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Physical Chemistry, Second Edition

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Fundamental Concepts of Thermodynamics

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Physical Chemistry, Second Edition

by Thomas Engel; Philip Reid

Publisher: Prentice Hall

Copyright Year: 2010

Publishing Date: 2009/05/20

eText ISBN-10: 0-321-63264-8

eText ISBN-13: 978-0-321-63264-7

Print ISBN-10: 0-321-61505-0

Print ISBN-13: 978-0-321-61505-3

Course: Physical Chemistry

Pages: 1088

eTextbook $81.00

(360 day subscription)

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Table of Contents | Description

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ABOUT THIS TITLE - TABLE OF CONTENTS

About the Authors, xv

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

2.4. 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

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ABOUT THIS TITLE - DESCRIPTION

For two-semester courses in Physical Chemistry or Quantum Chemistry.

This full-color, modern physical chemistry text offers arresting illustrations that set it apart from others of its kind. The authors focus on core topics of physical chemistry, presented within a modern framework of applications. Extensive math derivations are provided, yet the book retains the significant chemical rigor needed in physical chemistry.

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