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.
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 ΔH0rxn (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
(CP–CV) 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
3N - 6 or 3N - 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-3517Cl
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, Sz) 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
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.
