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Copyright, iv
About the Authors, xv
Preface, xvi
Chapter 1. Fundamental Concepts of Thermodynamics, 1
1.1. What Is Thermodynamics and Why Is It Useful?, 1
1.2. Basic Definitions Needed to Describe Thermodynamic Systems, 2
1.3. Thermometry, 4
1.4. Equations of State and the Ideal Gas Law, 6
1.5. A Brief Introduction to Real Gases, 9
Chapter 2. Heat, Work, Internal Energy, Enthalpy, and the First Law of Thermodynamics, 15
2.1. The Internal Energy and the First Law of Thermodynamics, 15
2.2. Work, 16
2.3. Heat, 19
2.4. Heat Capacity, 21
2.5. State Functions and Path Functions, 23
2.6. Equilibrium, Change, and Reversibility, 25
2.7. Comparing Work for Reversible and Irreversible Processes, 26
2.8. Determining ΔU and Introducing Enthalpy, a New State Function, 30
2.9. Calculating q, w, ΔU and ΔH for Processes Involving Ideal Gases, 31
2.10. The Reversible Adiabatic Expansion and Compression of an Ideal Gas, 35
Chapter 3. The Importance of State Functions: Internal Energy and Enthalpy, 41
3.1. The Mathematical Properties of State Functions, 41
3.2. The Dependence of U on V and T, 46
3.3. Does the Internal Energy Depend More Strongly on V or T?, 48
3.4. The Variation of Enthalpy with Temperature at Constant Pressure, 51
3.5. How are C_P and C_V Related?, 53
3.6. The Variation of Enthalpy with Pressure at Constant Temperature, 54
3.7. The Joule–Thomson Experiment, 57
3.8. Liquefying Gases Using an Isenthalpic Expansion, 59
Chapter 4. Thermochemistry, 63
4.1. Energy Stored in Chemical Bonds Is Released or Taken Up in Chemical Reactions, 63
4.2. Internal Energy and Enthalpy Changes Associated with Chemical Reactions, 64
4.3. Hess’s Law Is Based on Enthalpy Being a State Function, 67
4.4. The Temperature Dependence of Reaction Enthalpies, 69
4.5. The Experimental Determination of ΔU and ΔH for Chemical Reactions, 71
4.6. (Supplemental) Differential Scanning Calorimetry, 73
Chapter 5. Entropy and the Second and Third Laws of Thermodynamics, 79
5.1. The Universe Has a Natural Direction of Change, 79
5.2. Heat Engines and the Second Law of Thermodynamics, 80
5.3. Introducing Entropy, 85
5.4. Calculating Changes in Entropy, 86
5.5. Using Entropy to Calculate the Natural Direction of a Process in an Isolated System, 89
5.6. The Clausius Inequality, 91
5.7. The Change of Entropy in the Surroundings and ΔS_total = ΔS + ΔS_surroundings, 92
5.8. Absolute Entropies and the Third Law of Thermodynamics, 94
5.9. Standard States in Entropy Calculations, 98
5.10. Entropy Changes in Chemical Reactions, 98
5.11. (Supplemental) Energy Efficiency: Heat Pumps, Refrigerators, and Real Engines, 100
5.12. (Supplemental) Using the Fact That S Is a State Function to Determine the Dependence of S on V and T, 107
5.13. (Supplemental) The Dependence of S on T and P, 108
5.14. (Supplemental) The Thermodynamic Temperature Scale, 109
Chapter 6. Chemical Equilibrium, 115
6.1. The Gibbs Energy and the Helmholtz Energy, 116
6.2. The Differential Forms, of U, H, A, and G, 120
6.3. The Dependence of the Gibbs and Helmholtz Energies on P, V, and T, 121
6.4. The Gibbs Energy of a Reaction Mixture, 124
6.5. The Gibbs Energy of a Gas in a Mixture, 125
6.6. Calculating the Gibbs Energy of Mixing for Ideal Gases, 126
6.7. Calculating ΔG°_R for a Chemical Reaction, 127
6.8. Introducing the Equilibrium Constant for a Mixture of Ideal Gases, 129
6.9. Calculating the Equilibrium Partial Pressures in a Mixture of Ideal Gases, 131
6.10. The Variation of K_P with Temperature, 132
6.11. Equilibria Involving Ideal Gases and Solid or Liquid Phases, 134
6.12. Expressing the Equilibrium Constant in Terms of Mole Fraction or Molarity, 135
6.13. The Dependence of ξ_eq on T and P, 136
6.14. (Supplemental) A Case Study: The Synthesis of Ammonia, 137
6.15. (Supplemental) Expressing U and H and Heat Capacities Solely in Terms of Measurable Quantities, 142
6.16. (Supplemental) Measuring ΔG for the Unfolding of Single RNA Molecules, 146
6.17. (Supplemental) The Role of Mixing in Determining Equilibrium in a Chemical Reaction, 147
Chapter 7. The Properties of Real Gases, 155
7.1. Real Gases and Ideal Gases, 155
7.2. Equations of State for Real Gases and Their Range of Applicability, 156
7.3. The Compression Factor, 160
7.4. The Law of Corresponding States, 163
7.5. Fugacity and the Equilibrium Constant for Real Gases, 166
Chapter 8. Phase Diagrams and the Relative Stability of Solids, Liquids, and Gases, 173
8.1. What Determines the Relative Stability of the Solid, Liquid, and Gas Phases?, 173
8.2. The Pressure–Temperature Phase Diagram, 176
8.3. The Phase Rule, 181
8.4. The Pressure–Volume and Pressure–Volume–Temperature Phase Diagrams, 182
8.5. Providing a Theoretical Basis for the P–T Phase Diagram, 184
8.6. Using the Clausius–Clapeyron Equation to Calculate Vapor Pressure as a Function of T, 185
8.7. The Vapor Pressure of a Pure Substance Depends on the Applied Pressure, 188
8.8. Surface Tension, 189
8.9. (Supplemental) Chemistry in Supercritical Fluids, 192
8.10. (Supplemental) Liquid Crystal Displays, 193
Chapter 9. Ideal and Real Solutions, 199
9.1. Defining the Ideal Solution, 200
9.2. The Chemical Potential of a Component in the Gas and Solution Phases, 201
9.3. Applying the Ideal Solution Model to Binary Solutions, 202
9.4. The Temperature–Composition Diagram and Fractional Distillation, 206
9.5. The Gibbs–Duhem Equation, 208
9.6. Colligative Properties, 210
9.7. The Freezing Point Depression and Boiling Point Elevation, 210
9.8. The Osmotic Pressure, 213
9.9. Real Solutions Exhibit Deviations from Raoult’s Law, 214
9.10. The Ideal Dilute Solution, 217
9.11. Activities Are Defined with Respect to Standard States, 219
9.12. Henry’s Law and the Solubility of Gases in a Solvent, 222
9.13. Chemical Equilibrium in Solutions, 223
9.14. Solutions Formed from Partially Miscible Liquids, 227
9.15. The Solid–Solution Equilibrium, 228
Chapter 10. Electrolyte Solutions, 233
10.1. The Enthalpy, Entropy, and Gibbs Energy of Ion Formation in Solutions, 234
10.2. Understanding the Thermodynamics of Ion Formation and Solvation, 236
10.3. Activities and Activity Coefficients for Electrolyte Solutions, 238
10.4. Calculating γ± Using the Debye–Hückel Theory, 241
10.5. Chemical Equilibrium in Electrolyte Solutions, 245
Chapter 11. Electrochemical Cells, Batteries, and Fuel Cells, 249
11.1. The Effect of an Electrical Potential on the Chemical Potential of Charged Species, 250
11.2. Conventions and Standard States in Electrochemistry, 251
11.3. Measurement of the Reversible Cell Potential, 254
11.4. Chemical Reactions in Electrochemical Cells and the Nernst Equation, 254
11.5. Combining Standard Electrode Potentials to Determine the Cell Potential, 256
11.6. Obtaining Reaction Gibbs Energies and Reaction Entropies from Cell Potentials, 257
11.7. The Relationship between the Cell EMF and the Equilibrium Constant, 258
11.8. Determination of E° and Activity Coefficients Using an Electrochemical Cell, 260
11.9. Cell Nomenclature and Types of Electrochemical Cells, 260
11.10. The Electrochemical Series, 262
11.11. Thermodynamics of Batteries and Fuel Cells, 263
11.12. The Electrochemistry of Commonly Used Batteries, 263
11.13. Fuel Cells, 265
11.14. (Supplemental) Electrochemistry at the Atomic Scale, 267
11.15. (Supplemental) Using Electrochemistry for Nanoscale Machining, 273
11.16. (Supplemental) Absolute Half-Cell Potentials, 274
Chapter 12. From Classical to Quantum Mechanics, 281
12.1. Why Study Quantum Mechanics?, 281
12.2. Quantum Mechanics Arose Out of the Interplay of Experiments and Theory, 282
12.3. Blackbody Radiation, 283
12.4. The Photoelectric Effect, 285
12.5. Particles Exhibit Wave-Like Behavior, 287
12.6. Diffraction by a Double Slit, 287
12.7. Atomic Spectra and the Bohr Model of the Hydrogen Atom, 291
Chapter 13. The Schrödinger Equation, 297
13.1. What Determines if a System Needs to Be Described Using Quantum Mechanics?, 297
13.2. Classical Waves and the Nondispersive Wave Equation, 302
13.3. Waves Are Conveniently Represented as Complex Functions, 305
13.4. Quantum Mechanical Waves and the Schrödinger Equation, 307
13.5. Solving the Schrödinger Equation: Operators, Observables, Eigenfunctions, and Eigenvalues, 308
13.6. The Eigenfunctions of a Quantum Mechanical Operator Are Orthogonal, 310
13.7. The Eigenfunctions of a Quantum Mechanical Operator Form a Complete Set, 313
13.8. Summing Up the New Concepts, 314
Chapter 14. The Quantum Mechanical Postulates, 319
14.1. The Physical Meaning Associated with the Wave Function, 320
14.2. Every Observable Has a Corresponding Operator, 321
14.3. The Result of an Individual Measurement, 321
14.4. The Expectation Value, 322
14.5. The Evolution in Time of a Quantum Mechanical System, 325
Chapter 15. Using Quantum Mechanics on Simple Systems, 327
15.1. The Free Particle, 327
15.2. The Particle in a One-Dimensional Box, 329
15.3. Two- and Three-Dimensional Boxes, 333
15.4. Using the Postulates to Understand the Particle in the Box and Vice Versa, 334
Chapter 16. The Particle in the Box and the Real World, 345
16.1. The Particle in the Finite Depth Box, 345
16.2. Differences in Overlap between Core and Valence Electrons, 346
16.3. Pi Electrons in Conjugated Molecules Can Be Treated as Moving Freely in a Box, 347
16.4. Why Does Sodium Conduct Electricity and Why Is Diamond an Insulator?, 348
16.5. Tunneling through a Barrier, 350
16.6. The Scanning Tunneling Microscope, 351
16.7. Tunneling in Chemical Reactions, 354
16.8. (Supplemental) Quantum Wells and Quantum Dots, 355
Chapter 17. Commuting and Noncommuting Operators and the Surprising Consequences of Entanglement, 365
17.1. Commutation Relations, 365
17.2. The Stern–Gerlach Experiment, 367
17.3. The Heisenberg Uncertainty Principle, 370
17.4. (Supplemental) The Heisenberg Uncertainty Principle Expressed in Terms of Standard Deviations, 373
17.5. (Supplemental) A Thought Experiment Using a Particle in a Three-Dimensional Box, 376
17.6. (Supplemental) Entangled States, Teleportation, and Quantum Computers, 378
Chapter 18. A Quantum Mechanical Model for the Vibration and Rotation of Molecules, 387
18.1. Solving the Schrödinger Equation for the Quantum Mechanical Harmonic Oscillator, 387
18.2. Solving the Schrödinger Equation for Rotation in Two Dimensions, 392
18.3. Solving the Schrödinger Equation for Rotation in Three Dimensions, 395
18.4. The Quantization of Angular Momentum, 397
18.5. The Spherical Harmonic Functions, 399
18.6. (Optional Review) The Classical Harmonic Oscillator, 402
18.7. (Optional Review) Angular Motion and the Classical Rigid Rotor, 406
18.8. (Supplemental) Spatial Quantization, 407
Chapter 19. The Vibrational and Rotational Spectroscopy of Diatomic Molecules, 413
19.1. An Introduction to Spectroscopy, 413
19.2. Absorption, Spontaneous Emission, and Stimulated Emission, 415
19.3. An Introduction to Vibrational Spectroscopy, 417
19.4. The Origin of Selection Rules, 420
19.5. Infrared Absorption Spectroscopy, 422
19.6. Rotational Spectroscopy, 425
19.7. (Supplemental) Fourier Transform Infrared Spectroscopy, 430
19.8. (Supplemental) Raman Spectroscopy, 432
19.9. (Supplemental) How Does the Transition Rate between States Depend on Frequency?, 434
Chapter 20. The Hydrogen Atom, 445
20.1. Formulating the Schrödinger Equation, 445
20.2. Solving the Schrödinger Equation for the Hydrogen Atom, 446
20.3. Eigenvalues and Eigenfunctions for the Total Energy, 447
20.4. The Hydrogen Atom Orbitals, 453
20.5. The Radial Probability Distribution Function, 455
20.6. The Validity of the Shell Model of an Atom, 459
Chapter 21. Many-Electron Atoms, 463
21.1. Helium: The Smallest Many-Electron Atom, 463
21.2. Introducing Electron Spin, 465
21.3. Wave Functions Must Reflect the Indistinguishability of Electrons, 466
21.4. Using the Variational Method to Solve the Schrödinger Equation, 470
21.5. The Hartree–Fock Self-Consistent Field Method, 472
21.6. Understanding Trends in the Periodic Table from Hartree–Fock Calculations, 479
Chapter 22. Quantum States for Many-Electron Atoms and Atomic Spectroscopy, 487
22.1. Good Quantum Numbers, Terms, Levels, and States, 488
22.2. The Energy of a Configuration Depends on Both Orbital and Spin Angular Momentum, 489
22.3. Spin-Orbit Coupling Breaks Up a Term into Levels, 496
22.4. The Essentials of Atomic Spectroscopy, 497
22.5. Analytical Techniques Based on Atomic Spectroscopy, 500
22.6. The Doppler Effect, 502
22.7. The Helium-Neon Laser, 503
22.8. Laser Isotope Separation, 507
22.9. Auger Electron and X-Ray Photoelectron Spectroscopies, 508
22.10. Selective Chemistry of Excited States: O(³P) and O(¹D), 511
22.11. (Supplemental) Configurations with Paired and Unpaired Electron Spins Differ in Energy, 511
Chapter 23. The Chemical Bond in Diatomic Molecules, 517
23.1. The Simplest One-Electron Molecule: H₂⁺, 517
23.2. The Molecular Wave Function for Ground-State H₂⁺, 519
23.3. The Energy Corresponding to the H₂⁺ Molecular Wave Functions ψ_g and ψ_u, 520
23.4. A Closer Look at the H₂⁺ Molecular Wave Functions ψ_g and ψ_u, 523
23.5. Combining Atomic Orbitals to Form Molecular Orbitals, 526
23.6. Molecular Orbitals for Homonuclear Diatomic Molecules, 530
23.7. The Electronic Structure of Many-Electron Molecules, 534
23.8. Bond Order, Bond Energy, and Bond Length, 537
23.9. Heteronuclear Diatomic Molecules, 539
23.10. The Molecular Electrostatic Potential, 540
Chapter 24. Molecular Structure and Energy Levels for Polyatomic Molecules, 547
24.1. Lewis Structures and the VSEPR Model, 547
24.2. Describing Localized Bonds Using Hybridization for Methane, Ethene, and Ethyne, 550
24.3. Constructing Hybrid Orbitals for Nonequivalent Ligands, 553
24.4. Using Hybridization to Describe Chemical Bonding, 556
24.5. Predicting Molecular Structure Using Qualitative Molecular Orbital Theory, 558
24.6. How Different Are Localized and Delocalized Bonding Models?, 561
24.7. Qualitative Molecular Orbital Theory for Conjugated and Aromatic Molecules: The Hückel Model, 563
24.8. From Molecules to Solids, 568
24.9. Making Semiconductors Conductive at Room Temperature, 570
Chapter 25. Electronic Spectroscopy, 575
25.1. The Energy of Electronic Transitions, 575
25.2. Molecular Term Symbols, 576
25.3. Transitions between Electronic States of Diatomic Molecules, 579
25.4. The Vibrational Fine Structure of Electronic Transitions in Diatomic Molecules, 580
25.5. UV-Visible Light Absorption in Polyatomic Molecules, 582
25.6. Transitions among the Ground and Excited States, 584
25.7. Singlet–Singlet Transitions: Absorption and Fluorescence, 585
25.8. Intersystem Crossing and Phosphorescence, 587
25.9. Fluorescence Spectroscopy and Analytical Chemistry, 588
25.10. Ultraviolet Photoelectron Spectroscopy, 589
25.11. Single Molecule Spectroscopy, 591
25.12. Fluorescent Resonance Energy Transfer (FRET), 593
25.13. Linear and Circular Dichroism, 597
25.14. (Supplemental) Assigning + and – to ∑ Terms of Diatomic Molecules, 599
Chapter 26. Computational Chemistry, 603
26.1. The Promise of Computational Chemistry, 603
26.2. Potential Energy Surfaces, 604
26.3. Hartree–Fock Molecular Orbital Theory: A Direct Descendant of the Schrödinger Equation, 608
26.4. Properties of Limiting Hartree–Fock Models, 610
26.5. Theoretical Models and Theoretical Model Chemistry, 615
26.6. Moving Beyond Hartree–Fock Theory, 616
26.7. Gaussian Basis Sets, 621
26.8. Selection of a Theoretical Model, 624
26.9. Graphical Models, 637
26.10. Conclusion, 645
Chapter 27. Molecular Symmetry, 659
27.1. Symmetry Elements, Symmetry Operations, and Point Groups, 659
27.2. Assigning Molecules to Point Groups, 661
27.3. The H₂O Molecule and the C_2v Point Group, 663
27.4. Representations of Symmetry Operators, Bases for Representations, and the Character Table, 668
27.5. The Dimension of a Representation, 670
27.6. Using the C_2v Representations to Construct Molecular Orbitals for H₂O, 674
27.7. The Symmetries of the Normal Modes of Vibration of Molecules, 676
27.8. Selection Rules and Infrared versus Raman Activity, 680
27.9. (Supplemental) Using the Projection Operator Method to Generate MOs That Are Bases for Irreducible Representations, 681
Chapter 28. Nuclear Magnetic Resonance Spectroscopy, 687
28.1. Intrinsic Nuclear Angular Momentum and Magnetic Moment, 687
28.2. The Energy of Nuclei of Nonzero Nuclear Spin in a Magnetic Field, 689
28.3. The Chemical Shift for an Isolated Atom, 691
28.4. The Chemical Shift for an Atom Embedded in a Molecule, 692
28.5. Electronegativity of Neighboring Groups and Chemical Shifts, 693
28.6. Magnetic Fields of Neighboring Groups and Chemical Shifts, 694
28.7. Multiplet Splitting of NMR Peaks Arises through Spin–Spin Coupling, 695
28.8. Multiplet Splitting When More Than Two Spins Interact, 700
28.9. Peak Widths in NMR Spectroscopy, 702
28.10. Solid-State NMR, 704
28.11. NMR Imaging, 704
28.12. (Supplemental) The NMR Experiment in the Laboratory and Rotating Frames, 706
28.13. (Supplemental) Fourier Transform NMR Spectroscopy, 708
28.14. (Supplemental) Two-Dimensional NMR, 712
Chapter 29. Probability, 719
29.1. Why Probability?, 719
29.2. Basic Probability Theory, 720
29.3. Stirling’s Approximation, 728
29.4. Probability Distribution Functions, 729
29.5. Probability Distributions Involving Discrete and Continuous Variables, 731
29.6. Characterizing Distribution Functions, 734
Chapter 30. The Boltzmann Distribution, 743
30.1. Microstates and Configurations, 743
30.2. Derivation of the Boltzmann Distribution, 749
30.3. Dominance of the Boltzmann Distribution, 754
30.4. Physical Meaning of the Boltzmann Distribution Law, 756
30.5. The Definition of β, 757
Chapter 31. Ensemble and Molecular Partition Functions, 765
31.1. The Canonical Ensemble, 765
31.2. Relating Q to q for an Ideal Gas, 767
31.3. Molecular Energy Levels, 769
31.4. Translational Partition Function, 769
31.5. Rotational Partition Function: Diatomics, 772
31.6. Rotational Partition Function: Polyatomics, 780
31.7. Vibrational Partition Function, 781
31.8. The Equipartition Theorem, 787
31.9. Electronic Partition Function, 788
31.10. Review, 791
Chapter 32. Statistical Thermodynamics, 797
32.1. Energy, 797
32.2. Energy and Molecular Energetic Degrees of Freedom, 801
32.3. Heat Capacity, 806
32.4. Entropy, 810
32.5. Residual Entropy, 815
32.6. Other Thermodynamic Functions, 816
32.7. Chemical Equilibrium, 820
Chapter 33. Kinetic Theory of Gases, 829
33.1. Kinetic Theory of Gas Motion and Pressure, 829
33.2. Velocity Distribution in One Dimension, 832
33.3. The Maxwell Distribution of Molecular Speeds, 836
33.4. Comparative Values for Speed Distributions: v_ave, v_mp, and v_rms, 838
33.5. Gas Effusion, 840
33.6. Molecular Collisions, 842
33.7. The Mean Free Path, 846
Chapter 34. Transport Phenomena, 851
34.1. What Is Transport?, 851
34.2. Mass Transport: Diffusion, 853
34.3. The Time Evolution of a Concentration Gradient, 856
34.4. (Supplemental) Statistical View of Diffusion, 858
34.5. Thermal Conduction, 860
34.6. Viscosity of Gases, 864
34.7. Measuring Viscosity, 866
34.8. Diffusion in Liquids and Viscosity of Liquids, 868
34.9. (Supplemental) Sedimentation and Centrifugation, 870
34.10. Ionic Conduction, 873
Chapter 35. Elementary Chemical Kinetics, 883
35.1. Introduction to Kinetics, 884
35.2. Reaction Rates, 885
35.3. Rate Laws, 886
35.4. Reaction Mechanisms, 892
35.5. Integrated Rate Law Expressions, 893
35.6. (Supplemental) Numerical Approaches, 897
35.7. Sequential First-Order Reactions, 899
35.8. Parallel Reactions, 904
35.9. Temperature Dependence of Rate Constants, 906
35.10. Reversible Reactions and Equilibrium, 908
35.11. (Supplemental) Perturbation-Relaxation Methods, 911
35.12. (Supplemental) The Autoionization of Water: A T-Jump Example, 913
35.13. Potential Energy Surfaces, 914
35.14. Diffusion Controlled Reactions, 916
35.15. Activated Complex Theory, 918
Chapter 36. Complex Reaction Mechanisms, 929
36.1. Reaction Mechanisms and Rate Laws, 929
36.2. The Preequilibrium Approximation, 931
36.3. The Lindemann Mechanism, 933
36.4. Catalysis, 935
36.5. Radical-Chain Reactions, 946
36.6. Radical-Chain Polymerization, 949
36.7. Explosions, 950
36.8. Photochemistry, 952
36.9. Electron Transfer, 963
Appendix A. Math Supplement, 977
Appendix B. Data Tables, 999
Appendix C. Point Group Character Tables, 1017
Appendix D. Answers to Selected End-of-Chapter Problems, 1027
Index, 1043

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