Contents

 Preface

 Chapter 1. Brief Review of Some Elementary Thermodynamics—The Thermodynamic Functions                1

1.1 Introduction            1

1.2 Thermodynamic Systems                     2

1.3 The Zeroth Law of Thermodynamics: Temperature            3

1.4 The First Law of Thermodynamics: The Internal Energy, U            4

1.5 Some Forms of Work            7

1.6 The Internal Energy, U, in a Constant-Volume Change in State            8

1.7 The Enthalpy, H, in a Constant-Pressure Process            10

1.8 The Second Law of Thermodynamics: Entropy, S               12

1.9 The Combined First and Second Laws    15

1.10 The Gibbs Free Energy Function, G            16

1.11 The Helmholtz Free Energy Function, A                   18

1.12 Summary of the Five Thermodynamic State Functions and the Maxwell Relations            20

1.13 A Chemical Application of the Gibbs Free Energy Function, G                  24

1.14 The Calculation of an Equilibrium Constant that Cannot be Measured Conveniently            28

1.15 Summary              29

Problems            29

 Chapter 2. Quantum Theory—Historical Development              37

2.1 Introduction            37

2.2 The Physics of the Emission of Radiation by Heated Bodies            38

2.3 Early Attempts to Describe the Distribution of Wavelengths from Blackbody       Emission—The Ultraviolet Catastrophe            41

2.4 Planck's Discovery of the Quantization of Radiant Energy            47

2.5 Numerical Value of Planck's Constant, h            53

2.6 Optical Pyrometry—A Practical Example of the Use of the Planck Distribution Function            53

2.7 The Heat Capacity of Solids—The Einstein and the Debye Models            56

2.8 Summary—Entry of the Quantized Energy Concept            61

2.9 Wave–Particle Duality—The Photon Energy            63

2.10 Experimental Evidence for the Wave Nature of Electrons—Electron Diffraction            71

2.11 Summary              74

Problems            75

Chapter 3. The Schrödinger Equation            79

3.1 Introduction            79

3.2 The Classical Hamiltonian and the Schrödinger Equation            82

3.3 Solving the Schrödinger Equation for a Particle Moving Freely in One Dimension            87

3.4 The Born Interpretation of the Meaning of the Wavefunction, y         90

3.5 Normalization of Wavefunctions            91

3.6 Return to the Free Particle in One Dimension            93

3.7 Using Wavefunctions to Calculate Expectation Values  95

3.8 The Uncertainty Principle            102

3.9 Summary                106

Problems            107

Chapter 4. Application of Quantum Theory to the Energetics of Electrons, Atoms, and Molecules            111

4.1 Introduction            111

4.2 The Particle in an Infinite-Walled One-Dimensional Box                  111

4.3 The Particle in a Finite One-Dimensional Square Well            121

4.4 Quantum Mechanical Tunneling Through a Barrier  125

4.5 Particle in a Two- and Three-Dimensional Box      131

4.6 The Harmonic Oscillator            134

4.7 The Rigid Rotor   148

4.8 Observing Vibrations and Rotations of Molecules by Spectroscopy            158

4.9 Infrared Spectroscopy of a Diatomic Molecule            159

4.10 Infrared Spectroscopy of Polyatomic Molecules                     168

4.11 Electronic Excitations in Molecules            173

4.12 Summary              177

Problems            178

Chapter 5. Statistical Mechanics—Fundamental Ideas and Applications            183

5.1 Introduction            183

5.2 Probability and Statistics            186

5.3 Statistical Occupation of Energy Levels            195

5.4 The Boltzmann Distribution Function            205

5.5 Ensembles, Ensemble Averages, and Partition Functions            210

5.6 The Molecular Partition Function                       216

5.7 Connecting the Molecular Partition Function to the Internal Energy, U, for a System of Noninteracting Molecules            221

5.8 Connection of the Molecular Partition Function to the Entropy of a System of Noninteracting Molecules            223

5.9 Calculating the Partition Function for Various Quantized States in Molecules            229

5.10 Applications of the Partition Function to Chemical Thermodynamics Problems                  247

5.11 The Configuration Integral 268

5.12 Entropy and the Third Law of Thermodynamics                     277

5.13 Summary              283

Problems            284

Chapter 6. The Kinetic Theory of Gases  293

6.1 Introduction            293

6.2 Deviations from the Ideal Gas Law            296

6.3 Molecular Energies and Speeds of Molecules            299

6.4 The Maxwell–Boltzmann Distribution of Molecular Speeds 301

Problems            340

Chapter 7. Chemical Kinetics and the Rates of Chemical Reactions in Gases and on Surfaces            347

7.1 Introduction            347

7.2 Collision Theory—Reactive Hard-Sphere Molecules            347

7.3 Comparison of Experimental Results for Bimolecular Chemical Reactions in the Gas Phase            353

7.4 Transition State Theory of Chemical Reaction Rates            354

7.5 Connection of Transition State Theory to Collision Theory 359

7.6 Expression of the Transition State Theory Along Thermodynamic Lines of Reasoning            361

7.7 The Chemical Processes at Work in Chemical Reactions            365

7.8 Adsorption and Reactions on Surfaces            388

7.9 Summary            418

Problems            418

Chapter 8. Engineering Applications of Molecular Modeling            429

8.1 Introduction            429

8.2 Quantum Mechanical Modeling            431

8.3 Statistical Mechanical Modeling            437

8.4 Case Studies 441

8.5 Summary            460

Problems            461