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chem6_69730_fm_a-b,i_xxxii,1.indd 1 11/15/19 10:23 AM
vi Contents
3 Stoichiometry:
Mass, Formulas, and Reactions 86
3.1 Air, Life, and Molecules 88
Chemical Reactions and Earth’s Early Atmosphere 89
3.2 The Mole 91
Molar Mass 93 • Molecular Masses and Formula Masses 95 • Moles and Chemical
Equations 98
3.3 Writing Balanced Chemical Equations 100
3.4 Combustion Reactions 105
3.5 Stoichiometric Calculations and the Carbon Cycle 107
3.6 Limiting Reactants and Percent Yield 112
Calculations Involving Limiting Reactants 113 • Actual Yields versus Theoretical
Yields 116
3.7 Determining Empirical Formulas from Percent Composition 119
3.8 Comparing Empirical and Molecular Formulas 124
Molecular Mass and Mass Spectrometry 127
3.9 Combustion Analysis 128
Summary 134 • Particulate Preview Wrap-Up 134 • Problem-Solving
Summary 134 • Visual Problems 136 • Questions and Problems 139
4 Reactions in Solution:
Aqueous Chemistry in Nature 148
4.1 Ions and Molecules in Oceans and Cells 150
4.2 Expressing Concentrations 153
Concentration Units 153 • Molarity 154
4.3 Dilutions 159
Determining Concentration 162
4.4 Electrolytes and Nonelectrolytes 163
Ions in Solution 163
4.5 Acid–Base Reactions: Proton Transfer 165
4.6 Titrations 171
4.7 Precipitation Reactions 175
Precipitation Formation 176 • Using Precipitation in Analysis 180 • Saturated Solutions
and Supersaturation 182
4.8 Oxidation–Reduction Reactions Electron Transfer 184
Oxidation Numbers 184 • Changes in Oxidation Numbers in Redox Reactions 186
• Electron Transfer in Redox Reactions 187 • Balancing Redox Reactions by Using
Half-Reactions 188 • The Activity Series of Metals 191 • Redox in Nature 193
Summary 198 • Particulate Preview Wrap-Up 199 • Problem-Solving
Summary 199 • Visual Problems 200 • Questions and Problems 202
5 Properties of Gases:
The Air We Breathe 212
5.1 Air: An Invisible Necessity 214
5.2 Atmospheric Pressure and Collisions 215
5.3 The Gas Laws 220
Boyle’s Law: Relating Pressure and Volume 220 • Charles’s Law: Relating Volume
and Temperature 223 • Avogadro’s Law: Relating Volume and Quantity of
Gas 225 • Amontons’s Law: Relating Pressure and Temperature 226
5.4 The Ideal Gas Law 228
5.5 Gases in Chemical Reactions 232
5.6 Gas Density 235
5.7 Dalton’s Law and Mixtures of Gases 238
5.8 The Kinetic Molecular Theory of Gases 243
Explaining Boyle’s, Dalton’s, and Avogadro’s Laws 244 • Explaining Amontons’s and
Charles’s Laws 245 • Molecular Speeds and Kinetic Energy 246 • Graham’s Law:
Effusion and Diffusion 249
5.9 Real Gases 250
Deviations from Ideality 251 • The van der Waals Equation for Real Gases 252
Summary 255 • Particulate Preview Wrap-Up 256 • Problem-Solving
Summary 256 • Visual Problems 257 • Questions and Problems 261
6 Thermochemistry:
Energy Changes in Chemical Reactions 270
6.1 Sunlight Unwinding 272
6.2 Forms of Energy 273
Work, Potential Energy, and Kinetic Energy 273 • Kinetic Energy and Potential Energy at
the Molecular Level 276
6.3 Systems, Surroundings, and Energy Transfer 279
Isolated, Closed, and Open Systems 279 • Exothermic and Endothermic
Processes 281 • P–V Work and Energy Units 283
6.4 Enthalpy and Enthalpy Changes 286
6.5 Heating Curves, Molar Heat Capacity, and Specific Heat 289
Hot Soup on a Cold Day 289 • Cold Drinks on a Hot Day 294
6.6 Calorimetry: Measuring Heat Capacity and Enthalpies of Reaction 297
Determining Molar Heat Capacity and Specific Heat 297 • Enthalpies of Reaction 299
6.7 Hess’s Law 304
6.8 Standard Enthalpies of Formation and Reaction 308
6.9 Fuels, Fuel Values, and Food Values 313
Alkanes 313 • Fuel Value 316 • Food Value 317
Summary 321 • Particulate Preview Wrap-Up 321 • Problem-Solving
Summary 322 • Visual Problems 323 • Questions and Problems 325
8 Chemical Bonds:
What Makes a Gas a Greenhouse Gas? 392
8.1 Types of Chemical Bonds and the Greenhouse Effect 394
Forming Bonds from Atoms 395
8.2 Lewis Structures 398
Lewis Symbols 398 • Drawing Lewis Structures 399 • Lewis Structures of Molecules
with Double and Triple Bonds 401 • Lewis Structures of Ionic Compounds 404
8.3 Polar Covalent Bonds 405
Polarity and Type of Bond 407 • Vibrating Bonds and Greenhouse Gases 408
8.4 Resonance 409
8.5 Formal Charge: Choosing among Lewis Structures 414
Calculating Formal Charge of an Atom in a Resonance Structure 415
8.6 Exceptions to the Octet Rule 418
Odd-Electron Molecules 418 • Molecules in Which Atoms Form More than Four Bonds
420 • Lewis Structures: Atoms with More than an Octet 421 • Lewis Structures: Atoms
with Less than an Octet 423 • The Limits of Bonding Models 425
8.7 The Lengths and Strengths of Covalent Bonds 426
Bond Length 426 • Bond Energies 427
Summary 432 • Particulate Preview Wrap-Up 432 • Problem-Solving
Summary 432 • Visual Problems 433 • Questions and Problems 435
9 Molecular Geometry:
Shape Determines Function 444
9.1 Biological Activity and Molecular Shape 446
9.2 Valence-Shell Electron-Pair Repulsion (VSEPR) Theory 447
Central Atoms with No Lone Pairs 448 • Central Atoms with Lone Pairs 452
9.3 Polar Bonds and Polar Molecules 457
9.4 Valence Bond Theory 461
Bonds from Orbital Overlap 462 • Hybridization 463 • Tetrahedral Geometry: sp3
Hybrid Orbitals 463 • Trigonal Planar Geometry: sp2 Hybrid Orbitals 465 • Linear
Geometry: sp Hybrid Orbitals 467
9.5 Shape, Large Molecules, and Molecular Recognition 470
Drawing Larger Molecules 470 • Molecules with More than One Functional
Group 472 • Chirality and Molecular Recognition 473
9.6 Molecular Orbital Theory 477
Molecular Orbitals of Hydrogen and Helium 478 • Molecular Orbitals of Homonuclear
Diatomic Molecules 480 • Molecular Orbitals of Heteronuclear Diatomic
Molecules 484 • Molecular Orbitals of N21 and Spectra of Auroras 486 • Using MO
Theory to Explain Fractional Bond Orders and Resonance 486 • A Bonding Theory for
SN > 4 487 • Metallic Bonds and Conduction Bands 490 • Semiconductors 491
Summary 495 • Particulate Preview Wrap-Up 496 • Problem-Solving
Summary 496 • Visual Problems 496 • Questions and Problems 498
10 Intermolecular Forces:
The Uniqueness of Water 506
10.1 Intramolecular Forces versus Intermolecular Forces 508
10.2 Dispersion Forces 509
The Importance of Shape 510
10.3 Interactions Involving Polar Molecules 511
Ion–Dipole Interactions 511 • Dipole–Dipole Interactions 512 • Hydrogen Bonds 513
10.4 Vapor Pressure of Pure Liquids 519
Vapor Pressure and Temperature 520 • Volatility and the Clausius–Clapeyron
Equation 521
10.5 Phase Diagrams: Intermolecular Forces at Work 523
Phases and Phase Transitions 523
10.6 Some More Remarkable Properties of Water 526
Surface Tension, Capillary Action, and Viscosity 526 • The Densities of Cold Water and
Ice: Their Impact on Aquatic Life 528
10.7 Polarity and Solubility 529
Combinations of Intermolecular Forces 532
10.8 Solubility of Gases in Water 534
Summary 538 • Particulate Preview Wrap-Up 539 • Problem-Solving
Summary 539 • Visual Problems 539 • Questions and Problems 541
11 Solutions:
Properties and Behavior 548
11.1 Interactions between Ions 550
11.2 Energy Changes during Formation and Dissolution of Ionic Compounds 553
Calculating Lattice Energies by Using the Born–Haber Cycle 556 • Enthalpies of
Hydration 559
11.3 Vapor Pressure of Solutions 561
Raoult’s Law 562
11.4 Mixtures of Volatile Solutes 564
Vapor Pressures of Mixtures of Volatile Solutes 564
11.5 Colligative Properties of Solutions 569
Molality 570 • Boiling Point Elevation 572 • Freezing Point Depression 573 •
The van ’t Hoff Factor 575 • Osmosis and Osmotic Pressure 579 • Reverse
Osmosis 583 • Using Osmotic Pressure to Determine Molar Mass • 585
11.6 Ion Exchange • 587
Summary 590 • Particulate Preview Wrap-Up 590 • Problem-Solving
Summary 590 • Visual Problems 592 • Questions and Problems 595
12 Solids:
Crystals, Alloys, and Polymers 600
12.1 The Solid State 602
12.2 Structures of Metals 604
Stacking Patterns and Unit Cells 605 • Unit Cell Dimensions 607
12.3 Alloys and Medicine 612
Substitutional Alloys 613 • Interstitial Alloys 614
12.4 Ionic Solids and Salt Crystals 616
12.5 Allotropes of Carbon 620
12.6 Polymers 622
Polymers of Alkenes 622 • Polymers Containing Aromatic Rings 625 • Polymers of
Alcohols and Ethers 626 • Polyesters and Polyamides 628
Summary 635 • Particulate Preview Wrap-Up 636 • Problem-Solving
Summary 636 • Visual Problems 637 • Questions and Problems 640
13 Chemical Kinetics:
Reactions in the Atmosphere 648
13.1 Cars, Trucks, and Air Quality 650
13.2 Reaction Rates 652
Experimentally Determined Reaction Rates 654 • Average Reaction
Rates 656 • Instantaneous Reaction Rates 656
13.3 Effect of Concentration on Reaction Rate 659
Reaction Order and Rate Constants 659 • Integrated Rate Laws: First-Order
Reactions 664 • Reaction Half-Lives 668 • Integrated Rate Laws: Second-Order
Reactions 670 • Zero-Order Reactions 672
13.4 Reaction Rates, Temperature, and the Arrhenius Equation 674
13.5 Reaction Mechanisms 680
Elementary Steps 680 • Rate Laws and Reaction Mechanisms 682 • Mechanisms and
Zero-Order Reactions 686
13.6 Catalysts 687
Catalysts and the Ozone Layer 687 • Catalysts and Catalytic
Converters 690 • Enzymes: Biological Catalysts 691
Summary 694 • Particulate Preview Wrap-Up 695 • Problem-Solving
Summary 695 • Visual Problems 696 • Questions and Problems 698
15 Acid–Base Equilibria:
Proton Transfer in Biological Systems 754
15.1 Acids and Bases: A Balancing Act 756
15.2 The Molecular Structures and Strengths of Acids and Bases 757
Strong and Weak Acids 758 • Strong and Weak Bases 763
15.3 Conjugate Pairs and Their Complementary Strengths as Acids and Bases 764
Recognizing Conjugate Pairs 765 • Relative Strengths of Conjugate Acids and
Bases 766
15.4 pH and the Autoionization of Water 767
The pH Scale 768 • pOH, pKa, and pKb Values 771
15.5 Ka, Kb, and the Ionization of Weak Acids and Bases 772
Weak Acids 772 • Weak Bases 776
15.6 Calculating the pH of Acidic and Basic Solutions 778
Strong Acids and Strong Bases 778 • Weak Acids and Weak Bases 779 • pH of Very
Dilute Solutions of Strong Acids 781
15.7 Polyprotic Acids 783
Acid Rain 783 • Normal Rain 785
15.8 Acidic and Basic Salts 788
Summary 793 • Particulate Preview Wrap-Up 794 • Problem-Solving
Summary 794 • Visual Problems 796 • Questions and Problems 798
18 Electrochemistry:
The Quest for Clean Energy 898
18.1 Running on Electrons: Redox Chemistry Revisited 900
18.2 Voltaic and Electrolytic Cells 903
Cell Diagrams 903
18.3 Standard Potentials 907
18.4 Chemical Energy and Electrical Work 911
18.5 A Reference Point: The Standard Hydrogen Electrode 914
18.6 The Effect of Concentration on Ecell 916
The Nernst Equation 916 • E° and K 919
18.7 Relating Battery Capacity to Quantities of Reactants 920
Nickel–Metal Hydride Batteries 921 • Lithium-Ion Batteries 923
18.8 Corrosion: Unwanted Electrochemical Reactions 925
18.9 Electrolytic Cells and Rechargeable Batteries 928
18.10 Fuel Cells and Flow Batteries 931
Summary 936 • Particulate Preview Wrap-Up 936 • Problem-Solving
Summary 937 • Visual Problems 937 • Questions and Problems 939
19 Nuclear Chemistry:
Applications in Science and Medicine 946
19.1 Energy and Nuclear Stability 948
19.2 Unstable Nuclei and Radioactive Decay 950
19.3 Measuring and Expressing Radioactivity 956
19.4 Calculations Involving Half-Lives of Radionuclides 957
19.5 Radiometric Dating 959
19.6 Biological Effects of Radioactivity 962
Radiation Dosage 963 • Evaluating the Risks of Radiation 965
22 Transition Metals:
Biological and Medical Applications 1082
22.1 Transition Metals in Biology: Complex Ions 1084
22.2 Naming Complex Ions and Coordination Compounds 1088
Complex Ions with a Positive Charge 1088 • Complex Ions with a Negative
Charge 1090 • Coordination Compounds 1092
22.3 Polydentate Ligands and Chelation 1093
22.4 Crystal Field Theory 1097
22.5 Magnetism and Spin States 1102
22.6 Isomerism in Coordination Compounds 1104
Enantiomers and Linkage Isomers 1106
22.7 Coordination Compounds in Biochemistry 1108
Manganese and Photosynthesis 1108 • Transition Metals in Enzymes 1109
22.8 Coordination Compounds in Medicine 1113
Transition Metals in Diagnosis 1113 • Transition Metals in Therapy 1116
Summary 1121 • Particulate Preview Wrap-Up 1121 • Problem-Solving
Summary 1122 • Visual Problems 1122 • Questions and Problems 1125
Appendices APP-1
Glossary G-1
Answers to Particulate Review, Concept Tests, and Practice Exercises ANS-1
Answers to Selected End-of-Chapter Questions and Problems ANS-15
Credits C-1
Index I-1
xv
Acid rain and normal rain 783 Corrosion at sea 935 Olestra 1023
Bleach 789 Scintillation counters and Geiger Cholesterol and cardiovascular
pH of human blood 792 counters 956 disease 1025
Atmospheric carbon dioxide and ocean Radiometric dating 959 DNA and RNA 1025
acidification 804 Chernobyl and Fukushima 964 Origin of life on Earth 1029
Swimming pool pH test kits 816 Radon gas exposure 965 Hydrogenated oils 1031
Sapphire Pool in Yellowstone National Therapeutic and diagnostic Dietary reference intake (DRI) 1048
Park 826 radiology 967 Ion transport across cell
Milk of magnesia 834 Nuclear weapons and nuclear membranes 1051
Impact of ocean acidification 842 power 969 Osteoporosis and kidney stones 1054
Instant cold packs 854 Solar fusion 971 Chlorophyll 1054
Engine efficiency 869 Tokamak reactors and ITER 973 Teeth, bones, and shells 1054
Energy from glucose; glycolysis 881 Radium paint and the Radium Girls 975 Acid reflux and antacid drugs 1056
Prehistoric axes and copper refining 887 Rice and beans 1003 Bad breath, skunk odor, and smelly
Alkaline, nicad, and zinc–air Aspartame 1007 shoes 1063
batteries 909 Sickle-cell anemia and malaria 1010 Toothpaste and fluoridated water 1066
Lead–acid car batteries 917 Silk 1012 Goiter and Graves’ disease 1067
Hybrid vehicles and nickel–metal hydride Alzheimer’s disease 1012 Colonoscopy 1073
batteries 921 Hemoglobin and keratin 1013 Prussian blue pigment 1088
Electric vehicles and lithium–ion Enzymes 1013 Food preservatives 1096
batteries 923 Lactose intolerance 1013 Anticancer drugs (cisplatin) 1104
Statue of Liberty 925 Thalidomide 1014 Cytochrome proteins 1110
Rechargeable batteries 928 Blood type and glycoproteins 1016 Thalassemia and chelation therapy
Electroplating 930 Ethanol production from cellulose 1019 1116
Hydrogen-fueled vehicles and fuel Saturated fats, unsaturated fats, and trans Water quality in swimming pools 1120
cells 931 fats 1020
Redox flow batteries 934
xvii
Half-Life 957 Fusion of Hydrogen 972 Fiber Strength and Elasticity 1009
Radiation Penetration 963 Naming Branched Alkanes 991 Formation of Sucrose 1017
Transmutation 968 Chiral Centers 996 Naming Coordination Compounds 1088
Induced Fission and Chain Condensation of Biological Crystal Field Splitting 1098
Reactions 969 Polymers 1007
Stacey Lowery Bretz is a University Distinguished Professor in the Department of Chemistry and
Biochemistry at Miami University in Oxford, Ohio. She earned her BA in chemistry from Cornell
University, MS from Pennsylvania State University, and a PhD in chemistry education research
from Cornell University. She spent one year at the University of California, Berkeley, as a postdoc
in the Department of Chemistry. Her research expertise includes the development of assessments
to measure chemistry students’ thinking with multiple representations (particulate, symbolic, and
macroscopic) and to promote meaningful and inquiry learning in the chemistry laboratory. She
is a Fellow of the American Chemical Society and a Fellow of the American Association for the
Advancement of Science. She has been honored with both of Miami University’s highest teaching
awards: the E. Phillips Knox Award for Undergraduate Teaching and the Distinguished Teaching
Award for Excellence in Graduate Instruction and Mentoring. Stacey won the prestigious, interna-
tional award from the American Chemical Society for Achievement in Research for the Teaching
and Learning of Chemistry in 2020.
xix
D
ear Student,
We wrote this book with three overarching goals in mind: to make chem-
istry interesting, relevant, and memorable; to enable you to see the world
from a molecular point of view; and to help you become an expert problem-solver.
You have a number of resources available to assist you to succeed in your general
chemistry course. This textbook will be a valuable resource, and we have written
it with you, and the different ways you may use the book, in mind.
If you are someone who reads a chapter from the first page to the last, you will
see that the Sixth Edition introduces the chemical principles within a chapter by
using contexts drawn from daily life as well as from other disciplines, including
biology, environmental science, materials science, astronomy, geology, and medi-
cine. We believe that these contexts make chemistry more interesting, relevant,
and memorable.
Chemists’ unique perspective of natural processes and insights into the prop-
erties of substances, from high-performance alloys to the products of biotechnol-
ogy, are based on understanding these processes and substances at the particulate
PARTICUL ATE RE VIEW
level (the atomic and molecular level).
Particles in the Gas Phase A major goal of this book is to help
In Chapter 5 we focus on the properties of gases, you develop this microscale perspec-
including those that serve as fuels in combustion
reactions, as described in Chapter 3, and in other tive and link it to macroscopic
forms of energy production. One such fuel is hydrogen properties.
gas, which can be produced by passing an electric
current through water, causing molecules of liquid H2O With that in mind, we begin each
to decompose into molecules of H2 and O2 gas.
● Write a balanced chemical equation describing this decomposition reaction.
chapter with a Particulate Review
● In the circle on the right, draw the products that would be produced by decomposition
and Particulate Preview. The goal of
of six of the water molecules on the left. these tools is to prepare you for the
● Classify the products as elements, compounds, or a mixture. Choose all that apply.
material in the chapter. The Particu-
(Review Sections 1.1, 1.2, and 3.3 if you need help.)
(Answers to Particulate Review questions are in the back of the book.) late Review assesses important prior
knowledge that you need to interpret
particulate images in the chapter. The
PARTICUL ATE PRE VIEW
Particulate Preview asks you to spec-
Pressure, Volume, and Temperature ulate about new concepts you will see
As you read Chapter 5, look for ideas that will help you answer these in the chapter and is meant to focus
questions.
● Draw particulate images of the helium in the tank and in one of the
your reading.
balloons. How do these drawings differ? If you want a quick summary of
● Suppose the tank and several helium-filled balloons are placed in
xx
topic to topic in an order you select, or reviewing material for an exam, the Learn-
ing Outcomes can help you focus on the key information you need to know and
the skills you should develop.
In every section, you will find key terms in boldface in the text and in a run-
ning glossary in the margin. We have inserted the definitions throughout the
text, so you can continue reading without interruption but quickly find key terms
when doing homework or reviewing for a test. All key terms are also defined in
the Glossary in the back of the book. CONCEPT TEST
Approximately once per section, you will Which graph in Figure 5.18 correctly describes the relationship between the value of
V/n as n is increased at constant P and T?
find a Concept Test. These short, concep-
tual questions provide a self-check opportu-
nity by asking you to stop and answer a 5.22. Use representations [A] through [I] in
V V V V Figure P5.22
question relating to what you just read. We ––n ––
n ––
n226
to answer questions (a)–(f).
C H A P T EThe
R 5 pink ––
nballoons
Properties contain
of Gases
designed them to help you self-assess, and hydrogen, the yellow balloons contain nitrogen, and the
gray balloons contain oxygen. personal experience, adding more gas to
you will find answers to Concept Tests in (a) n n a. Identify three different n changes that
If some of this gas escapes, balloon volu
could ben responsible
(b) (c) (d) we may conclude that the volume of a
the back of the book. FIGURE 5.18
for the change in size of
(Answers to Concept Tests are in the back of the book.)
the pink balloon from [A] to [C].
quantity (number of moles) of gas in th
b. If the smaller pink balloon in [A] correspondsand to the
New concepts naturally build on previ- particulate view in [B], which of the changes identified
n is known as Avogadro’s law to h
who articulated that the volume of a ga
ous information, and you will find that many concepts are related to others in part (a)Cwould NNECTIONresult inIn Chapter
the larger
3 the pink
numberballoon in [C]
directly proportional to the quantity of
of particles in a mole was defined as the
described earlier in the book. We point out these relationships with Connection also corresponding to the particulate view in [B]?
Avogadro constant, in honor of Amedeo V
c. If the smaller yellowearlyballoon in [D] thatcorresponds to V ~ n or 5 constant
icons in the margins. These reminders will help you see the big picture and draw Avogadro’s
the particulate view
determining
work with gases
in [E],
atomic
led to
which particulate view
masses.
n
your own connections between concepts in the book. corresponds to the larger yellow balloon in [F] if no
CONCEPT TEST
At the end of each chapter are Visual Problems that ask you to interpret additional nitrogen has been added?
d. If the larger gray balloon in [I] corresponds toWhich the graph in Figure 5.18 correctly descr
atomic and molecular views of elements and compounds, along with graphs of particulate view in [E], which particulate viewV/n as n is increased at constant P and T?
represents
experimental data. The last Visual Problem in each chapter contains a visual the gas at a lower temperature?
e. If each gray balloon contains 1 mol of gas at 25°C, in
problem matrix. This grid consists of nine images followed by a series of ques-
which balloon are the collisions between the oxygen
tions that will test your ability to identify the similarities and differences among molecules and the––
V
n inside of the balloon more
V
n frequent?
––
V
––
n
the macroscopic and particulate images. f. Which balloon contains the gas with the shortest mean
free path?
n n n
(a) (b) (c)
5.22. Use representations [A] through [I] in Figure P5.22 A B C
to answer questions (a)–(f). The pink balloons contain FIGURE 5.18 (Answers to Concept Tests are in the back of the bo
FIGURE P5.22
chem6_69730_ch05_0212-0269.indd 226
D E F
If you’re looking for additional help visualizing a concept, we have nearly 140
animations and simulations, denoted by the ChemTour and Stepwise Anima-
tion icons. These animations, available at digital.wwnorton.com/chem6, show
chemical concepts and processes to help you visualize events at the macro, micro,
and symbolic level. Many of the ChemTours are interactive, allowing you to
manipulate variables and observe changes in a graph or a process. Questions at
the end of ChemTours offer step-by-step assistance in solving problems and pro-
vide useful feedback.
Another goal of the book is to help you improve your problem-solving skills.
Sometimes the hardest parts of solving a problem is knowing where to start and
distinguishing between information that is relevant and information that is not.
Once you are clear on where you are starting and where you are going, planning
for and arriving at a solution become much easier.
To help you hone your problem-solving skills, we have developed a framework
that is introduced in Chapter 1 and used consistently throughout the book. It is a
four-step approach we call COAST, which is our acronym for (1) Collect and
Organize, (2) Analyze, (3) Solve, and (4) Think About It. We use these four steps
in every Sample Exercise and in the solutions to odd-numbered problems in the
Student Solutions Manual. They are also used in the hints and feedback embed-
ded in the Smartwork5 online homework program. To summarize the four steps:
Collect and Organize helps you understand where to begin. In this step we often
point out what you must find and what is given, including the relevant information
that is provided in the problem statement or available elsewhere in the book.
Analyze is where we map out a strategy for solving the problem. As part of that
strategy we often estimate what a reasonable answer might be.
Solve applies our strategy from the second step to the information and relation-
ships identified in the first step as we solve the problem. We walk you through each
step in the solution, using dimensional analysis consistently, so that you can follow
the logic as well as the math.
Think About It reminds us that calculating or determining an answer is not the
last step when solving a problem. We check whether the answer is reasonable in
light of our estimate. Is it realistic? Are the units correct? Is the number of signifi-
cant figures appropriate?
Many students use the Sample Exercises more than any other part of the
book. Sample Exercises take the concepts being discussed and illustrate how to
apply them to solve problems. We hope that repeated application of COAST will
help you refine your problem-solving skills and become an expert problem-solver.
When you finish a Sample Exercise, you’ll find a Practice Exercise to try on your
own. Notice that the Sample Exercises and the Learning Objectives are connected.
We think this will help you focus efficiently on the main ideas in the chapter.
Students sometimes comment that the questions on an exam are more chal-
lenging than the Sample Exercises in a book. To address this, we have an Inte-
grating Concepts Sample Exercise near the end of each chapter. These exercises
require you to use more than one concept from the chapter and may expect you to
use concepts from earlier chapters to solve a problem. Please invest your time
working through these problems because we think they will further enhance your
problem-solving skills and give you an increased appreciation of how chemistry is
used in the world.
If you use the book mostly as a reference and problem-solving guide, we have
a learning path for you as well. It starts with a Summary and a Problem-Solving
Summary at the end of each chapter. The first is a brief synopsis of the chapter,
organized by Learning Outcomes and referencing sections from the chapter. Key
figures have been added to this Summary to provide visual cues as you review. The
Problem-Solving Summary organizes the chapter by problem type and summa-
rizes relevant concepts and equations you need to solve each type of problem. The
Problem-Solving Summary also points you back to the relevant Sample Exercises
that model how to solve each problem and cross-references the Learning Out-
comes at the beginning of the chapter.
PROBLEM-SOLVING SUMMARY
Type of Problem Concepts and Equations Sample Exercises
Calculating pressure of any gas; Divide the force by the area over which the force is applied, using 5.1, 5.2
calculating atmospheric pressure the equation
F
P5 (5.1)
A
Calculating changes in P, V, or T in Rearrange 5.3, 5.4, 5.5, 5.6
response to changing conditions P1V1 PV
5 2 2 (5.18)
T1 T2
for whichever variable is sought and then substitute given values.
(T must be in kelvins, and n must be constant.)
Determining n from P, V, and T Rearrange 5.7, 5.8, 5.9
PV 5 nRT (5.15)
for n and then substitute given values of P, T, and V. (T must be in
kelvins.)
Calculating the density of a gas and Substitute values for pressure, absolute temperature, and molar 5.10, 5.11
calculating molar mass from density mass into the equation
P}
d5 (5.21)
RT
Substitute values for pressure, absolute temperature, and density
into the equation
dRT
}5 (5.22)
P
Calculating mole fraction for one Divide the number of moles of the component gas by the total 5.12
component gas in a mixture number of moles in the mixture:
n
Xx 5 x (5.24)
ntotal
Calculating partial pressure of one Substitute the mole fraction of the component gas and the total 5.13, 5.14
component gas in a mixture and total pressure in the equation
pressure in the mixture Px 5 Xx Ptotal (5.25)
Solve the equation
Ptotal 5 P1 1 P2 1 P3 1 P4 1 . . . (5.23)
for the partial pressure of the component gas and then substitute
given values for other partial pressures and total pressure.
Following the summaries are groups of questions and problems. The first
group is the Visual Problems. Concept Review Questions and Problems come
next, arranged by topic in the same order as they appear in the chapter. Concept
Reviews are qualitative and often ask you to explain why or how something hap-
pens. Problems are paired and can be quantitative, conceptual, or a combination
of both. Contextual problems have a title that describes the context in which the
problem is placed. Additional Problems can come from any section or combina-
tion of sections in the chapter. Some of them incorporate concepts from previous
chapters. Problems marked with an asterisk (*) are more challenging and often
require multiple steps to solve.
5.87. Biological Effects of Radon Exposure Radon is a naturally 5.155. Anesthesia A common anesthesia gas is halothane, with
occurring radioactive gas found in the ground and in the structure shown in Figure P5.155. Liquid halothane
building materials. It is easily inhaled and emits a particles boils at 50.2°C and 1.00 atm. If halothane behaved as an
when it decays. Cumulative radon exposure is a significant ideal gas, what volume would 10.0 mL of liquid halothane
risk factor for lung cancer. (d 5 1.87 g/mL) occupy at 60°C and 1.00 atm of pressure?
a. Calculate the density of radon at 298 K and 1.00 atm of What is the density of halothane vapor at 55°C and
pressure. 1.00 atm of pressure?
b. Are radon concentrations likely to be greater in the
basement or on the top floor of a building?
Cl F
Br C C F
*5.88. Four empty balloons, each with a mass of 10.0 g, are
inflated to a volume of 20.0 L. The first balloon contains H F
He; the second, Ne; the third, CO2; and the fourth, CO.
FIGURE P5.155
If the density of air at 25°C and 1.00 atm is 0.00117 g/mL,
which of the balloons float in this air?
Before some blazing logs, which fill a deep fireplace with warmth
that overflows to just the right extent into the room, stands, slightly
skewed, a sofa. The sofa is a comfortable one. It is short, deep, and
low; and the arms have a suggestion of longing to be filled that is
truly seductive. In addition, two down cushions imply that the sofa is
quite prepared to fit itself to any figure, be it long, short, broad, or
narrow. Altogether, it is a most satisfactory sofa.
But the satisfactoriness does not end here. Seated at one end of
that sofa is a girl, clearly in that neither grass nor hay period, which
begins at sixteen and ends at eighteen. Not that it is intended to
suggest that because the girl is neither hay nor grass she is
unattractive. Quite the reverse. New-mown hay is the sweetest, and
the girl, if neither child nor woman, is, in her way, just as sweet.
In algebra, when a, b, and c are computed, it is possible to find the
unknown quantity x. Applying an algebraic formula to the above, we
at once deduce what is necessary to complete the factors. It may be
stated thus: a, a sofa, plus b, a charming girl; and as a, a sofa, must
be divided by two, we find the unknown quantity to be x, a man, and
the product of our a, b, and x to equal xxx, or triple bliss. Nor is this
wrong. The sofa does not do more than seat two people comfortably,
yet at the present moment there are little spaces at both ends.
Concerning the other details of this a ÷ 2 + b + x − 0 (i. e. Mrs.
Grundy), it seems needless to enlarge.
“And isn’t it wonderful, Freddy, that you should love me and I
should love you?” cooed the girl.
“Just out of sight,” replied Freddy.
Most people would agree with the above remarks, though the
circumstance of a man and woman occasionally loving each other is a
phenomenon recognised, if not approved, by science. But though
these two did not know it, there was a wonder here. Freddy has been
spoken of in the masculine gender, because, as Shakespeare wrote:
“The Lord made him, therefore let him pass for a man.” Otherwise
his manliness was open to debate. Lovable the girl unquestionably
was, or at least very fast verging upon it, but it passeth human
intelligence how Freddy could inspire any sort of feeling except an
intense longing for a gun loaded with goose-shot.
“And that we should have loved each other for so long, and never
either of us dreamed that we cared one little bit for each other,”
continued the girl.
Freddy did not assent to this sentiment as readily as to the former.
Freddy had been quite sure that Frances had been pining for his love
in secret for some months. So he only remarked: “We got there all
the same.”
“Yes,” assented Frances. “And we’ll love each other always, now.”
“But I say,” inquired Freddy, “what do you think your father and
mother will say?”
“Why, they’ll be delighted,” cried the girl. “It couldn’t be better.
Cousins,—and just the same age—and, and— Oh, lots of other
reasons, I’m sure, but I can’t think of them now.”
“Let’s tell them together,” suggested Freddy, courageously.
“Freddy! Of course not. That isn’t the right way. No, you must
request an interview with papa in his library, and plead eloquently
with him.”
“I suppose I must,” answered Freddy, with a noticeable limpness
in his voice and vertebræ.
“Wouldn’t it be fun if he should refuse his consent!” exclaimed the
girl.
Freddy did not recognise the comical quality. “I don’t see it,” he
moaned.
“Why, it would be so romantic! He would of course order you to
leave the house, and never, never darken his doors again. That’s what
the father always does.”
“You think that’s fun?”
“Such fun! Then, of course, we should have to arrange for romantic
meetings, and secret interviews, and you would write little letters
and put them in a prayer-book in our pew; and watch to get a
glimpse of me as I go in and out of places; and stand on the opposite
side of the street each night, till you saw the light in my room put
out. Oh! What fun it will be!”
“It might be raining,” complained Freddy.
“All the better. That would prove your devotion. Don’t you love me
enough to do that?”
“Yes,” said Freddy, meekly, “but I hate getting wet. Sometimes one
catches a nasty cold.”
“Any one who tells a girl he loves her with a fervour and passion
never yet equalled by man should not think of such things,” asserted
Frances, disapprovingly.
Freddy had an idea that a girl who reciprocated such a passion
should not seem so happy over the prospect of her lover undergoing
the exposure, but the youth did not know how to express it. So he
proposed: “Let’s keep it a secret for the present.”
“Let’s,” assented Frances. “We won’t tell any one for a long time,
but just have it all to ourselves. And when I am riding in the morning
you must join me; the groom will think it’s all right. And whenever
papa and mama are to be out in the evening, I’ll put a lamp in my
window, and—”
Ting!
It seemed as if some of the electric current which made that
distant muffled ring had switched and passed through the happy
pair. Both started guiltily, and then both listened with the greatest
intentness; so intensely, that after a moment’s pause they could hear
the soft gliding sound of the footman’s list slippers as they travelled
down the hallway; could hear the click of the lock as he opened the
front door; could hear the murmur of voices; could hear the door
closed. Then, after a moment’s silence, a voice, for the first time
articulate to them, said: “I’ll wait in the morning room.”
“Freddy,” gasped the girl, “it’s that horrid Mr. Potter. Quick!”
Both had arisen from the sofa, and Freddy looked about in a very
badly perplexed condition. He was quite willing, but about what was
he to be quick?
“Sit down in that chair,” whispered the girl, pointing to one at a
more than proper distance, and Freddy sprinted for it, and sat down.
The girl resumed her seat on the little sofa, and putting her hands in
a demure position, rather contradictory to her quick breathing and
flushed cheeks, began: “As you were saying, the De Reszke brothers
were the only redeeming— Oh! Good evening, Mr. Potter.”
“Good evening, Frances,” responded a tall, rather slender, strong-
featured man, attired in evening dress, who had leisurely strolled
into the room, and who did not offer to go through the form of
shaking hands. “Talking to the fire?”
“No. Freddy and I were chatting about the opera.”
Mr. Potter put on his glasses and languidly surveyed the region of
the fireplace. Then he turned and extended his investigation, till his
eyes settled on Freddy, stuck away in the dim distance.
“Oh, are you there, youngster?” he remarked, in a tone of voice
implying that the question carried no interest with it. He looked at
his watch. “Isn’t it rather late for you two?”
“It’s only quarter past ten,” answered Frances, bristling
indignantly. “And if it were twelve it wouldn’t make any difference.”
To herself she said, “How I hate that man! Just because he’s thirty-
four, he always treats us as if we were children; and the way he
tramples on poor, dear Freddy is outrageous!”
“You don’t seem to be very sociably inclined,” said Mr. Potter.
“From the distance between you I should think you two chicks had
been quarrelling. Come, make it up.”
“Not at all,” cried Frances, indignantly. “I never lose my temper;
except when you are here.”
“Is that the reason you haven’t asked me to sit down?” asked
Potter, smiling.
“Of course you are to sit down, if you want,” exclaimed Frances.
“Here.” And she moved the four inches towards her end of the sofa
that had not been occupied under the previous arrangement.
Mr. Potter seated himself leisurely in Freddy’s old place, and
arranged one of the cushions to fit the small of his back. “I came to
say good-bye to your mother,” he explained, “and as I’m too busy to
stop in to-morrow, I decided to wait. You youngsters needn’t think it
necessary to sit up to entertain me. Won’t Freddy’s mother be
sending his nurse for him if he stays much later?”
“I’m so glad you are going to Europe,” remarked Frances. “I hope
you’ll stay a long while.”
Mr. Potter put his glasses on again and looked at Frances calmly.
“Hello!” he said mentally, “the kitten’s learning how to hiss.” Aloud
he announced: “I shall only be gone for a month or two,—just the
voyage and a change.”
“What a pity!” responded Frances, bitingly.
“I thought you’d miss me,” replied Mr. Potter, genially.
Frances gave an uneasy movement on the sofa, a cross between an
angry shake of the shoulders and a bounce.
“Where are you going?” questioned Freddy at this point, feeling
that as a grown man he must bear his part of the chat.
“Look here, littleun,” said Mr. Potter, “if you expect me to talk to
you back there, you—” At this point he suddenly ceased speaking, as
if something more interesting than his unfinished remark had
occurred to him.
“Freddy found it too warm by the fire,” explained Frances hastily,
guilty at heart, if to outward appearance brazen. But Mr. Potter did
not hear what she said, and sat looking into the fire with a suddenly
serious look, which nevertheless had a laugh not very far underneath.
After quite a pause, Frances said: “How entertaining you are!”
“Yes,” assented Mr. Potter, coming back from his thoughts; “I
always enjoy myself, and I find that other people do the same.” Then
he again relapsed into meditation.
“Isn’t he just as horrid as can be?” raged Frances, inwardly. “He
believes just because some women think him clever, and because
men like him, and because he’s a good business man, and because
mama’s always praising him to his face, as she would any one who
was papa’s partner, that he is perfect. And no matter how you try to
snub him, he is so conceited that he won’t see it. Horrid old thing!”
Aloud she asked, “What are you thinking about?”
Mr. Potter laughed. “That’s a great secret,” he asserted.
⁂
An hour later, Mr. Potter was seated in a library, smoking, with a
glass of seltzer—and something else—at his elbow. Opposite to him
sat a man of perhaps twice his years, equally equipped with a cigar
and seltzer—and something else.
“Well,” remarked the senior, “I think if we can get the whole issue
at 82½ and place them at 87 and accrued interest, we had better do
it.”
“That’s settled then,” agreed Mr. Potter. “Now, is there anything
else? I don’t want to have cablegrams following me, since I’m going
for a rest.”
“No,” replied the other. “I know I shall want my partner’s advice
often enough, but I’ll get on without you. Take a rest. You can afford
it. There’s nothing else.”
“Then if you are through with business, I want to speak to you of
Frances,” said Mr. Potter.
Mr. De Witt turned and looked at Mr. Potter quickly. “What
about?”
“Do you know that that girl’s grown up, and we none of us have
realised it?”
“Well?”
“And do you know that she has seen next to no people,—that her
morning ride, her studies, and her afternoon drive with her mother
are the only events of her day?”
“Well?”
“And that her summers, off in that solitary country house of yours,
with never a bit of company but Freddy De Witt and myself, are
horribly dull and monotonous?”
“Well?”
“And that to kill time she reads a great many more novels than is
good for any one?”
“Come, come, Champney, what are you driving at?”
“One more question. Mrs. De Witt and you are dining out almost
nightly. What do you suppose Frances does evenings?”
“Does? Plays a bit, and reads a bit, and goes to bed like a good
child.”
“But I tell you she isn’t a child any longer, so you can’t expect her
to behave like one. It dawned upon me this evening, and the quicker
it dawns upon you the better.”
“Why?”
“Do you want her to make a fool of herself over Freddy?”
“Freddy!”
“Yes, Freddy.”
“Ridiculous! Impossible!”
“Because they are a long way towards it, and if you want to end it,
you’ll have to use drastic measures.”
“Her own cousin, and only eighteen! I never heard of such folly.”
“But I tell you those two think they are in love with each other, and
if you don’t do something, they’ll really become so before long.
Thinking a thing is two-thirds of the way to doing it, as is shown by
the mind cure.”
“I’ll put an end to it at once,” growled Mr. De Witt. “Never heard of
such nonsense.”
“And how will you end it?” inquired Mr. Potter, smiling a little.
“End it? Tell them to stop their foolishness. Send him about his
business.”
“I thought that would probably be your way. Don’t you think it
would be better to get an injunction from the courts?”
“What good would an injunction do?” asked Mr. De Witt, crossly.
“Just as much good as your method. You can no more stop boys’
and girls’ love by calling it foolishness than the courts can. If you do
as you propose, you’ll probably have a runaway match, or some other
awful bit of folly.”
“Well, what can I do?”
“The best thing is to pack your trunks and travel a bit. That will
give her something else to think about, and she’ll forget all about the
little chap.”
“But I can’t leave the business.”
“The business will run itself. Or, if it won’t, what’s a year’s profits
compared to your only daughter’s life happiness?”
“But the bonds?”
“Don’t bid on them.”
“I can’t go. I can’t leave my business. Why, I haven’t been away
from it for more than a week in forty years.”
“All the more reason for going now.”
“I have it. Her mother and she shall sail with you.”
“Oh, get out!” ejaculated Champney, “I’m going for a rest.” Mr.
Potter had been the slave for many years of two selfish sisters and a
whining mother,—a mother who loved to whine,—and womankind
meant to him an absolute and entire nuisance.
“That’s it,” said the senior partner, regardless of this protest. “You
arrange to stay for six months instead of two. I’ll do your work
gladly.”
“I can’t,” groaned Potter.
“Come, Champney,” wheedled the elder, “you say yourself that my
little girl’s life happiness depends on her going. For my sake! Come! I
did a good turn for you—or at least you’ve always said I did—in the
partnership. Now do one for me.”
Potter sighed. He was used to being martyrised where women were
concerned and had not learned how to resist. “Well, if you say so. But
I’ll have to leave them there. Two months is my limit.”
“All right,” assented the senior, gleefully.
“Perhaps,” thought Potter, “perhaps they won’t be able to pack in
time.” And the idea seemed to please him.
For half an hour longer they chatted, and then Potter rose.
“Tell me, Champney,” inquired the senior, “how did you find out
about it?”
“Oh,” laughed Champney, “that’s telling.”
⁂
The next day there was woe in Israel. Mr. De Witt was cross over
the “children’s folly,” as he called it. Mrs. De Witt was deeply insulted
at such sudden and peremptory marching orders. “Men are so
thoughtless,” she groaned; “as if one could be ready to go on a day’s
notice!” Champney was blue over the spoiling of his trip. Freddy,
when he heard the news, was the picture of helplessness and misery,
and only added to the friction by coming round and getting in
everybody’s way, in the rush of the packing. As for Frances, she
dropped many a secret tear into the trunks as her belongings were
bestowed therein. Never, it seemed to her, had true love been so
crossed.
“I know Mr. Potter is at the bottom of it.” (Frances was not
alluding to the trunk before which she knelt.) “He’s always doing
mean things, yet he never will acknowledge them. He won’t even pay
me the respect of denying them.” Frances slapped a shawl she was
packing, viciously. “To think of having to travel with him! He won’t
even look at me. No. He doesn’t even pay me the compliment of
looking at me. I don’t believe he’s even noticed my eyes and
eyelashes.” Frances gazed into a hand-glass she was about to place in
the trunk, and seemed less cross for a moment after the scrutiny.
“He’s just as snubby as he can be. I hate snubby people, and I’ll be
just as snubby to him as I know how. I’ll—”
“Good afternoon, Frances,” interrupted a voice, which made that
young lady nearly jump into the trunk she was bending over. “I came
up to see if I could do anything for you or your mother, and she sent
me in to ask you.”
Frances was rather flushed, but that may have been due to the
stooping position. “I don’t think of anything,” she answered.
“I’ve had some chairs sent on board, and laid in novels and
smoked glasses and puzzles; and oysters, and game, and fruit, and
butter,” said Champney, with a suggestion of weariness, “and I don’t
think of anything else. If you can suggest something more, I’ll get it.”
“I don’t know— Yes. You might change your mind and let us stay at
home,” snapped Frances.
“Don’t blame me for that,” laughed Champney. “That’s your
father’s doings.”