## Molecular Physical Chemistry for Engineers

John T. Yates University of Virginia

Karl Johnson University of Pittsburgh

### Contents

Preface

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

1.1 Introduction

1.2 Thermodynamic Systems

1.3 The Zeroth Law of Thermodynamics: Temperature

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

1.5 Some Forms of Work

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

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

1.8 The Second Law of Thermodynamics: Entropy, *S *

1.9 The Combined First and Second Laws

1.10 The Gibbs Free Energy Function, *G*

1.11 The Helmholtz Free Energy Function, *A*

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

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

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

1.15 Summary

Problems

**Chapter 2. Quantum Theory—Historical Development**

2.1 Introduction

2.2 The Physics of the Emission of Radiation by Heated Bodies

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

2.4 Planck’s Discovery of the Quantization of Radiant Energy

2.5 Numerical Value of Planck’s Constant, *h*

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

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

2.8 Summary—Entry of the Quantized Energy Concept

2.9 Wave–Particle Duality—The Photon Energy

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

2.11 Summary

Problems

**Chapter 3. The Schrödinger Equation**

3.1 Introduction

3.2 The Classical Hamiltonian and the Schrödinger Equation

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

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

3.5 Normalization of Wavefunctions

3.6 Return to the Free Particle in One Dimension

3.7 Using Wavefunctions to Calculate Expectation Values

3.8 The Uncertainty Principle

3.9 Summary

Problems

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

4.1 Introduction

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

4.3 The Particle in a Finite One-Dimensional Square Well

4.4 Quantum Mechanical Tunneling Through a Barrier

4.5 Particle in a Two- and Three-Dimensional Box

4.6 The Harmonic Oscillator

4.7 The Rigid Rotor

4.8 Observing Vibrations and Rotations of Molecules by Spectroscopy

4.9 Infrared Spectroscopy of a Diatomic Molecule

4.10 Infrared Spectroscopy of Polyatomic Molecules

4.11 Electronic Excitations in Molecules

4.12 Summary

Problems

**Chapter 5. Statistical Mechanics—Fundamental Ideas and Applications**

5.1 Introduction

5.2 Probability and Statistics

5.3 Statistical Occupation of Energy Levels

5.4 The Boltzmann Distribution Function

5.5 Ensembles, Ensemble Averages, and Partition Functions

5.6 The Molecular Partition Function

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

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

5.9 Calculating the Partition Function for Various Quantized States in Molecules

5.10 Applications of the Partition Function to Chemical Thermodynamics Problems

5.11 The Configuration Integral

5.12 Entropy and the Third Law of Thermodynamics

5.13 Summary

Problems

**Chapter 6. The Kinetic Theory of Gases**

6.1 Introduction

6.2 Deviations from the Ideal Gas Law

6.3 Molecular Energies and Speeds of Molecules

6.4 The Maxwell–Boltzmann Distribution of Molecular Speeds

Problems

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

7.1 Introduction

7.2 Collision Theory—Reactive Hard-Sphere Molecules

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

7.4 Transition State Theory of Chemical Reaction Rates

7.5 Connection of Transition State Theory to Collision Theory

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

7.7 The Chemical Processes at Work in Chemical Reactions

7.8 Adsorption and Reactions on Surfaces

7.9 Summary

Problems

**Chapter 8. Engineering Applications of Molecular Modeling**

8.1 Introduction

8.2 Quantum Mechanical Modeling

8.3 Statistical Mechanical Modeling

8.4 Case Studies

8.5 Summary

Problems