Physical chemistry: thermodynamics, statistical thermodynamics, and kinetics

Cover......Page 1
Title Page......Page 2
Copyright Page......Page 3
Brief Contents......Page 5
Detailed Contents......Page 6
About the Authors......Page 10
Preface......Page 11
Acknowledgments......Page 12
Math Essential 1: Units, Significant Figures, and Solving End of Chapter Problems......Page 18
  1.1. What Is Thermodynamics and Why Is It Useful?......Page 22
  1.2. The Macroscopic Variables Volume, Pressure, and Temperature......Page 23
  1.3. Basic Definitions Needed to Describe Thermodynamic Systems......Page 27
  1.4. Equations of State and the Ideal Gas Law......Page 29
  1.5. A Brief Introduction to Real Gases......Page 31
Math Essential 2: Differentiation and Integration......Page 38
  2.1. Internal Energy and the First Law of Thermodynamics......Page 46
  2.2. Heat......Page 47
  2.3. Work......Page 48
  2.4. Equilibrium, Change, and Reversibility......Page 50
  2.5. The Work of Reversible Compression or Expansion of an Ideal Gas......Page 51
  2.6. The Work of Irreversible Compression or Expansion of an Ideal Gas......Page 53
  2.7. Other Examples of Work......Page 54
  2.8. State Functions and Path Functions......Page 56
  2.9. Comparing Work for Reversible and Irreversible Processes......Page 58
  2.10. Changing the System Energy from a Molecular- Level Perspective......Page 62
  2.11. Heat Capacity......Page 64
  2.12. Determining U and Introducing the State Function Enthalpy......Page 67
  2.13. Calculating q, w, U, and H for Processes Involving Ideal Gases......Page 68
  2.14. Reversible Adiabatic Expansion and Compression of an Ideal Gas......Page 72
Math Essential 3: Partial Derivatives......Page 80
  3.1. Mathematical Properties of State Functions......Page 82
  3.2. Dependence of U on V and T......Page 85
  3.3. Does the Internal Energy Depend More Strongly on V or T?......Page 87
  3.4. Variation of Enthalpy with Temperature at Constant Pressure......Page 91
  3.5. How are CP and CV Related?......Page 93
  3.6. Variation of Enthalpy with Pressure at Constant Temperature......Page 94
  3.7. The Joule–Thomson Experiment......Page 96
  3.8. Liquefying Gases Using an Isenthalpic Expansion......Page 98
  4.1. Energy Stored in Chemical Bonds Is Released or Absorbed in Chemical Reactions......Page 104
  4.2. Internal Energy and Enthalpy Changes Associated with Chemical Reactions......Page 105
  4.3. Hess’s Law Is Based on Enthalpy Being a State Function......Page 108
  4.4. Temperature Dependence of Reaction Enthalpies......Page 110
  4.5. Experimental Determination of U and H for Chemical Reactions......Page 112
  4.6. Differential Scanning Calorimetry......Page 114
  5.1. What Determines the Direction of Spontaneous Change in a Process?......Page 124
  5.2. The Second Law of Thermodynamics, Spontaneity, and the Sign of S......Page 126
  5.3. Calculating Changes in Entropy as T, P, or V Change......Page 127
  5.4. Understanding Changes in Entropy at the Molecular Level......Page 131
  5.5. The Clausius Inequality......Page 133
  5.6. The Change of Entropy in the Surroundings and Stot = S + Ssur......Page 134
  5.7. Absolute Entropies and the Third Law of Thermodynamics......Page 136
  5.9. Entropy Changes in Chemical Reactions......Page 140
  5.10. Heat Engines and the Carnot Cycle......Page 142
  5.11. How Does S Depend on V and T ?......Page 147
  5.12. Dependence of S on T and P......Page 148
  5.13. Energy Efficiency, Heat Pumps, Refrigerators, and Real Engines......Page 149
  6.1. Gibbs Energy and Helmholtz Energy......Page 164
  6.2. Differential Forms of U, H, A, and G......Page 168
  6.3. Dependence of Gibbs and Helmholtz Energies on P, V, and T......Page 170
  6.4. Gibbs Energy of a Reaction Mixture......Page 172
  6.5. Calculating the Gibbs Energy of Mixing for Ideal Gases......Page 174
  6.6. Calculating the Equilibrium Position for a Gas-Phase Chemical Reaction......Page 176
  6.7. Introducing the Equilibrium Constant for a Mixture of Ideal Gases......Page 179
  6.8. Calculating the Equilibrium Partial Pressures in a Mixture of Ideal Gases......Page 183
  6.9. Variation of KP with Temperature......Page 184
  6.10. Equilibria Involving Ideal Gases and Solid or Liquid Phases......Page 186
  6.11. Expressing the Equilibrium Constant in Terms of Mole Fraction or Molarity......Page 188
  6.12. Expressing U, H, and Heat Capacities Solely in Terms of Measurable Quantities......Page 189
  6.13. A Case Study: The Synthesis of Ammonia......Page 193
  6.14. Measuring G for the Unfolding of Single RNA Molecules......Page 197
  7.1. Real Gases and Ideal Gases......Page 206
  7.2. Equations of State for Real Gases and Their Range of Applicability......Page 207
  7.3. The Compression Factor......Page 211
  7.4. The Law of Corresponding States......Page 214
  7.5. Fugacity and the Equilibrium Constant for Real Gases......Page 217
  8.1. What Determines the Relative Stability of the Solid, Liquid, and Gas Phases?......Page 224
  8.2. The Pressure–Temperature Phase Diagram......Page 227
  8.4. Pressure–Volume and Pressure–Volume– Temperature Phase Diagrams......Page 234
  8.5. Providing a Theoretical Basis for the P–T Phase Diagram......Page 236
  8.6. Using the Clausius–Clapeyron Equation to Calculate Vapor Pressure as a Function of T......Page 238
  8.7. Dependence of Vapor Pressure of a Pure Substance on Applied Pressure......Page 240
  8.8. Surface Tension......Page 241
  8.9. Chemistry in Supercritical Fluids......Page 244
  8.10. Liquid Crystal Displays......Page 245
  9.1. Defining the Ideal Solution......Page 254
  9.2. The Chemical Potential of a Component in the Gas and Solution Phases......Page 256
  9.3. Applying the Ideal Solution Model to Binary Solutions......Page 257
  9.4. The Temperature–Composition Diagram and Fractional Distillation......Page 261
  9.5. The Gibbs–Duhem Equation......Page 263
  9.6. Colligative Properties......Page 264
  9.7. Freezing Point Depression and Boiling Point Elevation......Page 265
  9.8. Osmotic Pressure......Page 267
  9.9. Deviations from Raoult’s Law in Real Solutions......Page 269
  9.10. The Ideal Dilute Solution......Page 271
  9.11. Activities are Defined with Respect to Standard States......Page 273
  9.12. Henry’s Law and the Solubility of Gases in a Solvent......Page 277
  9.13. Chemical Equilibrium in Solutions......Page 278
  9.14. Solutions Formed from Partially Miscible Liquids......Page 281
  9.15. Solid–Solution Equilibrium......Page 283
  10.1. Enthalpy, Entropy, and Gibbs Energy of Ion Formation in Solutions......Page 290
  10.2. Understanding the Thermodynamics of Ion Formation and Solvation......Page 292
  10.3. Activities and Activity Coefficients for Electrolyte Solutions......Page 295
  10.4. Calculating g+- Using the Debye–Hückel Theory......Page 297
  10.5. Chemical Equilibrium in Electrolyte Solutions......Page 301
  11.1. The Effect of an Electrical Potential on the Chemical Potential of Charged Species......Page 308
  11.2. Conventions and Standard States in Electrochemistry......Page 310
  11.4. Chemical Reactions in Electrochemical Cells and the Nernst Equation......Page 313
  11.5. Combining Standard Electrode Potentials to Determine the Cell Potential......Page 315
  11.7. Relationship Between the Cell EMF and the Equilibrium Constant......Page 317
  11.8. Determination of E ~ and Activity Coefficients Using an Electrochemical Cell......Page 319
  11.9. Cell Nomenclature and Types of Electrochemical Cells......Page 320
  11.10. The Electrochemical Series......Page 321
  11.11. Thermodynamics of Batteries and Fuel Cells......Page 322
  11.12. Electrochemistry of Commonly Used Batteries......Page 323
  11.13. Fuel Cells......Page 327
  11.14. Electrochemistry at the Atomic Scale......Page 329
  11.15. Using Electrochemistry for Nanoscale Machining......Page 332
  12.1. Why Probability?......Page 338
  12.2. Basic Probability Theory......Page 339
  12.3. Stirling’s Approximation......Page 347
  12.4. Probability Distribution Functions......Page 348
  12.5. Probability Distributions Involving Discrete and Continuous Variables......Page 350
  12.6. Characterizing Distribution Functions......Page 353
Math Essential 4: Lagrange Multipliers......Page 364
  13.1. Microstates and Configurations......Page 366
  13.2. Derivation of the Boltzmann Distribution......Page 372
  13.3. Dominance of the Boltzmann Distribution......Page 377
  13.4. Physical Meaning of the Boltzmann Distribution Law......Page 379
  13.5. The Definition of β......Page 380
  14.1. The Canonical Ensemble......Page 390
  14.2. Relating Q to q for an Ideal Gas......Page 392
  14.3. Molecular Energy Levels......Page 394
  14.4. Translational Partition Function......Page 395
  14.5. Rotational Partition Function: Diatomic Molecules......Page 397
  14.6. Rotational Partition Function: Polyatomic Molecules......Page 405
  14.7. Vibrational Partition Function......Page 407
  14.8. The Equipartition Theorem......Page 412
  14.9. Electronic Partition Function......Page 413
  14.10. Review......Page 417
  15.1. Energy......Page 424
  15.2. Energy and Molecular Energetic Degrees of Freedom......Page 428
  15.3. Heat Capacity......Page 433
  15.4. Entropy......Page 438
  15.5. Residual Entropy......Page 443
  15.6. Other Thermodynamic Functions......Page 444
  15.7. Chemical Equilibrium......Page 448
  16.1. Kinetic Theory of Gas Motion and Pressure......Page 458
  16.2. Velocity Distribution in One Dimension......Page 459
  16.3. The Maxwell Distribution of Molecular Speeds......Page 463
  16.4. Comparative Values for Speed Distributions......Page 466
  16.5. Gas Effusion......Page 468
  16.6. Molecular Collisions......Page 470
  16.7. The Mean Free Path......Page 474
  17.1. What Is Transport?......Page 480
  17.2. Mass Transport: Diffusion......Page 482
  17.3. Time Evolution of a Concentration Gradient......Page 486
  17.4. Statistical View of Diffusion......Page 488
  17.5. Thermal Conduction......Page 490
  17.6. Viscosity of Gases......Page 493
  17.7. Measuring Viscosity......Page 496
  17.8. Diffusion and Viscosity of Liquids......Page 497
  17.9. Ionic Conduction......Page 499
  18.1. Introduction to Kinetics......Page 510
  18.2. Reaction Rates......Page 511
  18.3. Rate Laws......Page 513
  18.4. Reaction Mechanisms......Page 518
  18.5. Integrated Rate Law Expressions......Page 519
  18.6. Numerical Approaches......Page 524
  18.7. Sequential First-Order Reactions......Page 525
  18.8. Parallel Reactions......Page 530
  18.9. Temperature Dependence of Rate Constants......Page 532
  18.10. Reversible Reactions and Equilibrium......Page 534
  18.11. Perturbation-Relaxation Methods......Page 538
  18.12. The Autoionization of Water: A Temperature- Jump Example......Page 540
  18.13. Potential Energy Surfaces......Page 541
  18.14. Activated Complex Theory......Page 543
  18.15. Diffusion-Controlled Reactions......Page 547
  19.1. Reaction Mechanisms and Rate Laws......Page 558
  19.2. The Preequilibrium Approximation......Page 560
  19.3. The Lindemann Mechanism......Page 562
  19.4. Catalysis......Page 564
  19.5. Radical-Chain Reactions......Page 575
  19.6. Radical-Chain Polymerization......Page 578
  19.7. Explosions......Page 579
  19.8. Feedback, Nonlinearity, and Oscillating Reactions......Page 581
  19.9. Photochemistry......Page 584
  19.10. Electron Transfer......Page 596
  20.1. What Are Macromolecules?......Page 610
  20.2. Macromolecular Structure......Page 611
  20.3. Random-Coil Model......Page 613
  20.4. Biological Polymers......Page 616
  20.5. Synthetic Polymers......Page 624
  20.6. Characterizing Macromolecules......Page 627
  20.7. Self-Assembly, Micelles, and Biological Membranes......Page 634
Appendix A: Data Tables......Page 642
Credits......Page 660
Index......Page 661
Answers to Selected Numerical Problems......Page 678
Back Cover......Page 689