# Essentials of Physical Chemistry

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## Book Description

At a time when U.S. high school students are producing low scores in mathematics and science on international examinations, a thorough grounding in physical chemistry should not be considered optional for science undergraduates. Based on the author’s thirty years of teaching,** Essentials of Physical Chemistry** merges coverage of calculus with chemistry and molecular physics in a friendly yet thorough manner. Reflecting the latest ACS guidelines, the book can be used as a one or two semester course, and includes special topics suitable for senior projects.

The book begins with a math and physics review to ensure all students start on the same level, and then discusses the basics of thermodynamics and kinetics with mathematics tuned to a level that stretches students’ abilities. It then provides material for an optional second semester course that shows students how to apply their enhanced mathematical skills in a brief historical development of the quantum mechanics of molecules. Emphasizing spectroscopy, the text is built on a foundation of quantum chemistry and more mathematical detail and examples. It contains sample classroom-tested exams to gauge how well students know how to use relevant formulas and to display successful understanding of key concepts.

- Coupling the development of mathematical skills with chemistry concepts encourages students to learn mathematical derivations
- Mini-biographies of famous scientists make the presentation more interesting from a "people" point of view
- Stating the basic concepts of quantum chemistry in terms of analogies provides a pedagogically useful technique

Covering key topics such as the critical point of a van der Waals gas, the Michaelis–Menten equation, and the entropy of mixing, this classroom-tested text highlights applications across the range of chemistry, forensic science, pre-medical science and chemical engineering. In a presentation of fundamental topics held together by clearly established mathematical models, the book supplies a quantitative discussion of the merged science of physical chemistry.

## Table of Contents

Foreword

Author

List of Constants

Introduction: Mathematics and Physics Review**Ideal and Real Gas Behavior**Introduction to the ‘‘First Encounter with Physical Chemistry’’

Phenomenological Derivation of the Ideal Gas Equation

Charles’ (Jacques-Alexandre-César Charles) Law

Useful Units

Molecular Weight from Gas Density (the Dumas Bulb Method)

Dalton’s Law of Partial Pressures

Nonideal Gas Behavior

Supercritical Fluid Chromatography

Summary

Problems

References

**Viscosity of Laminar Flow**

Introduction

Measurement of Viscosity

Viscosity of Blood

Staudinger’s Rule for Polymer Molecular Weight

Summary

Problems

Bibliography

References

**The Kinetic Molecular Theory of Gases**

Introduction

Kinetic Molecular Theory of Gases

Weighted Averaging: A Very Important Concept

Summary

Problems

References

**The First Law of Thermodynamics**

Introduction

Historical Development of Thermodynamics

Definitions

First Law of Thermodynamics

Isothermal Processes

Enthalpy and Heat Capacities

Adiabatic Processes

Adiabatic Nozzle Expansion Spectroscopy

Diesel Engine Compression

Calorimetry and Thermochemistry

Hess’s Law of Heat Summation

Standard Heats of Formation at 298.15° K and 1.000 Bar Pressure

Temperature Dependence of Reaction Enthalpies

Polynomial Curve Fitting

Application to

**Δ**

*H*

^{0}

_{rxn}(T > 289.15° K)

Other Types of Thermochemistry

Perspective

Key Formulas and Equations

Problems

Testing, Grading, and Learning?

References

**The Second and Third Laws of Thermodynamics**

Introduction

Carnot Cycle/Engine

Efficiency of Real Heat Engines

Entropy and Spontaneity

Summary of the Second Law of Thermodynamics

Eight Basic Equations of Thermodynamics

Third Law of Thermodynamics

Simple Statistical Treatment of Liquids and Gases

Summary

Testing, Grading, and Learning?

Problems

Bibliography

References

**Gibbs’ Free Energy and Equilibria**

Introduction

Temperature Dependence of Equilibrium Constants

van’t Hoff Equation

Vapor Pressure of Liquids

Phase Equilibria

How Ice Skates Work

Gibbs Phase Rule

Iodine Triple Point

(C

_{P}–C

_{V}) for Liquids and Solids

Open Systems: Gibbs–Duhem Equation for Partial Molal Volumes

Chemical Potential for Open Systems

Modeling Liquids

Summary

Problems

Testing, Grading, and Learning?

Bibliography

References

**Basic Chemical Kinetics**

Introduction

First-Order Reactions

Promethium: An Introduction to Nuclear Chemistry

Madame Curie and Radioactivity

Radium

Second-Order Rate Processes: [A] = [B]

Second-Order Rate Processes: [A] ≠ [B]

Arrhenius Activation Energy

The Classic A —> B —> C Consecutive First-Order Reaction

Splitting the Atom

Problems

References

More Kinetics and Some Mechanisms

Introduction

Beyond Arrhenius to the Eyring Transition State

Example

Graphical–Analytical Method for ΔH‡ and ΔS‡

Summary of Graphical Method Results at T = 25 °C

Further Consideration of SN1 Solvolysis

Chain Reactions and the Steady State

Enzyme Kinetics

Example: A Hypothetical Enzyme

Kinetics Conclusions

Problems

Testing, Grading, and Learning?

Bibliography

References

**Basic Spectroscopy**

Introduction

Planck’s Discovery

Balmer’s Integer Formula

A Very Useful Formula

Preliminary Summary of the Bohr Atom

Significance of the Bohr Quantum Number

*n*

Orbital Screening

X-Ray Emission

Forensic/Analytical Use of Auger X-Rays

X-Ray Fluorescence

X-Ray Diffraction

Electronic Absorption Spectroscopy/Spectrophotometry

Interpreting Electronic Spectra

General Principles of Spectroscopy

Problems

Bibliography

References

**Early Experiments in Quantum Physics**

Introduction

Stefan–Boltzmann Law: Relating Heat and Light—Part I

Blackbody Radiation: Relating Heat and Light—Part II

Photoelectric Effect

De Broglie Matter Waves

Davisson–Germer Experiment

Summary

Problems

References

**The Schrödinger Wave Equation**

Introduction

Definition of a Commutator

Postulates of Quantum Mechanics

Particle on a Ring

Comparison of PIB and POR Applications

Additional Theorems in Quantum Mechanics

Summary

Problems

Study, Test, and Learn?

References

**The Quantized Harmonic Oscillator, Vibrational Spectroscopy**

Introduction

Harmonic Oscillator Details

Harmonic Oscillator Results

Reduced Mass

Isotope Shift in the Vibrational Fundamental Frequency

Hermite Recursion Rule

Infrared Dipole Selection Rule

3

*N*- 6 or 3

*N*- 5 Vibrations?

Raman Spectroscopy

Summary

Problems

References

**The Quantized Rigid Rotor and the Vib-Rotor**

Introduction

Three-Dimensional Particle-in-a-Box

Rigid Rotor

Angular Wave Functions

Angular Momentum

Rotational Spectrum of CO

Fourier Transform Spectrometry

FT-IR Imaging and Microscopy

Dipole Requirement

Vib-Rotor Infrared Spectroscopy

Bond Length of H-

^{35}

_{17}Cl

Summary

Problems

References

**The Schrödinger Hydrogen Atom**

Introduction

Strategy to Solve the Problem

Associated Laguerre Polynomials

Interpretation

Pictures of Angular Orbitals

Powell Equivalent d-Orbitals

Unsöld’s Theorem

Aufbau Principle and the Scaled H atom

Term Symbols and Spin Angular Momentum

Hund’s Rule

|L, S

_{z}) versus |J, Jz) Coupling

Summary

Problems

References

**Quantum Thermodynamics**

Introduction

(Energy) Partition Function

Average Translation Energy in One Dimension

Average Rotational Energy of a Diatomic Molecule

Average Vibrational Energy

High-Temperature Limit for Vibrational Heat Capacity

Heat Capacity of a Polyatomic Species: Water

Combining Partition Functions

Statistical Formulas for Other Thermodynamic Functions

Statistical Formula for

*S*(

*T*)

Sakur–Tetrode Formula for Absolute Entropy of a Gas

Summary

Problems

References

**Approximate Methods and Linear Algebra**

Introduction

Simple First-Order Perturbation Theory

Principles of Perturbation Theory

Variation Method

Molecular Orbitals and the Secular Equation

Chemical Bonds of Ethylene

Elementary Linear Algebra

Unitary Similarity Diagonalization of a Square Hermitian Matrix

Jacobi Algorithm for Diagonalization Using a Computer

Order Matters!

Summary

Problems

Testing, Grading, and Learning!

Study, Test, and Learn?

References

**Electronic Structure of Molecules**

Introduction

Hartree–Fock–Roothan LCAO Calculations

Chemical Effects in Orbital Screening

Many-Electron Wave Functions

Atomic Units

Roothaan’s LCAO Hartree–Fock Equation

Practical Implementation and Examples

Dipole Moment of BH

Excited States of BH

Mesoionic Bond Orders

Summary

Problems

References

**Point Group Theory and Electrospray Mass Spectrometry**

Introduction

Basic Point Group Theory

Calculation of Molecular Vibrations

Future Development of Electrospray Mass Spectrometry?

‘‘Making Elephants Fly’’

Summary

Problems

References

**Essentials of Nuclear Magnetic Resonance**

Introduction

Early NMR Spectrometers

NMR Spin Hamiltonian

Forensic Application of 1D-NMR

Nuclear Magnetic Resonance: Pulse Analysis

Rotating Coordinate System

Detection of Magnetic Fields

Bloch Equations

Complex Fourier Transform

2D-NMR COSY

Coherent Spectroscopy

Product Operator COSY Analysis Using Dr. Brown’s Automated Software

Anatomy of a 2D Experiment

Summary

Problems

References

**Appendix A**: Relation between Legendre and Associated Legendre Polynomials

**Appendix B:**The Hartree–Fock–Roothaan SCF Equation

**Appendix C:**Gaussian Lobe Basis Integrals

**Appendix D:**Spin-Orbit Coupling in the H Atom

**Index**

Use of PCLOBE

Use of PCLOBE

## Author(s)

### Biography

**Don Shillady** is a native of Montgomery County, Pennsylvania, U.S.A. He earned a B.S. in Chemistry from Drexel University, a Masters in Physical Chemistry from Princeton University and a Ph.D. in Physical Chemistry from the University of Virginia (1970). He has enjoyed teaching Physical Chemistry, Physical Chemistry Laboratory and Quantum Chemistry at Virginia Commonwealth University since 1970. He has edited three specialty monographs: one in Chemical Education and two on the Biological Effects of Electromagnetic Waves as well as coauthored a recent text "Electronic Molecular Structure, Connections Between Theory and Software" with Prof. Carl Trindle. He is now an emeritus Professor of Chemistry at Virginia Commonwealth University but still teaches a rapid two semester course in Physical Chemistry each summer at VCU. He has authored/coauthored 77 research publications and still maintains interest in properties of metal clusters, optical activity of large organic molecules, and Quantum Chemistry software.