical Formulas from Percent Composition Finally, with regard to deriving empirical formulas, consider instances in which a compound’s percent composition is available rather than the absolute masses of the compound’s constituent elements. In such cases, the percent composition can be used to calculate the ...
Derivation of Molecular Formulas Recall that empirical formulas are symbols representing the relative numbers of a compound’s elements. Determining the absolute numbers of atoms that compose a single molecule of a covalent compound requires knowledge of both its empirical formula and its molecular mass or molar mass. T...
For example, consider a covalent compound whose empirical formula is determined to be CH2O. The empirical formula mass for this compound is approximately 30 amu (the sum of 12 amu for one C atom, 2 amu for two H atoms, and 16 amu for one O atom). If the compound’s molecular mass is determined to be 180 amu, this indica...
Note that this same approach may be used when the molar mass (g/mol) instead of the molecular mass (amu) is used. In this case, one mole of empirical formula units and molecules is considered, as opposed to single units and molecules. Determination of the Molecular Formula for Nicotine Nicotine, an alkaloid in the nig...
The C-to-N and H-to-N molar ratios are adequately close to whole numbers, and so the empirical formula is C5H7N. The empirical formula mass for this compound is therefore 81.13 amu/formula unit, or 81.13 g/mol formula unit. Calculate the molar mass for nicotine from the given mass and molar amount of compound:
Molarity LEARNING OBJECTIVES By the end of this section, you will be able to: Describe the fundamental properties of solutions Calculate solution concentrations using molarity Perform dilution calculations using the dilution equation Preceding sections of this chapter focused on the composition of substances: samples o...
Solution Since the molar amount of solute and the volume of solution are both given, the molarity can be calculated using the definition of molarity. Per this definition, the solution volume must be converted from mL to L: Check Your Learning A teaspoon of table sugar contains about 0.01 mol sucrose. What is the molar...
Calculating Molar Concentrations from the Mass of Solute Distilled white vinegar () is a solution of acetic acid, CH3CO2H, in water. A 0.500-L vinegar solution contains 25.2 g of acetic acid. What is the concentration of the acetic acid solution in units of molarity? FIGURE 3.15 Distilled white vinegar is a solution o...
Determining the Mass of Solute in a Given Volume of Solution How many grams of NaCl are contained in 0.250 L of a 5.30-M solution? Solution The volume and molarity of the solution are specified, so the amount (mol) of solute is easily computed as demonstrated in :
When performing calculations stepwise, as in , it is important to refrain from rounding any intermediate calculation results, which can lead to rounding errors in the final result. In , the molar amount of NaCl computed in the first step, 1.325 mol, would be properly rounded to 1.32 mol if it were to be reported; howev...
Dilution of Solutions Dilution is the process whereby the concentration of a solution is lessened by the addition of solvent. For example, a glass of iced tea becomes increasingly diluted as the ice melts. The water from the melting ice increases the volume of the solvent (water) and the overall volume of the solution ...
where the subscripts “1” and “2” refer to the solution before and after the dilution, respectively. Since the dilution process does not change the amount of solute in the solution, n1 = n2. Thus, these two equations may be set equal to one another: This relation is commonly referred to as the dilution equation. Althou...
Determining the Concentration of a Diluted Solution If 0.850 L of a 5.00-M solution of copper nitrate, Cu(NO3)2, is diluted to a volume of 1.80 L by the addition of water, what is the molarity of the diluted solution? Solution The stock concentration, C1, and volume, V1, are provided as well as the volume of the dilute...
Volume of a Concentrated Solution Needed for Dilution What volume of 1.59 M KOH is required to prepare 5.00 L of 0.100 M KOH? Solution Given are the concentration of a stock solution, C1, and the volume and concentration of the resultant diluted solution, V2 and C2. Find the volume of the stock solution, V1 by rearrang...
Calculation of Percent by Mass A 5.0-g sample of spinal fluid contains 3.75 mg (0.00375 g) of glucose. What is the percent by mass of glucose in spinal fluid? Solution The spinal fluid sample contains roughly 4 mg of glucose in 5000 mg of fluid, so the mass fraction of glucose should be a bit less than one part in 1000...
Volume Percentage Liquid volumes over a wide range of magnitudes are conveniently measured using common and relatively inexpensive laboratory equipment. The concentration of a solution formed by dissolving a liquid solute in a liquid solvent is therefore often expressed as a volume percentage, %vol or (v/v)%: Calculat...
Check Your Learning A 50.0-g sample of industrial wastewater was determined to contain 0.48 mg of mercury. Express the mercury concentration of the wastewater in ppm and ppb units. Answer: 9.6 ppm, 9600 ppb Key Terms aqueous solution solution for which water is the solvent Avogadro’s number (NA) experimentally determi...