Mathematics for Physical Chemistry
- 2nd Edition - April 21, 1999
- Author: Robert G. Mortimer
- Language: English
Mathematics for Physical Chemistry is the ideal textbook for upper-level undergraduates or graduate students who want to sharpen their mathematics skills while they are enroll… Read more
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Mathematics for Physical Chemistry is the ideal textbook for upper-level undergraduates or graduate students who want to sharpen their mathematics skills while they are enrolled in a physical chemistry course. Solved examples and problems, interspersed throughout the presentation and intended to be worked when met in the text, encourage self-study by students new to the material. The author provides readers with a review of calculus and differential equations that will enable them to succeed in a physical chemistry course. An ideal reference text for practicing chemists as well.
@bul:* Completeness: contains all of the mathematics needed in undergraduate physical chemistry
* Clarity: all sentences, examples, and equations have been constructed to make them as clear as possible
* Applications-oriented: Designed for applications of mathematics, not for mathematical theory; written for a chemist who needs to use mathematics, not for a mathematician who needs to study the underlying theory
* Clarity: all sentences, examples, and equations have been constructed to make them as clear as possible
* Applications-oriented: Designed for applications of mathematics, not for mathematical theory; written for a chemist who needs to use mathematics, not for a mathematician who needs to study the underlying theory
Juniors, seniors, and graduate students enrolled in physical chemistry courses; students in lower- and upper-division honors chemistry courses.
Preface
Chapter 1 Systems, States, and Processes
1.1 Scientific Inquiry
1.2 Systems and States
1.3 Units of Measurement. SI Units
1.4 State Functions
1.5 The Relationship Between Macrostates and Microstates
1.6 Processes
Problems
Chapter 2 The Equilibrium Macroscopic States of Gases and Liquids
2.1 Mathematical Functions and the Equilibrium Macroscopic State of a Simple System
2.2 Real Liquids and Solids
2.3 Real Gases
2.4 The Coexistence of Phases and the Critical Point
Problems
Chapter 3 Work, Heat, and Energy: The First Law of Thermodynamics
3.1 Work and the State of a System
3.2 Heat
3.3 Internal Energy; The First Law.
3.4 Calculation of Amounts of Heat and Energy Changes
3.5 Enthalpy - A Convenience Variable
3.6 Calculation of Enthalpy Changes for Non-chemical Processes
3.7 Calculation of Enthalpy Changes for a Class of Chemical Reactions
3.8 Energy Changes of Chemical Reactions
Problems
Chapter 4 The Second and Third Laws of Thermodynamics: Entropy
4.1 The Second Law of Thermodynamics and the Carnot Heat Engine
4.2 The Mathematical Statement of the Second Law. Entropy.
4.3 The Calculation of Entropy Changes
4.4 Statistical Entropy
4.5 The Third Law of Thermodynamics and Absolute Entropies
Problems
Chapter 5 The Thermodynamics of Real Systems
5.1 Criteria for Spontaneous Processes and for Equilibrium.
The Gibbs and Helmholtz Energies.
5.2 Fundamental Relations for Closed Simple Systems
5.3 Gibbs Energy Calculations
5.4 The Description of Multicomponent and Open Systems
5.5 Additional Useful Thermodynamic Identities
5.6 Euler's Theorem and the Gibbs-Duhem Relation
Problems
Chapter 6 Phase Equilibrium
6.1 The Fundamental Fact of Phase Equilibrium.
6.2 The Gibbs Phase Rule
6.3 Phase Equilibria in a One-Component System
6.4 The Gibbs Energy and Phase Transitions.
6.5 Surface Structure and Thermodynamics
6.6 Surfaces in Multicomponent Systems
Problems
Chapter7 Multicomponent Systems
7.1 Ideal Solutions
7.2 Henry's Law and Ideally Dilute Nonelectrolyte Solutions
7.3 The Activity and the Description of General Systems
7.4 Activity Coefficients in Electrolyte Solutions
7.5 Phase Diagrams for Nonideal Mixtures
7.6 Colligative Properties
Problems
Chapter 8 Chemical Equilibrium
8.1 Gibbs Energy Changes and Equilibria of Chemical Reactions: The Equilibrium Constant.
8.2 Reactions involving Gases and Pure Substances.
8.3 Chemical Equilibrium in Solution
8.4 Equilibria in Solutions of Strong Electrolytes.
8.5 Acid-Base Equilibrium Calculations.
8.6 Temperature and Pressure Dependence of Equilibrium Constants: The Principle of le Chatelier.
8.7 Chemical Reactions and Biological Systems.
Problems
Chapter 9 The Thermodynamics of Electrochemical Systems
9.1 The Chemical Potential and the Electric Potential
9.2 Electrochemical Cells at Equilibrium
9.3 Half-Cell Potentials and Cell Potentials
9.4 The Determination of Activity Coefficients of Electrolytes
9.5 Thermodynamic Information from Electrochemistry
Problems
Chapter 10 Gas Kinetic Theory. The Molecular Theory of Dilute Gases at Equilibrium
10.1 The Model System for a Dilute Gas
10.2 The Velocity Probability Distribution
10.3 The Distribution of Molecular Speeds
10.4 The Pressure of an Ideal Gas
10.5 Wall Collisions and Effusion
10.6 The Model System with Potential Energy
10.7 The Hard Sphere Gas
10.9 The Molecular Structure of Liquids
Problems
Chapter 11 Transport Processes
11.1 The Macroscopic Description of Nonequilibrium States
11.2 Transport Processes
11.3 Transport Processes in the Hard Sphere Gas
11.4 The Structure of Liquids and Transport Processes in Liquids
11.5 Transport in Electrolyte Solutions
Problems
Chapter 12 The Rates of Chemical Reactions
12.1 The Macroscopic Description of Chemically Reacting Systems
12.2 Forward Reactions with one Reactant.
12.3 Forward Reactions With More than One Reactant
12.4 Inclusion of a Reverse Reaction. Chemical Equilibrium
12.5 Consecutive Reactions
12.6 The Experimental Study of Fast Reactions
Problems
Chapter 13 The Molecular Nature of Chemical Reactions
13.1 Elementary Processes in Gases
13.2 Elementary Reactions in Liquid Solutions
13.3 Reaction Mechanisms and Rate Laws
13.4 Some Additional Mechanisms, Including Chain and Photochemical Mechanisms. Competing Mechanisms
13.5 Catalysis
13.6 The Temperature Dependence of Rate Constants. The Collision Theory of Gaseous Reactions
13.7 Experimental Molecular Study of Chemical Reactions
Problems
Chapter 14 The Principles of Quantum Mechanics I: The Schrodinger Equation
14.1 Classical Mechanics
14.2 Properties of Waves in Classical Mechanics.
14.2 The Old Quantum Theory
14.4 DeBroglie Waves and the Schrödinger Equation.
14.5 The Particle in a Box. The Free Particle.
14.6 The Harmonic Oscillator
Problems
Chapter 15 The Principles of Quantum Mechanics II: The Postulates of Quantum Mechanics
15.1 The First Two Postulates of Quantum Mechanics.
15.2 Mathematical Operators
15.3 Postulate III. Mathematical Operators in Quantum Mechanics
15.4 Postulate IV. Expectation Values
15.5 Postulate V. The Determination of the State of a System
Problems
Chapter 16 The Electronic States of Atoms I: The Hydrogen Atom and the Simple Orbital Approximation for Multi-electron Atoms
16.1 The Central Force Problem and the Hydrogen Atom. Angular Momentum
16.2 The Hydrogen-like Atom
16.3 The Helium Atom in the "Zero-order" Orbital Approximation
16.4 Atoms with More than Two Electrons
Problems
Chapter 17 The Electronic States of Atoms II: Higher-Order Approximations for Multi-electron Atoms
17.1 The Variation Method and its Application to the Helium Atom
17.2 The Perturbation Method and its Application to the Helium Atom
17.3 The Self-Consistent Field Method
17.4 Excited States of the Helium Atom
17.5 Atoms with More than Two Electrons
Problems
Chapter 18 The Electronic States of Molecules
18.1 The Born-Oppenheimer Approximation. The Hydrogen Molecule Ion.
18.2 LCAO-MO's - Molecular Orbitals That Are Linear Combinations of Atomic Orbitals
18.3 Homonuclear Diatomic Molecules
18.4 Heteronuclear Diatomic Molecules
18.5 Symmetry in Polyatomic Molecules. Groups of Symmetry Operators
18.6 Matrix Representations of Groups
18.7 Electronic Structure of Polyatomic Molecules
18.8 More Advanced Treatments of Molecular Electronic Structure
Problems
Chapter 19 Translational, Rotational, and Vibrational States of Atoms and Molecules
19.1 Translational Motions of Atoms
19.2 The Nonelectronic States of Diatomic Molecules
19.3 Rotation and Vibration in Polyatomic Molecules
19.4 The Equilibrium Populations of Molecular States
Problems
Chapter 20 Spectroscopy and Photochemistry
20.1 Spectroscopic Study of Energy Levels
20.2 Spectra of Atoms
20.3 Rotational and Vibrational Spectra of Diatomic Molecules
20.4 Electronic Spectra of Diatomic Molecules
20.5 Spectra of Polyatomic Molecules
20.6 Fluorescence, Phosphorescence, and Photochemistry
20.7 Other Types of Spectroscopy
20.8 Magnetic Resonance Spectroscopy
20.9 Fourier Transform Spectroscopy
Problems
Chapter 21 Equilibrium Statistical Mechanics
21.1 The Quantum Statistical Mechanics of a Sample System of Four Molecules
21.2 The Probability Distribution for a Dilute Gas
21.3 The Probability Distribution and the Molecular Partition Function
21.4 The Calculation of Molecular Partition Functions
21.5 Calculations of Thermodynamic Functions of Dilute Gases
21.6 Chemical Equilibrium in Dilute Gases
21.7 The Activated Complex Theory of Bimolecular Chemical Reactions in Dilute Gases
21.8 The Canonical Ensemble
Problems
Chapter 22 The Structure of Condensed Phases
22.1 General Features of Solids and Liquids
22.2 Crystals
22.3 Crystal Vibrations
22.4 The Electronic Structure of Solids
22.5 Classical Statistical Mechanics
22.6 The Structure of Liquids
22.7 Polymer Formation and Conformation
22.8 Rubber Elasticity
22.9 Polymers in Solution
Problems.
Chapter 23 Theories of Nonequilibrium Processes
23.1 Theories of Chemical Reactions
23.2 The Molecular Case History of a Chemical Reaction
23.3 Theories of Transport Processes in Fluid Systems
23.4 Nonequilibrium Electrochemistry
23.5 Electrical Conductivity in Solids
23.6 Oscillatory Chemical Reactions and Chemical Chaos
Problems
Appendixes
A. Tables of Numerical Data
B. Some Useful Mathematics
C. A Short Table of Integrals
D. Classical Mechanics
E. Some Derivations of Thermodynamic Formulas and Methods
F. Some Mathematics in Quantum Mechanics
G. The Perturbation Method
H. The Hückel Method
I. Symbols Used in this Book
Chapter 1 Systems, States, and Processes
1.1 Scientific Inquiry
1.2 Systems and States
1.3 Units of Measurement. SI Units
1.4 State Functions
1.5 The Relationship Between Macrostates and Microstates
1.6 Processes
Problems
Chapter 2 The Equilibrium Macroscopic States of Gases and Liquids
2.1 Mathematical Functions and the Equilibrium Macroscopic State of a Simple System
2.2 Real Liquids and Solids
2.3 Real Gases
2.4 The Coexistence of Phases and the Critical Point
Problems
Chapter 3 Work, Heat, and Energy: The First Law of Thermodynamics
3.1 Work and the State of a System
3.2 Heat
3.3 Internal Energy; The First Law.
3.4 Calculation of Amounts of Heat and Energy Changes
3.5 Enthalpy - A Convenience Variable
3.6 Calculation of Enthalpy Changes for Non-chemical Processes
3.7 Calculation of Enthalpy Changes for a Class of Chemical Reactions
3.8 Energy Changes of Chemical Reactions
Problems
Chapter 4 The Second and Third Laws of Thermodynamics: Entropy
4.1 The Second Law of Thermodynamics and the Carnot Heat Engine
4.2 The Mathematical Statement of the Second Law. Entropy.
4.3 The Calculation of Entropy Changes
4.4 Statistical Entropy
4.5 The Third Law of Thermodynamics and Absolute Entropies
Problems
Chapter 5 The Thermodynamics of Real Systems
5.1 Criteria for Spontaneous Processes and for Equilibrium.
The Gibbs and Helmholtz Energies.
5.2 Fundamental Relations for Closed Simple Systems
5.3 Gibbs Energy Calculations
5.4 The Description of Multicomponent and Open Systems
5.5 Additional Useful Thermodynamic Identities
5.6 Euler's Theorem and the Gibbs-Duhem Relation
Problems
Chapter 6 Phase Equilibrium
6.1 The Fundamental Fact of Phase Equilibrium.
6.2 The Gibbs Phase Rule
6.3 Phase Equilibria in a One-Component System
6.4 The Gibbs Energy and Phase Transitions.
6.5 Surface Structure and Thermodynamics
6.6 Surfaces in Multicomponent Systems
Problems
Chapter7 Multicomponent Systems
7.1 Ideal Solutions
7.2 Henry's Law and Ideally Dilute Nonelectrolyte Solutions
7.3 The Activity and the Description of General Systems
7.4 Activity Coefficients in Electrolyte Solutions
7.5 Phase Diagrams for Nonideal Mixtures
7.6 Colligative Properties
Problems
Chapter 8 Chemical Equilibrium
8.1 Gibbs Energy Changes and Equilibria of Chemical Reactions: The Equilibrium Constant.
8.2 Reactions involving Gases and Pure Substances.
8.3 Chemical Equilibrium in Solution
8.4 Equilibria in Solutions of Strong Electrolytes.
8.5 Acid-Base Equilibrium Calculations.
8.6 Temperature and Pressure Dependence of Equilibrium Constants: The Principle of le Chatelier.
8.7 Chemical Reactions and Biological Systems.
Problems
Chapter 9 The Thermodynamics of Electrochemical Systems
9.1 The Chemical Potential and the Electric Potential
9.2 Electrochemical Cells at Equilibrium
9.3 Half-Cell Potentials and Cell Potentials
9.4 The Determination of Activity Coefficients of Electrolytes
9.5 Thermodynamic Information from Electrochemistry
Problems
Chapter 10 Gas Kinetic Theory. The Molecular Theory of Dilute Gases at Equilibrium
10.1 The Model System for a Dilute Gas
10.2 The Velocity Probability Distribution
10.3 The Distribution of Molecular Speeds
10.4 The Pressure of an Ideal Gas
10.5 Wall Collisions and Effusion
10.6 The Model System with Potential Energy
10.7 The Hard Sphere Gas
10.9 The Molecular Structure of Liquids
Problems
Chapter 11 Transport Processes
11.1 The Macroscopic Description of Nonequilibrium States
11.2 Transport Processes
11.3 Transport Processes in the Hard Sphere Gas
11.4 The Structure of Liquids and Transport Processes in Liquids
11.5 Transport in Electrolyte Solutions
Problems
Chapter 12 The Rates of Chemical Reactions
12.1 The Macroscopic Description of Chemically Reacting Systems
12.2 Forward Reactions with one Reactant.
12.3 Forward Reactions With More than One Reactant
12.4 Inclusion of a Reverse Reaction. Chemical Equilibrium
12.5 Consecutive Reactions
12.6 The Experimental Study of Fast Reactions
Problems
Chapter 13 The Molecular Nature of Chemical Reactions
13.1 Elementary Processes in Gases
13.2 Elementary Reactions in Liquid Solutions
13.3 Reaction Mechanisms and Rate Laws
13.4 Some Additional Mechanisms, Including Chain and Photochemical Mechanisms. Competing Mechanisms
13.5 Catalysis
13.6 The Temperature Dependence of Rate Constants. The Collision Theory of Gaseous Reactions
13.7 Experimental Molecular Study of Chemical Reactions
Problems
Chapter 14 The Principles of Quantum Mechanics I: The Schrodinger Equation
14.1 Classical Mechanics
14.2 Properties of Waves in Classical Mechanics.
14.2 The Old Quantum Theory
14.4 DeBroglie Waves and the Schrödinger Equation.
14.5 The Particle in a Box. The Free Particle.
14.6 The Harmonic Oscillator
Problems
Chapter 15 The Principles of Quantum Mechanics II: The Postulates of Quantum Mechanics
15.1 The First Two Postulates of Quantum Mechanics.
15.2 Mathematical Operators
15.3 Postulate III. Mathematical Operators in Quantum Mechanics
15.4 Postulate IV. Expectation Values
15.5 Postulate V. The Determination of the State of a System
Problems
Chapter 16 The Electronic States of Atoms I: The Hydrogen Atom and the Simple Orbital Approximation for Multi-electron Atoms
16.1 The Central Force Problem and the Hydrogen Atom. Angular Momentum
16.2 The Hydrogen-like Atom
16.3 The Helium Atom in the "Zero-order" Orbital Approximation
16.4 Atoms with More than Two Electrons
Problems
Chapter 17 The Electronic States of Atoms II: Higher-Order Approximations for Multi-electron Atoms
17.1 The Variation Method and its Application to the Helium Atom
17.2 The Perturbation Method and its Application to the Helium Atom
17.3 The Self-Consistent Field Method
17.4 Excited States of the Helium Atom
17.5 Atoms with More than Two Electrons
Problems
Chapter 18 The Electronic States of Molecules
18.1 The Born-Oppenheimer Approximation. The Hydrogen Molecule Ion.
18.2 LCAO-MO's - Molecular Orbitals That Are Linear Combinations of Atomic Orbitals
18.3 Homonuclear Diatomic Molecules
18.4 Heteronuclear Diatomic Molecules
18.5 Symmetry in Polyatomic Molecules. Groups of Symmetry Operators
18.6 Matrix Representations of Groups
18.7 Electronic Structure of Polyatomic Molecules
18.8 More Advanced Treatments of Molecular Electronic Structure
Problems
Chapter 19 Translational, Rotational, and Vibrational States of Atoms and Molecules
19.1 Translational Motions of Atoms
19.2 The Nonelectronic States of Diatomic Molecules
19.3 Rotation and Vibration in Polyatomic Molecules
19.4 The Equilibrium Populations of Molecular States
Problems
Chapter 20 Spectroscopy and Photochemistry
20.1 Spectroscopic Study of Energy Levels
20.2 Spectra of Atoms
20.3 Rotational and Vibrational Spectra of Diatomic Molecules
20.4 Electronic Spectra of Diatomic Molecules
20.5 Spectra of Polyatomic Molecules
20.6 Fluorescence, Phosphorescence, and Photochemistry
20.7 Other Types of Spectroscopy
20.8 Magnetic Resonance Spectroscopy
20.9 Fourier Transform Spectroscopy
Problems
Chapter 21 Equilibrium Statistical Mechanics
21.1 The Quantum Statistical Mechanics of a Sample System of Four Molecules
21.2 The Probability Distribution for a Dilute Gas
21.3 The Probability Distribution and the Molecular Partition Function
21.4 The Calculation of Molecular Partition Functions
21.5 Calculations of Thermodynamic Functions of Dilute Gases
21.6 Chemical Equilibrium in Dilute Gases
21.7 The Activated Complex Theory of Bimolecular Chemical Reactions in Dilute Gases
21.8 The Canonical Ensemble
Problems
Chapter 22 The Structure of Condensed Phases
22.1 General Features of Solids and Liquids
22.2 Crystals
22.3 Crystal Vibrations
22.4 The Electronic Structure of Solids
22.5 Classical Statistical Mechanics
22.6 The Structure of Liquids
22.7 Polymer Formation and Conformation
22.8 Rubber Elasticity
22.9 Polymers in Solution
Problems.
Chapter 23 Theories of Nonequilibrium Processes
23.1 Theories of Chemical Reactions
23.2 The Molecular Case History of a Chemical Reaction
23.3 Theories of Transport Processes in Fluid Systems
23.4 Nonequilibrium Electrochemistry
23.5 Electrical Conductivity in Solids
23.6 Oscillatory Chemical Reactions and Chemical Chaos
Problems
Appendixes
A. Tables of Numerical Data
B. Some Useful Mathematics
C. A Short Table of Integrals
D. Classical Mechanics
E. Some Derivations of Thermodynamic Formulas and Methods
F. Some Mathematics in Quantum Mechanics
G. The Perturbation Method
H. The Hückel Method
I. Symbols Used in this Book
- Edition: 2
- Published: April 21, 1999
- Language: English
RM
Robert G. Mortimer
Robert G. Mortimer is a Professor Emeritus of Chemistry at Rhodes College in Memphis, Tennessee. He has taught physical chemistry at Indiana University and Rhodes College for over 40 years. He has carried out both experimental and theoretical research in the area of nonequilibrium processes in fluid systems.
Affiliations and expertise
Professor Emeritus of Chemistry, Rhodes College, Memphis, TN, USA