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Copyright: 1997

Publisher: University Science Books

Published: 1997

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As the first modern physical chemistry textbook to cover quantum mechanics before thermodynamics and kinetics, this book provides a contemporary approach to the study of physical chemistry. By beginning with quantum chemistry, students will learn the fundamental principles upon which all modern physical chemistry is built.

The text includes a special set of "MathChapters" to review and summarize the mathematical tools required to master the material * *Thermodynamics is simultaneously taught from a bulk and microscopic viewpoint that enables the student to understand how bulk properties of materials are related to the properties of individual constituent molecules.

This new text includes a variety of modern research topics in physical chemistry as well as hundreds of worked problems and examples.

**McQuarrie, Donald A. : University of California, Davis**

Simon, John D. : Duke University

**Chapter 1. The Dawn of the Quantum Theory **

1-1. Blackbody Radiation Could Not Be Explained by Classical Physics

1-2. Planck Used a Quantum Hypothesis to Derive the Blackbody Radiation Law

1-3. Einstein Explained the Photoelectric Effect with a Quantum Hypothesis

1-4. The Hydrogen Atomic Spectrum Consists of Several Series of Lines

1-5. The Rydberg Formula Accounts for All the Lines in the Hydrogen Atomic Spectrum

1-6. Louis de Broglie Postulated That Matter Has Wavelike Properties

1-7. de Broglie Waves Are Observed Experimentally

1-8. The Bohr Theory of the Hydrogen Atom Can Be Used to Derive the Rydberg Formula

1-9. The Heisenberg Uncertainty Principle States That the Position and the Momentum of a Particle Cannot be Specified Simultaneously with Unlimited Precision

Problems

MathChapter A / Complex Numbers

**Chapter 2. The Classical Wave Equation **

2-1. The One-Dimensional Wave Equation Describes the Motion of a Vibrating String

2-2. The Wave Equation Can Be Solved by the Method of Separation of Variables

2-3. Some Differential Equations Have Oscillatory Solutions

2-4. The General Solution to the Wave Equation Is a Superposition of Normal Modes

2-5. A Vibrating Membrane Is Described by a Two- Dimensional Wave Equation

Problems

MathChapter B / Probability and Statistics

**Chapter 3. The Schrodinger Equation and a Particle In a Box **

3-1. The Schrodinger Equation Is the Equation for Finding the Wave Function of a Particle

3-2. Classical-Mechanical Quantities Are Represented by Linear Operators in Quantum Mechanics

3-3. The Schrodinger Equation Can be Formulated as an Eigenvalue Problem

3-4. Wave Functions Have a Probabilistic Interpretation

3-5. The Energy of a Particle in a Box Is Quantized

3-6. Wave Functions Must Be Normalized

3-7. The Average Momentum of a Particle in a Box is Zero

3-8. The Uncertainty Principle Says That sigmapsigmax>h/2

3-9. The Problem of a Particle in a Three-Dimensional Box is a Simple Extension of the One-Dimensional Case

Problems

MathChapter C / Vectors

**Chapter 4. Some Postulates and General Principles of Quantum Mechanics **

4-1. The State of a System Is Completely Specified by its Wave Function

4-2. Quantum-Mechanical Operators Represent Classical-Mechanical Variables

4-3. Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators

4-4. The Time Dependence of Wave Functions Is Governed by the Time-Dependent Schrodinger Equation

4-5. The Eigenfunctions of Quantum Mechanical Operators Are Orthogonal

4-6. The Physical Quantities Corresponding to Operators That Commute Can Be Measured Simultaneously to Any Precision

Problems

MathChapter D / Spherical Coordinates

**Chapter 5. The Harmonic Oscillator and the Rigid Rotator : Two Spectroscopic Models **

5-1. A Harmonic Oscillator Obeys Hooke's Law

5-2. The Equation for a Harmonic-Oscillator Model of a Diatomic Molecule Contains the Reduced Mass of the Molecule

5-3. The Harmonic-Oscillator Approximation Results from the Expansion of an Internuclear Potential Around its Minimum

5-4. The Energy Levels of a Quantum-Mechanical Harmonic Oscillator Are Ev = hw(v + 1/2) with v= 0,1,2...

5-5. The Harmonic Oscillator Accounts for the Infrared Spectrum of a Diatomic Molecule

5-6. The Harmonic-Oscillator Wave Functions Involve Hermite Polynomials

5-7. Hermite Polynomials Are Either Even or Odd Functions

5-8. The Energy Levels of a Rigid Rotator Are E = h 2J(J+1)/2I

5-9. The Rigid Rotator Is a Model for a Rotating Diatomic Molecule

Problems

**Chapter 6. The Hydrogen Atom **

6-1. The Schrodinger Equation for the Hydrogen Atom Can Be Solved Exactly

6-2. The Wave Functions of a Rigid Rotator Are Called Spherical Harmonics

6-3. The Precise Values of the Three Components of Angular Momentum Cannot Be Measured Simultaneously

6-4. Hydrogen Atomic Orbitals Depend upon Three Quantum Numbers

6-5. s Orbitals Are Spherically Symmetric

6-6. There Are Three p Orbitals for Each Value of the Principle Quantum Number, n>= 2

6-7. The Schrodinger Equation for the Helium Atom Cannot Be Solved Exactly

Problems

MathChapter E / Determinants

**Chapter 7. Approximation Methods **

7-1. The Variational Method Provides an Upper Bound to the Ground-State Energy of a System

7-2. A Trial Function That Depends Linearly on the Variational Parameters Leads to a Secular Determinant

7-3. Trial Functions Can Be Linear Combinations of Functions That Also Contain Variational Parameters

7-4. Perturbation Theory Expresses the Solution to One Problem in Terms of Another Problem Solved Previously

Problems

**Chapter 8. Multielectron Atoms **

8-1. Atomic and Molecular Calculations Are Expressed in Atomic Units

8-2. Both Pertubation Theory and the Variational Method Can Yield Excellent Results for Helium

8-3. Hartree-Fock Equations Are Solved by the Self-Consistent Field Method

8-4. An Electron Has An Intrinsic Spin Angular Momentum

8-5. Wave Functions Must Be Antisymmetric in the Interchange of Any Two Electrons

8-6. Antisymmetric Wave Functions Can Be Represented by Slater Determinants

8-7. Hartree-Fock Calculations Give Good Agreement with Experimental Data

8-8. A Term Symbol Gives a Detailed Description of an Electron Configuration

8-9. The Allowed Values of J are L+S, L+S-1, .....,|L-S|

8-10. Hund's Rules Are Used to Determine the Term Symbol of the Ground Electronic State

8-11. Atomic Term Symbols Are Used to Describe Atomic Spectra

Problems

**Chapter 9. The Chemical Bond : Diatomic Molecules **

9-1. The Born-Oppenheimer Approximation Simplifies the Schrodinger Equation for Molecules

9-2. H2+ Is the Prototypical Species of Molecular-Orbital Theory

9-3. The Overlap Integral Is a Quantitative Measure of the Overlap of Atomic Orbitals Situated on Different Atoms

9-4. The Stability of a Chemical Bond Is a Quantum-Mechanical Effect

9-5. The Simplest Molecular Orbital Treatment of H2+ Yields a Bonding Orbital and an Antibonding Orbital

9-6. A Simple Molecular-Orbital Treatment of H2 Places Both Electrons in a Bonding Orbital

9-7. Molecular Orbitals Can Be Ordered According to Their Energies

9-8. Molecular-Orbital Theory Predicts that a Stable Diatomic Helium Molecule Does Not Exist

9-9. Electrons Are Placed into Moleular Orbitals in Accord with the Pauli Exclusion Principle

9-10. Molecular-Orbital Theory Correctly Predicts that Oxygen Molecules Are Paramagnetic

9-11. Photoelectron Spectra Support the Existence of Molecular Orbitals

9-12. Molecular-Orbital Theory Also Applies to Heteronuclear Diatomic Molecules

9-13. An SCF-LCAO-MO Wave Function Is a Molecular Orbital Formed from a Linear Combination of Atomic Orbitals and Whose Coefficients Are Determined Self-Consistently

9-14. Electronic States of Molecules Are Designated by Molecular Term Symbols

9-15. Molecular Term Symbols Designate the Symmetry Properties of Molecular Wave Functions

9-16. Most Molecules Have Excited Electronic States

Problems

**Chapter 10. Bonding in Polyatomic Molecules **

10-1. Hybrid Orbitals Account for Molecular Shape

10-2. Different Hybrid Orbitals Are Used for the Bonding Electrons and the Lone Pair Electrons in Water

10-3. Why is BeH2 Linear and H2O Bent?

10-4. Photoelectron Spectroscopy Can Be Used to Study Molecular Orbitals

10-5. Conjugated Hydrocarbons and Aromatic Hydrocarbons Can Be Treated by a Pi-Electron Approximation

10-6. Butadiene is Stabilized by a Delocalization Energy

Problems

**Chapter 11. Computational Quantum Chemistry **

11-1. Gaussian Basis Sets Are Often Used in Modern Computational Chemistry

11-2. Extended Basis Sets Account Accurately for the Size and Shape of Molecular Charge Distributions

11-3. Asterisks in the Designation of a Basis Set Denote Orbital Polarization Terms

11-4. The Ground-State Energy of H2 can be Calculated Essentially Exactly

11-5. Gaussian 94 Calculations Provide Accurate Information About Molecules

Problems

MathChapter F / Matrices

**Chapter 12. Group Theory : The Exploitation of Symmetry **

12-1. The Exploitation of the Symmetry of a Molecule Can Be Used to Significantly Simplify Numerical Calculations

12-2. The Symmetry of Molecules Can Be Described by a Set of Symmetry Elements

12-3. The Symmetry Operations of a Molecule Form a Group

12-4. Symmetry Operations Can Be Represented by Matrices

12-5. The C3V Point Group Has a Two-Dimenstional Irreducible Representation

12-6. The Most Important Summary of the Properties of a Point Group Is Its Character Table

12-7. Several Mathematical Relations Involve the Characters of Irreducible Representations

12-8. We Use Symmetry Arguments to Prediect Which Elements in a Secular Determinant Equal Zero

12-9. Generating Operators Are Used to Find Linear Combinations of Atomic Orbitals That Are Bases for Irreducible Representations

Problems

**Chapter 13. Molecular Spectroscopy **

13-1. Different Regions of the Electromagnetic Spectrum Are Used to Investigate Different Molecular Processes

13-2. Rotational Transitions Accompany Vibrational Transitions

13-3. Vibration-Rotation Interaction Accounts for the Unequal Spacing of the Lines in the P and R Branches of a Vibration-Rotation Spectrum

13-4. The Lines in a Pure Rotational Spectrum Are Not Equally Spaced

13-5. Overtones Are Observed in Vibrational Spectra

13-6. Electronic Spectra Contain Electronic, Vibrational, and Rotational Information

13-7. The Franck-Condon Principle Predicts the Relative Intensities of Vibronic Transitions

13-8. The Rotational Spectrum of a Polyatomic Molecule Depends Upon the Principal Moments of Inertia of the Molecule

13-9. The Vibrations of Polyatomic Molecules Are Represented by Normal Coordinates

13-10. Normal Coordinates Belong to Irreducible Representation of Molecular Point Groups

13-11. Selection Rules Are Derived from Time-Dependent Perturbation Theory

13-12. The Selection Rule in the Rigid Rotator Approximation Is Delta J = (plus or minus) 1

13-13. The Harmonic-Oscillator Selection Rule Is Delta v = (plus or minus) 1

13-14. Group Theory Is Used to Determine the Infrared Activity of Normal Coordinate Vibrations

Problems

**Chapter 14. Nuclear Magnetic Resonance Spectroscopy **

14-1. Nuclei Have Intrinsic Spin Angular Momenta

14-2. Magnetic Moments Interact with Magnetic Fields

14-3. Proton NMR Spectrometers Operate at Frequencies Between 60 MHz and 750 MHz

14-4. The Magnetic Field Acting upon Nuclei in Molecules Is Shielded

14-5. Chemical Shifts Depend upon the Chemical Environment of the Nucleus

14-6. Spin-Spin Coupling Can Lead to Multiplets in NMR Spectra

14-7. Spin-Spin Coupling Between Chemically Equivalent Protons Is Not Observed

14-8. The n+1 Rule Applies Only to First-Order Spectra

14-9. Second-Order Spectra Can Be Calculated Exactly Using the Variational Method

Problems

**Chapter 15. Lasers, Laser Spectroscopy, and Photochemistry **

15-1. Electronically Excited Molecules Can Relax by a Number of Processes

15-2. The Dynamics of Spectroscopic Transitions Between the Electronic States of Atoms Can Be Modeled by Rate Equations

15-3. A Two-Level System Cannot Achieve a Population Inversion

15-4. Population Inversion Can Be Achieved in a Three-Level System

15-5. What is Inside a Laser?

15-6. The Helium-Neon Laser is an Electrical-Discharge Pumped, Continuous-Wave, Gas-Phase Laser

15-7. High-Resolution Laser Spectroscopy Can Resolve Absorption Lines that Cannot be Distinguished by Conventional Spectrometers

15-8. Pulsed Lasers Can by Used to Measure the Dynamics of Photochemical Processes

Problems

MathChapter G / Numerical Methods

**Chapter 16. The Properties of Gases **

16-1. All Gases Behave Ideally If They Are Sufficiently Dilute

16-2. The van der Waals Equation and the Redlich-Kwong Equation Are Examples of Two-Parameter Equations of State

16-3. A Cubic Equation of State Can Describe Both the Gaseous and Liquid States

16-4. The van der Waals Equation and the Redlich-Kwong Equation Obey the Law of Corresponding States

16-5. The Second Virial Coefficient Can Be Used to Determine Intermolecular Potentials

16-6. London Dispersion Forces Are Often the Largest Contributer to the r-6 Term in the Lennard-Jones Potential

16-7. The van der Waals Constants Can Be Written in Terms of Molecular Parameters

Problems

**Chapter 17. The Boltzmann Factor And Partition Functions **

17-1. The Boltzmann Factor Is One of the Most Important Quantities in the Physical Sciences

17-2. The Probability That a System in an Ensemble Is in the State j with Energy Ej (N,V) Is Proportional to e-Ej(N,V)/kBT

17-3. We Postulate That the Average Ensemble Energy Is Equal to the Observed Energy of a System

17-4. The Heat Capacity at Constant Volume Is the Temperature Derivative of the Average Energy

17-5. We Can Express the Pressure in Terms of a Partition Function

17-6. The Partition Function of a System of Independent, Distinguishable Molecules Is the Product of Molecular Partition Functions

17-7. The Partition Function of a System of Independent, Indistinguishable Atoms or Molecules Can Usually Be Written as [q(V,T)]N/N!

17-8. A Molecular Partition Function Can Be Decomposed into Partition Functions for Each Degree of Freedom

Problems

MathChapter I / Series and Limits

**Chapter 18. Partition Functions And Ideal Gases **

18-1. The Translational Partition Function of a Monatomic Ideal Gas is (2pi mkBT /h2) 3/2V

18-2. Most Atoms Are in the Ground Electronic State at Room Temperature

18-3. The Energy of a Diatomic Molecule Can Be Approximated as a Sum of Separate Terms

18-4. Most Molecules Are in the Ground Vibrational State at Room Temperature

18-5. Most Molecules Are in Excited Rotational States at Ordinary Temperatures

18-6. Rotational Partition Functions Contain a Symmetry Number

18-7. The Vibrational Partition Function of a Polyatomic Molecule Is a Product of Harmonic Oscillator Partition Functions for Each Normal Coordinate

18-8. The Form of the Rotational Partition Function of a Polyatomic Molecule Depends Upon the Shape of the Molecule

18-9. Calculated Molar Heat Capacities Are in Very Good Agreement with Experimental Data

Problems

**Chapter 19. The First Law of Thermodynamics **

19-1. A Common Type of Work is Pressure-Volume Work

19-2. Work and Heat Are Not State Functions, but Energy is a State Function

19-3. The First Law of Thermodynamics Says the Energy Is a State Function

19-4. An Adiabatic Process Is a Process in Which No Energy as Heat Is Transferred

19-5. The Temperature of a Gas Decreases in a Reversible Adiabatic Expansion

19-6. Work and Heat Have a Simple Molecular Interpretation

19-7. The Enthalpy Change Is Equal to the Energy Transferred as Heat in a Constant-Pressure Process Involving Only P-V Work

19-8. Heat Capacity Is a Path Function

19-9. Relative Enthalpies Can Be Determined from Heat Capacity Data and Heats of Transition

19-10. Enthalpy Changes for Chemical Equations Are Additive

19-11. Heats of Reactions Can Be Calculated from Tabulated Heats of Formation

19-12. The Temperature Dependence of deltarH is Given in Terms of the Heat Capacities of the Reactants and Products

Problems

MathChapter J / The Binomial Distribution and Stirling's Approximation

**Chapter 20. Entropy and The Second Law of Thermodynamics **

20-1. The Change of Energy Alone Is Not Sufficient to Determine the Direction of a Spontaneous Process

20-2. Nonequilibrium Isolated Systems Evolve in a Direction That Increases Their Disorder

20-3. Unlike qrev, Entropy Is a State Function

20-4. The Second Law of Thermodynamics States That the Entropy of an Isolated System Increases as a Result of a Spontaneous Process

20-5. The Most Famous Equation of Statistical Thermodynamics is S = kB ln W

20-6. We Must Always Devise a Reversible Process to Calculate Entropy Changes

20-7. Thermodynamics Gives Us Insight into the Conversion of Heat into Work

20-8. Entropy Can Be Expressed in Terms of a Partition Function

20-9. The Molecular Formula S = kB in W is Analogous to the Thermodynamic Formula dS = deltaqrev/T

Problems

**Chapter 21. Entropy And The Third Law of Thermodynamics **

21-1. Entropy Increases With Increasing Temperature

21-2. The Third Law of Thermodynamics Says That the Entropy of a Perfect Crystal is Zero at 0 K

21-3. deltatrsS = deltatrsH / Ttrs at a Phase Transition

21-4. The Third Law of Thermodynamics Asserts That CP -> 0 as T -> 0

21-5. Practical Absolute Entropies Can Be Determined Calorimetrically

21-6. Practical Absolute Entropies of Gases Can Be Calculated from Partition Functions

21-7. The Values of Standard Entropies Depend Upon Molecular Mass and Molecular Structure

21-8. The Spectroscopic Entropies of a Few Substances Do Not Agree with the Calorimetric Entropies

21-9. Standard Entropies Can Be Used to Calculate Entropy Changes of Chemical Reactions

Problems

**Chapter 22. Helmholtz and Gibbs Energies **

22-1. The Sign of the Helmholtz Energy Change Determines the Direction of a Spontaneous Process in a System at Constant Volume and Temperature

22-2. The Gibbs Energy Determines the Direction of a Spontaneous Process for a System at Constant Pressure and Temperature

22-3. Maxwell Relations Provide Several Useful Thermodynamic Formulas

22-4. The Enthalpy of an Ideal Gas Is Independent of Pressure

22-5. The Various Thermodynamic Functions Have Natural Independent Variables

22-6. The Standard State for a Gas at Any Temperature Is the Hypothetical Ideal Gas at One Bar

22-7. The Gibbs-Helmholtz Equation Describes the Temperature Dependance of the Gibbs Energy

22-8. Fugacity Is a Measure of the Nonideality of a Gas

Problems

**Chapter 23. Phase Equilibria **

23-1. A Phase Diagram Summarizes the Solid-Liquid-Gas Behavior of a Substance

23-2. The Gibbs Energy of a Substance Has a Close Connection to Its Phase Diagram

23-3. The Chemical Potentials of a Pure Substance in Two Phases in Equilibrium Are Equal

23-4. The Clausius-Clapeyron Equation Gives the Vapor Pressure of a Substance As a Function of Temperature

23-5. Chemical Potential Can be Evaluated From a Partition Function

Problems

**Chapter 24. Solutions I: Liquid-Liquid Solutions**

24-1. Partial Molar Quantities Are Important Thermodynamic Properites of Solutions

24-2. The Gibbs-Duhem Equation Relates the Change in the Chemical Potential of One Component of a Solution to the Change in the Chemical Potential of the Other

24-3. The Chemical Potential of Each Component Has the Same Value in Each Phase in Which the Component Appears

24-4. The Components of an Ideal Solution Obey Raoult's Law for All Concentrations

24-5. Most Solutions are Not Ideal

24-6. The Gibbs-Duhem Equation Relats the Vapor Pressures of the Two Components of a Volatile Binary Solution

24-7. The Central Thermodynamic Quantity for Nonideal Solutions is the Activity

24-8. Activities Must Be Calculated with Respect to Standard States

24-9. We Can Calculate the Gibbs Energy of Mixing of Binary Solutions in Terms of the Activity Coefficient

Problems

**Chapter 25. Solutions II: Solid-Liquid Solutions**

25-1. We Use a Raoult's Law Standard State for the Solvent and a Henry's Law Standard State for the Solute for Solutionsof Solids Dissolved in Liquids

25-2. The Activity of a Nonvolatile Solute Can Be Obtained from the Vapor Pressure of the Solvent

25-3. Colligative Properties Are Solution Properties That Depend Only Upon the Number Density of Solute Particles

25-4. Osmotic Pressure Can Be Used to Determine the Molecular Masses of Polymers

25-5. Solutions of Electrolytes Are Nonideal at Relatively Low Concentrations

25-6. The Debye-Hukel Theory Gives an Exact Expression of 1n gamma(plus or minus) For Very Dilute Solutions

25-7. The Mean Spherical Approximation Is an Extension of the Debye-Huckel Theory to Higher Concentrations

Problems

**Chapter 26. Chemical Equilibrium **

26-1. Chemical Equilibrium Results When the Gibbs Energy Is a Minimun with Respect to the Extent of Reaction

26-2. An Equilibrium Constant Is a Function of Temperature Only

26-3. Standard Gibbs Energies of Formation Can Be Used to Calculate Equilibrium Constants

26-4. A Plot of the Gibbs Energy of a Reaction Mixture Against the Extent of Reaction Is a Minimum at Equilibrium

26-5. The Ratio of the Reaction Quotient to the Equilibrium Constant Determines the Direction in Which a Reaction Will Proceed

26-6. The Sign of deltar G And Not That of deltar Go Determines the Direction of Reaction Spontaneity

26-7. The Variation of an Equilibrium Constant with Temperature Is Given by the Van't Hoff Equation

26-8. We Can Calculate Equilibrium Constants in Terms of Partition Functions

26-9. Molecular Partition Functions and Related Thermodynamic Data Are Extensively Tabulated

26-10. Equilibrium Constants for Real Gases Are Expressed in Terms of Partial Fugacities

26-11. Thermodynamic Equilibrium Constants Are Expressed in Terms of Activities

26-12. The Use of Activities Makes a Significant Difference in Solubility Calculations Involving Ionic Species

Problems

**Chapter 27. The Kinetic Theory of Gases **

27-1. The Average Translational Kinetic Energy of the Molecules in a Gas Is Directly Proportional to the Kelvin Temperature

27-2. The Distribution of the Components of Molecular Speeds Are Described by a Gaussian Distribution

27-3. The Distribution of Molecular Speeds Is Given by the Maxwell-Boltzmann Distribution

27-4. The Frequency of Collisions that a Gas Makes with a Wall Is Proportional to its Number Density and to the Average Molecular Speed

27-5. The Maxwell-Boltzmann Distribution Has Been Verified Experimentally

27-6. The Mean Free Path Is the Average Distance a Molecule Travels Between Collisions

27-7. The Rate of a Gas-Phase Chemical Reaction Depends Upon the Rate of Collisions in Which the Relative Kinetic Energy Exceeds Some Critical Value

Problems

**Chapter 28. Chemical Kinetics I : Rate Laws **

28-1. The Time Dependence of a Chemical Reaction Is Described by a Rate Law

28-2. Rate Laws Must Be Determined Experimentally

28-3. First-Order Reactions Show an Exponential Decay of Reactant Concentration with Time

28-4. The Rate Laws for Different Reaction Orders Predict Different Behaviors for the Time-Dependent Reactant Concentration

28-5. Reactions Can Also Be Reversible

28-6. The Rate Constants of a Reversible Reaction Can Be Determined Using Relaxation Techniques

28-7. Rate Constants Are Usually Strongly Temperature Dependent

28-8. Transition-State Theory Can Be Used to Estimate Reaction Rate Constants

Problems

**Chapter 29. Chemical Kinetics II : Reaction Mechanisms **

29-1. A Mechanism is a Sequence of Single-Step Chemical Reactions called Elementary Reactions

29-2. The Principle of Detailed Balance States that when a Complex Reaction is at Equilibrium, the Rate of the Forward Process is Equal to the Rate of the Reverse Process for Each and Every Step of the Reaction Mechanism

29-3. When Are Consecutive and Single-Step Reactions Distinguishable?

29-4. The Steady-State Approximation Simplifies Rate Expressions yy Assuming that d[I]/dt=0, where I is a Reaction Intermediate

29-5. The Rate Law for a Complex Reaction Does Not Imply a Unique Mechanism

29-6. The Lindemann Mechanism Explains How Unimolecular Reactions Occur

29-7. Some Reaction Mechanisms Involve Chain Reactions

29-8. A Catalyst Affects the Mechanism and Activation Energy of a Chemical Reaction

29-9. The Michaelis-Menten Mechanism Is a Reaction Mechanism for Enzyme Catalysis

Problems

**Chapter 30. Gas-Phase Reaction Dynamics **

30-1. The Rate of Bimolecular Gas-Phase Reaction Can Be Calculated Using Hard-Sphere Collision Theory and an Energy-Dependent Reaction Cross Section

30-2. A Reaction Cross Section Depends Upon the Impact Parameter

30-3. The Rate Constant for a Gas-Phase Chemical Reaction May Depend on the Orientations of the Colliding Molecules

30-4. The Internal Energy of the Reactants Can Affect the Cross Section of a Reaction

30-5. A Reactive Collision Can Be Described in a Center-of-Mass Coordinate System

30-6. Reactive Collisions Can be Studied Using Crossed Molecular Beam Machines

30-7. The Reaction F(g) +D2 (g) => DF(g) + D(g) Can Produce Vibrationally Excited DF(g) Molecules

30-8. The Velocity and Angular Distribution of the Products of a Reactive Collision Provide a Molecular Picture of the Chemical Reaction

30-9. Not All Gas-Phase Chemical Reactions Are Rebound Reactions

30-10. The Potential-Energy Surface for the Reaction F(g) + D2(g) => DF(g) + D(g) Can Be Calculated Using Quantum Mechanics

Problems

**Chapter 31. Solids and Surface Chemistry **

31-1. The Unit Cell Is the Funamental Building Block of a Crystal

31-2. The Orientation of a Lattice Plane Is Described by its Miller Indices

31-3. The Spacing Between Lattice Planes Can Be Determined from X-Ray Diffraction Measurements

31-4. The Total Scattering Intensity Is Related to the Periodic Structure of the Electron Density in the Crystal

31-5. The Structure Factor and the Electron Density Are Related by a Fourier Transform

31-6. A Gas Molecule Can Physisorb or Chemisorb to a Solid Surface

31-7. Isotherms Are Plots of Surface Coverage as a Function of Gas Pressure at Constant Temperature

31-8. The Langmuir Isotherm Can Be Used to Derive Rate Laws for Surface-Catalyzed Gas-Phase Reactions

31-9. The Structure of a Surface is Different from that of a Bulk Solid

31-10. The Reaction Between H2(g) and N 2(g) to Make NH3 (g) Can Be Surface Catalyzed

Problems

Answers to the Numerical Problems

llustration Credits

Index

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Summary

As the first modern physical chemistry textbook to cover quantum mechanics before thermodynamics and kinetics, this book provides a contemporary approach to the study of physical chemistry. By beginning with quantum chemistry, students will learn the fundamental principles upon which all modern physical chemistry is built.

The text includes a special set of "MathChapters" to review and summarize the mathematical tools required to master the material * *Thermodynamics is simultaneously taught from a bulk and microscopic viewpoint that enables the student to understand how bulk properties of materials are related to the properties of individual constituent molecules.

This new text includes a variety of modern research topics in physical chemistry as well as hundreds of worked problems and examples.

Author Bio

**McQuarrie, Donald A. : University of California, Davis**

Simon, John D. : Duke University

Table of Contents

**Chapter 1. The Dawn of the Quantum Theory **

1-1. Blackbody Radiation Could Not Be Explained by Classical Physics

1-2. Planck Used a Quantum Hypothesis to Derive the Blackbody Radiation Law

1-3. Einstein Explained the Photoelectric Effect with a Quantum Hypothesis

1-4. The Hydrogen Atomic Spectrum Consists of Several Series of Lines

1-5. The Rydberg Formula Accounts for All the Lines in the Hydrogen Atomic Spectrum

1-6. Louis de Broglie Postulated That Matter Has Wavelike Properties

1-7. de Broglie Waves Are Observed Experimentally

1-8. The Bohr Theory of the Hydrogen Atom Can Be Used to Derive the Rydberg Formula

1-9. The Heisenberg Uncertainty Principle States That the Position and the Momentum of a Particle Cannot be Specified Simultaneously with Unlimited Precision

Problems

MathChapter A / Complex Numbers

**Chapter 2. The Classical Wave Equation **

2-1. The One-Dimensional Wave Equation Describes the Motion of a Vibrating String

2-2. The Wave Equation Can Be Solved by the Method of Separation of Variables

2-3. Some Differential Equations Have Oscillatory Solutions

2-4. The General Solution to the Wave Equation Is a Superposition of Normal Modes

2-5. A Vibrating Membrane Is Described by a Two- Dimensional Wave Equation

Problems

MathChapter B / Probability and Statistics

**Chapter 3. The Schrodinger Equation and a Particle In a Box **

3-1. The Schrodinger Equation Is the Equation for Finding the Wave Function of a Particle

3-2. Classical-Mechanical Quantities Are Represented by Linear Operators in Quantum Mechanics

3-3. The Schrodinger Equation Can be Formulated as an Eigenvalue Problem

3-4. Wave Functions Have a Probabilistic Interpretation

3-5. The Energy of a Particle in a Box Is Quantized

3-6. Wave Functions Must Be Normalized

3-7. The Average Momentum of a Particle in a Box is Zero

3-8. The Uncertainty Principle Says That sigmapsigmax>h/2

3-9. The Problem of a Particle in a Three-Dimensional Box is a Simple Extension of the One-Dimensional Case

Problems

MathChapter C / Vectors

**Chapter 4. Some Postulates and General Principles of Quantum Mechanics **

4-1. The State of a System Is Completely Specified by its Wave Function

4-2. Quantum-Mechanical Operators Represent Classical-Mechanical Variables

4-3. Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators

4-4. The Time Dependence of Wave Functions Is Governed by the Time-Dependent Schrodinger Equation

4-5. The Eigenfunctions of Quantum Mechanical Operators Are Orthogonal

4-6. The Physical Quantities Corresponding to Operators That Commute Can Be Measured Simultaneously to Any Precision

Problems

MathChapter D / Spherical Coordinates

**Chapter 5. The Harmonic Oscillator and the Rigid Rotator : Two Spectroscopic Models **

5-1. A Harmonic Oscillator Obeys Hooke's Law

5-2. The Equation for a Harmonic-Oscillator Model of a Diatomic Molecule Contains the Reduced Mass of the Molecule

5-3. The Harmonic-Oscillator Approximation Results from the Expansion of an Internuclear Potential Around its Minimum

5-4. The Energy Levels of a Quantum-Mechanical Harmonic Oscillator Are Ev = hw(v + 1/2) with v= 0,1,2...

5-5. The Harmonic Oscillator Accounts for the Infrared Spectrum of a Diatomic Molecule

5-6. The Harmonic-Oscillator Wave Functions Involve Hermite Polynomials

5-7. Hermite Polynomials Are Either Even or Odd Functions

5-8. The Energy Levels of a Rigid Rotator Are E = h 2J(J+1)/2I

5-9. The Rigid Rotator Is a Model for a Rotating Diatomic Molecule

Problems

**Chapter 6. The Hydrogen Atom **

6-1. The Schrodinger Equation for the Hydrogen Atom Can Be Solved Exactly

6-2. The Wave Functions of a Rigid Rotator Are Called Spherical Harmonics

6-3. The Precise Values of the Three Components of Angular Momentum Cannot Be Measured Simultaneously

6-4. Hydrogen Atomic Orbitals Depend upon Three Quantum Numbers

6-5. s Orbitals Are Spherically Symmetric

6-6. There Are Three p Orbitals for Each Value of the Principle Quantum Number, n>= 2

6-7. The Schrodinger Equation for the Helium Atom Cannot Be Solved Exactly

Problems

MathChapter E / Determinants

**Chapter 7. Approximation Methods **

7-1. The Variational Method Provides an Upper Bound to the Ground-State Energy of a System

7-2. A Trial Function That Depends Linearly on the Variational Parameters Leads to a Secular Determinant

7-3. Trial Functions Can Be Linear Combinations of Functions That Also Contain Variational Parameters

7-4. Perturbation Theory Expresses the Solution to One Problem in Terms of Another Problem Solved Previously

Problems

**Chapter 8. Multielectron Atoms **

8-1. Atomic and Molecular Calculations Are Expressed in Atomic Units

8-2. Both Pertubation Theory and the Variational Method Can Yield Excellent Results for Helium

8-3. Hartree-Fock Equations Are Solved by the Self-Consistent Field Method

8-4. An Electron Has An Intrinsic Spin Angular Momentum

8-5. Wave Functions Must Be Antisymmetric in the Interchange of Any Two Electrons

8-6. Antisymmetric Wave Functions Can Be Represented by Slater Determinants

8-7. Hartree-Fock Calculations Give Good Agreement with Experimental Data

8-8. A Term Symbol Gives a Detailed Description of an Electron Configuration

8-9. The Allowed Values of J are L+S, L+S-1, .....,|L-S|

8-10. Hund's Rules Are Used to Determine the Term Symbol of the Ground Electronic State

8-11. Atomic Term Symbols Are Used to Describe Atomic Spectra

Problems

**Chapter 9. The Chemical Bond : Diatomic Molecules **

9-1. The Born-Oppenheimer Approximation Simplifies the Schrodinger Equation for Molecules

9-2. H2+ Is the Prototypical Species of Molecular-Orbital Theory

9-3. The Overlap Integral Is a Quantitative Measure of the Overlap of Atomic Orbitals Situated on Different Atoms

9-4. The Stability of a Chemical Bond Is a Quantum-Mechanical Effect

9-5. The Simplest Molecular Orbital Treatment of H2+ Yields a Bonding Orbital and an Antibonding Orbital

9-6. A Simple Molecular-Orbital Treatment of H2 Places Both Electrons in a Bonding Orbital

9-7. Molecular Orbitals Can Be Ordered According to Their Energies

9-8. Molecular-Orbital Theory Predicts that a Stable Diatomic Helium Molecule Does Not Exist

9-9. Electrons Are Placed into Moleular Orbitals in Accord with the Pauli Exclusion Principle

9-10. Molecular-Orbital Theory Correctly Predicts that Oxygen Molecules Are Paramagnetic

9-11. Photoelectron Spectra Support the Existence of Molecular Orbitals

9-12. Molecular-Orbital Theory Also Applies to Heteronuclear Diatomic Molecules

9-13. An SCF-LCAO-MO Wave Function Is a Molecular Orbital Formed from a Linear Combination of Atomic Orbitals and Whose Coefficients Are Determined Self-Consistently

9-14. Electronic States of Molecules Are Designated by Molecular Term Symbols

9-15. Molecular Term Symbols Designate the Symmetry Properties of Molecular Wave Functions

9-16. Most Molecules Have Excited Electronic States

Problems

**Chapter 10. Bonding in Polyatomic Molecules **

10-1. Hybrid Orbitals Account for Molecular Shape

10-2. Different Hybrid Orbitals Are Used for the Bonding Electrons and the Lone Pair Electrons in Water

10-3. Why is BeH2 Linear and H2O Bent?

10-4. Photoelectron Spectroscopy Can Be Used to Study Molecular Orbitals

10-5. Conjugated Hydrocarbons and Aromatic Hydrocarbons Can Be Treated by a Pi-Electron Approximation

10-6. Butadiene is Stabilized by a Delocalization Energy

Problems

**Chapter 11. Computational Quantum Chemistry **

11-1. Gaussian Basis Sets Are Often Used in Modern Computational Chemistry

11-2. Extended Basis Sets Account Accurately for the Size and Shape of Molecular Charge Distributions

11-3. Asterisks in the Designation of a Basis Set Denote Orbital Polarization Terms

11-4. The Ground-State Energy of H2 can be Calculated Essentially Exactly

11-5. Gaussian 94 Calculations Provide Accurate Information About Molecules

Problems

MathChapter F / Matrices

**Chapter 12. Group Theory : The Exploitation of Symmetry **

12-1. The Exploitation of the Symmetry of a Molecule Can Be Used to Significantly Simplify Numerical Calculations

12-2. The Symmetry of Molecules Can Be Described by a Set of Symmetry Elements

12-3. The Symmetry Operations of a Molecule Form a Group

12-4. Symmetry Operations Can Be Represented by Matrices

12-5. The C3V Point Group Has a Two-Dimenstional Irreducible Representation

12-6. The Most Important Summary of the Properties of a Point Group Is Its Character Table

12-7. Several Mathematical Relations Involve the Characters of Irreducible Representations

12-8. We Use Symmetry Arguments to Prediect Which Elements in a Secular Determinant Equal Zero

12-9. Generating Operators Are Used to Find Linear Combinations of Atomic Orbitals That Are Bases for Irreducible Representations

Problems

**Chapter 13. Molecular Spectroscopy **

13-1. Different Regions of the Electromagnetic Spectrum Are Used to Investigate Different Molecular Processes

13-2. Rotational Transitions Accompany Vibrational Transitions

13-3. Vibration-Rotation Interaction Accounts for the Unequal Spacing of the Lines in the P and R Branches of a Vibration-Rotation Spectrum

13-4. The Lines in a Pure Rotational Spectrum Are Not Equally Spaced

13-5. Overtones Are Observed in Vibrational Spectra

13-6. Electronic Spectra Contain Electronic, Vibrational, and Rotational Information

13-7. The Franck-Condon Principle Predicts the Relative Intensities of Vibronic Transitions

13-8. The Rotational Spectrum of a Polyatomic Molecule Depends Upon the Principal Moments of Inertia of the Molecule

13-9. The Vibrations of Polyatomic Molecules Are Represented by Normal Coordinates

13-10. Normal Coordinates Belong to Irreducible Representation of Molecular Point Groups

13-11. Selection Rules Are Derived from Time-Dependent Perturbation Theory

13-12. The Selection Rule in the Rigid Rotator Approximation Is Delta J = (plus or minus) 1

13-13. The Harmonic-Oscillator Selection Rule Is Delta v = (plus or minus) 1

13-14. Group Theory Is Used to Determine the Infrared Activity of Normal Coordinate Vibrations

Problems

**Chapter 14. Nuclear Magnetic Resonance Spectroscopy **

14-1. Nuclei Have Intrinsic Spin Angular Momenta

14-2. Magnetic Moments Interact with Magnetic Fields

14-3. Proton NMR Spectrometers Operate at Frequencies Between 60 MHz and 750 MHz

14-4. The Magnetic Field Acting upon Nuclei in Molecules Is Shielded

14-5. Chemical Shifts Depend upon the Chemical Environment of the Nucleus

14-6. Spin-Spin Coupling Can Lead to Multiplets in NMR Spectra

14-7. Spin-Spin Coupling Between Chemically Equivalent Protons Is Not Observed

14-8. The n+1 Rule Applies Only to First-Order Spectra

14-9. Second-Order Spectra Can Be Calculated Exactly Using the Variational Method

Problems

**Chapter 15. Lasers, Laser Spectroscopy, and Photochemistry **

15-1. Electronically Excited Molecules Can Relax by a Number of Processes

15-2. The Dynamics of Spectroscopic Transitions Between the Electronic States of Atoms Can Be Modeled by Rate Equations

15-3. A Two-Level System Cannot Achieve a Population Inversion

15-4. Population Inversion Can Be Achieved in a Three-Level System

15-5. What is Inside a Laser?

15-6. The Helium-Neon Laser is an Electrical-Discharge Pumped, Continuous-Wave, Gas-Phase Laser

15-7. High-Resolution Laser Spectroscopy Can Resolve Absorption Lines that Cannot be Distinguished by Conventional Spectrometers

15-8. Pulsed Lasers Can by Used to Measure the Dynamics of Photochemical Processes

Problems

MathChapter G / Numerical Methods

**Chapter 16. The Properties of Gases **

16-1. All Gases Behave Ideally If They Are Sufficiently Dilute

16-2. The van der Waals Equation and the Redlich-Kwong Equation Are Examples of Two-Parameter Equations of State

16-3. A Cubic Equation of State Can Describe Both the Gaseous and Liquid States

16-4. The van der Waals Equation and the Redlich-Kwong Equation Obey the Law of Corresponding States

16-5. The Second Virial Coefficient Can Be Used to Determine Intermolecular Potentials

16-6. London Dispersion Forces Are Often the Largest Contributer to the r-6 Term in the Lennard-Jones Potential

16-7. The van der Waals Constants Can Be Written in Terms of Molecular Parameters

Problems

**Chapter 17. The Boltzmann Factor And Partition Functions **

17-1. The Boltzmann Factor Is One of the Most Important Quantities in the Physical Sciences

17-2. The Probability That a System in an Ensemble Is in the State j with Energy Ej (N,V) Is Proportional to e-Ej(N,V)/kBT

17-3. We Postulate That the Average Ensemble Energy Is Equal to the Observed Energy of a System

17-4. The Heat Capacity at Constant Volume Is the Temperature Derivative of the Average Energy

17-5. We Can Express the Pressure in Terms of a Partition Function

17-6. The Partition Function of a System of Independent, Distinguishable Molecules Is the Product of Molecular Partition Functions

17-7. The Partition Function of a System of Independent, Indistinguishable Atoms or Molecules Can Usually Be Written as [q(V,T)]N/N!

17-8. A Molecular Partition Function Can Be Decomposed into Partition Functions for Each Degree of Freedom

Problems

MathChapter I / Series and Limits

**Chapter 18. Partition Functions And Ideal Gases **

18-1. The Translational Partition Function of a Monatomic Ideal Gas is (2pi mkBT /h2) 3/2V

18-2. Most Atoms Are in the Ground Electronic State at Room Temperature

18-3. The Energy of a Diatomic Molecule Can Be Approximated as a Sum of Separate Terms

18-4. Most Molecules Are in the Ground Vibrational State at Room Temperature

18-5. Most Molecules Are in Excited Rotational States at Ordinary Temperatures

18-6. Rotational Partition Functions Contain a Symmetry Number

18-7. The Vibrational Partition Function of a Polyatomic Molecule Is a Product of Harmonic Oscillator Partition Functions for Each Normal Coordinate

18-8. The Form of the Rotational Partition Function of a Polyatomic Molecule Depends Upon the Shape of the Molecule

18-9. Calculated Molar Heat Capacities Are in Very Good Agreement with Experimental Data

Problems

**Chapter 19. The First Law of Thermodynamics **

19-1. A Common Type of Work is Pressure-Volume Work

19-2. Work and Heat Are Not State Functions, but Energy is a State Function

19-3. The First Law of Thermodynamics Says the Energy Is a State Function

19-4. An Adiabatic Process Is a Process in Which No Energy as Heat Is Transferred

19-5. The Temperature of a Gas Decreases in a Reversible Adiabatic Expansion

19-6. Work and Heat Have a Simple Molecular Interpretation

19-7. The Enthalpy Change Is Equal to the Energy Transferred as Heat in a Constant-Pressure Process Involving Only P-V Work

19-8. Heat Capacity Is a Path Function

19-9. Relative Enthalpies Can Be Determined from Heat Capacity Data and Heats of Transition

19-10. Enthalpy Changes for Chemical Equations Are Additive

19-11. Heats of Reactions Can Be Calculated from Tabulated Heats of Formation

19-12. The Temperature Dependence of deltarH is Given in Terms of the Heat Capacities of the Reactants and Products

Problems

MathChapter J / The Binomial Distribution and Stirling's Approximation

**Chapter 20. Entropy and The Second Law of Thermodynamics **

20-1. The Change of Energy Alone Is Not Sufficient to Determine the Direction of a Spontaneous Process

20-2. Nonequilibrium Isolated Systems Evolve in a Direction That Increases Their Disorder

20-3. Unlike qrev, Entropy Is a State Function

20-4. The Second Law of Thermodynamics States That the Entropy of an Isolated System Increases as a Result of a Spontaneous Process

20-5. The Most Famous Equation of Statistical Thermodynamics is S = kB ln W

20-6. We Must Always Devise a Reversible Process to Calculate Entropy Changes

20-7. Thermodynamics Gives Us Insight into the Conversion of Heat into Work

20-8. Entropy Can Be Expressed in Terms of a Partition Function

20-9. The Molecular Formula S = kB in W is Analogous to the Thermodynamic Formula dS = deltaqrev/T

Problems

**Chapter 21. Entropy And The Third Law of Thermodynamics **

21-1. Entropy Increases With Increasing Temperature

21-2. The Third Law of Thermodynamics Says That the Entropy of a Perfect Crystal is Zero at 0 K

21-3. deltatrsS = deltatrsH / Ttrs at a Phase Transition

21-4. The Third Law of Thermodynamics Asserts That CP -> 0 as T -> 0

21-5. Practical Absolute Entropies Can Be Determined Calorimetrically

21-6. Practical Absolute Entropies of Gases Can Be Calculated from Partition Functions

21-7. The Values of Standard Entropies Depend Upon Molecular Mass and Molecular Structure

21-8. The Spectroscopic Entropies of a Few Substances Do Not Agree with the Calorimetric Entropies

21-9. Standard Entropies Can Be Used to Calculate Entropy Changes of Chemical Reactions

Problems

**Chapter 22. Helmholtz and Gibbs Energies **

22-1. The Sign of the Helmholtz Energy Change Determines the Direction of a Spontaneous Process in a System at Constant Volume and Temperature

22-2. The Gibbs Energy Determines the Direction of a Spontaneous Process for a System at Constant Pressure and Temperature

22-3. Maxwell Relations Provide Several Useful Thermodynamic Formulas

22-4. The Enthalpy of an Ideal Gas Is Independent of Pressure

22-5. The Various Thermodynamic Functions Have Natural Independent Variables

22-6. The Standard State for a Gas at Any Temperature Is the Hypothetical Ideal Gas at One Bar

22-7. The Gibbs-Helmholtz Equation Describes the Temperature Dependance of the Gibbs Energy

22-8. Fugacity Is a Measure of the Nonideality of a Gas

Problems

**Chapter 23. Phase Equilibria **

23-1. A Phase Diagram Summarizes the Solid-Liquid-Gas Behavior of a Substance

23-2. The Gibbs Energy of a Substance Has a Close Connection to Its Phase Diagram

23-3. The Chemical Potentials of a Pure Substance in Two Phases in Equilibrium Are Equal

23-4. The Clausius-Clapeyron Equation Gives the Vapor Pressure of a Substance As a Function of Temperature

23-5. Chemical Potential Can be Evaluated From a Partition Function

Problems

**Chapter 24. Solutions I: Liquid-Liquid Solutions**

24-1. Partial Molar Quantities Are Important Thermodynamic Properites of Solutions

24-2. The Gibbs-Duhem Equation Relates the Change in the Chemical Potential of One Component of a Solution to the Change in the Chemical Potential of the Other

24-3. The Chemical Potential of Each Component Has the Same Value in Each Phase in Which the Component Appears

24-4. The Components of an Ideal Solution Obey Raoult's Law for All Concentrations

24-5. Most Solutions are Not Ideal

24-6. The Gibbs-Duhem Equation Relats the Vapor Pressures of the Two Components of a Volatile Binary Solution

24-7. The Central Thermodynamic Quantity for Nonideal Solutions is the Activity

24-8. Activities Must Be Calculated with Respect to Standard States

24-9. We Can Calculate the Gibbs Energy of Mixing of Binary Solutions in Terms of the Activity Coefficient

Problems

**Chapter 25. Solutions II: Solid-Liquid Solutions**

25-1. We Use a Raoult's Law Standard State for the Solvent and a Henry's Law Standard State for the Solute for Solutionsof Solids Dissolved in Liquids

25-2. The Activity of a Nonvolatile Solute Can Be Obtained from the Vapor Pressure of the Solvent

25-3. Colligative Properties Are Solution Properties That Depend Only Upon the Number Density of Solute Particles

25-4. Osmotic Pressure Can Be Used to Determine the Molecular Masses of Polymers

25-5. Solutions of Electrolytes Are Nonideal at Relatively Low Concentrations

25-6. The Debye-Hukel Theory Gives an Exact Expression of 1n gamma(plus or minus) For Very Dilute Solutions

25-7. The Mean Spherical Approximation Is an Extension of the Debye-Huckel Theory to Higher Concentrations

Problems

**Chapter 26. Chemical Equilibrium **

26-1. Chemical Equilibrium Results When the Gibbs Energy Is a Minimun with Respect to the Extent of Reaction

26-2. An Equilibrium Constant Is a Function of Temperature Only

26-3. Standard Gibbs Energies of Formation Can Be Used to Calculate Equilibrium Constants

26-4. A Plot of the Gibbs Energy of a Reaction Mixture Against the Extent of Reaction Is a Minimum at Equilibrium

26-5. The Ratio of the Reaction Quotient to the Equilibrium Constant Determines the Direction in Which a Reaction Will Proceed

26-6. The Sign of deltar G And Not That of deltar Go Determines the Direction of Reaction Spontaneity

26-7. The Variation of an Equilibrium Constant with Temperature Is Given by the Van't Hoff Equation

26-8. We Can Calculate Equilibrium Constants in Terms of Partition Functions

26-9. Molecular Partition Functions and Related Thermodynamic Data Are Extensively Tabulated

26-10. Equilibrium Constants for Real Gases Are Expressed in Terms of Partial Fugacities

26-11. Thermodynamic Equilibrium Constants Are Expressed in Terms of Activities

26-12. The Use of Activities Makes a Significant Difference in Solubility Calculations Involving Ionic Species

Problems

**Chapter 27. The Kinetic Theory of Gases **

27-1. The Average Translational Kinetic Energy of the Molecules in a Gas Is Directly Proportional to the Kelvin Temperature

27-2. The Distribution of the Components of Molecular Speeds Are Described by a Gaussian Distribution

27-3. The Distribution of Molecular Speeds Is Given by the Maxwell-Boltzmann Distribution

27-4. The Frequency of Collisions that a Gas Makes with a Wall Is Proportional to its Number Density and to the Average Molecular Speed

27-5. The Maxwell-Boltzmann Distribution Has Been Verified Experimentally

27-6. The Mean Free Path Is the Average Distance a Molecule Travels Between Collisions

27-7. The Rate of a Gas-Phase Chemical Reaction Depends Upon the Rate of Collisions in Which the Relative Kinetic Energy Exceeds Some Critical Value

Problems

**Chapter 28. Chemical Kinetics I : Rate Laws **

28-1. The Time Dependence of a Chemical Reaction Is Described by a Rate Law

28-2. Rate Laws Must Be Determined Experimentally

28-3. First-Order Reactions Show an Exponential Decay of Reactant Concentration with Time

28-4. The Rate Laws for Different Reaction Orders Predict Different Behaviors for the Time-Dependent Reactant Concentration

28-5. Reactions Can Also Be Reversible

28-6. The Rate Constants of a Reversible Reaction Can Be Determined Using Relaxation Techniques

28-7. Rate Constants Are Usually Strongly Temperature Dependent

28-8. Transition-State Theory Can Be Used to Estimate Reaction Rate Constants

Problems

**Chapter 29. Chemical Kinetics II : Reaction Mechanisms **

29-1. A Mechanism is a Sequence of Single-Step Chemical Reactions called Elementary Reactions

29-2. The Principle of Detailed Balance States that when a Complex Reaction is at Equilibrium, the Rate of the Forward Process is Equal to the Rate of the Reverse Process for Each and Every Step of the Reaction Mechanism

29-3. When Are Consecutive and Single-Step Reactions Distinguishable?

29-4. The Steady-State Approximation Simplifies Rate Expressions yy Assuming that d[I]/dt=0, where I is a Reaction Intermediate

29-5. The Rate Law for a Complex Reaction Does Not Imply a Unique Mechanism

29-6. The Lindemann Mechanism Explains How Unimolecular Reactions Occur

29-7. Some Reaction Mechanisms Involve Chain Reactions

29-8. A Catalyst Affects the Mechanism and Activation Energy of a Chemical Reaction

29-9. The Michaelis-Menten Mechanism Is a Reaction Mechanism for Enzyme Catalysis

Problems

**Chapter 30. Gas-Phase Reaction Dynamics **

30-1. The Rate of Bimolecular Gas-Phase Reaction Can Be Calculated Using Hard-Sphere Collision Theory and an Energy-Dependent Reaction Cross Section

30-2. A Reaction Cross Section Depends Upon the Impact Parameter

30-3. The Rate Constant for a Gas-Phase Chemical Reaction May Depend on the Orientations of the Colliding Molecules

30-4. The Internal Energy of the Reactants Can Affect the Cross Section of a Reaction

30-5. A Reactive Collision Can Be Described in a Center-of-Mass Coordinate System

30-6. Reactive Collisions Can be Studied Using Crossed Molecular Beam Machines

30-7. The Reaction F(g) +D2 (g) => DF(g) + D(g) Can Produce Vibrationally Excited DF(g) Molecules

30-8. The Velocity and Angular Distribution of the Products of a Reactive Collision Provide a Molecular Picture of the Chemical Reaction

30-9. Not All Gas-Phase Chemical Reactions Are Rebound Reactions

30-10. The Potential-Energy Surface for the Reaction F(g) + D2(g) => DF(g) + D(g) Can Be Calculated Using Quantum Mechanics

Problems

**Chapter 31. Solids and Surface Chemistry **

31-1. The Unit Cell Is the Funamental Building Block of a Crystal

31-2. The Orientation of a Lattice Plane Is Described by its Miller Indices

31-3. The Spacing Between Lattice Planes Can Be Determined from X-Ray Diffraction Measurements

31-4. The Total Scattering Intensity Is Related to the Periodic Structure of the Electron Density in the Crystal

31-5. The Structure Factor and the Electron Density Are Related by a Fourier Transform

31-6. A Gas Molecule Can Physisorb or Chemisorb to a Solid Surface

31-7. Isotherms Are Plots of Surface Coverage as a Function of Gas Pressure at Constant Temperature

31-8. The Langmuir Isotherm Can Be Used to Derive Rate Laws for Surface-Catalyzed Gas-Phase Reactions

31-9. The Structure of a Surface is Different from that of a Bulk Solid

31-10. The Reaction Between H2(g) and N 2(g) to Make NH3 (g) Can Be Surface Catalyzed

Problems

Answers to the Numerical Problems

llustration Credits

Index

Publisher Info

Publisher: University Science Books

Published: 1997

International: No

Published: 1997

International: No

The text includes a special set of "MathChapters" to review and summarize the mathematical tools required to master the material * *Thermodynamics is simultaneously taught from a bulk and microscopic viewpoint that enables the student to understand how bulk properties of materials are related to the properties of individual constituent molecules.

This new text includes a variety of modern research topics in physical chemistry as well as hundreds of worked problems and examples.

**McQuarrie, Donald A. : University of California, Davis**

Simon, John D. : Duke University

**Chapter 1. The Dawn of the Quantum Theory **

1-1. Blackbody Radiation Could Not Be Explained by Classical Physics

1-2. Planck Used a Quantum Hypothesis to Derive the Blackbody Radiation Law

1-3. Einstein Explained the Photoelectric Effect with a Quantum Hypothesis

1-4. The Hydrogen Atomic Spectrum Consists of Several Series of Lines

1-5. The Rydberg Formula Accounts for All the Lines in the Hydrogen Atomic Spectrum

1-6. Louis de Broglie Postulated That Matter Has Wavelike Properties

1-7. de Broglie Waves Are Observed Experimentally

1-8. The Bohr Theory of the Hydrogen Atom Can Be Used to Derive the Rydberg Formula

1-9. The Heisenberg Uncertainty Principle States That the Position and the Momentum of a Particle Cannot be Specified Simultaneously with Unlimited Precision

Problems

MathChapter A / Complex Numbers

**Chapter 2. The Classical Wave Equation **

2-1. The One-Dimensional Wave Equation Describes the Motion of a Vibrating String

2-2. The Wave Equation Can Be Solved by the Method of Separation of Variables

2-3. Some Differential Equations Have Oscillatory Solutions

2-4. The General Solution to the Wave Equation Is a Superposition of Normal Modes

2-5. A Vibrating Membrane Is Described by a Two- Dimensional Wave Equation

Problems

MathChapter B / Probability and Statistics

**Chapter 3. The Schrodinger Equation and a Particle In a Box **

3-1. The Schrodinger Equation Is the Equation for Finding the Wave Function of a Particle

3-2. Classical-Mechanical Quantities Are Represented by Linear Operators in Quantum Mechanics

3-3. The Schrodinger Equation Can be Formulated as an Eigenvalue Problem

3-4. Wave Functions Have a Probabilistic Interpretation

3-5. The Energy of a Particle in a Box Is Quantized

3-6. Wave Functions Must Be Normalized

3-7. The Average Momentum of a Particle in a Box is Zero

3-8. The Uncertainty Principle Says That sigmapsigmax>h/2

3-9. The Problem of a Particle in a Three-Dimensional Box is a Simple Extension of the One-Dimensional Case

Problems

MathChapter C / Vectors

**Chapter 4. Some Postulates and General Principles of Quantum Mechanics **

4-1. The State of a System Is Completely Specified by its Wave Function

4-2. Quantum-Mechanical Operators Represent Classical-Mechanical Variables

4-3. Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators

4-4. The Time Dependence of Wave Functions Is Governed by the Time-Dependent Schrodinger Equation

4-5. The Eigenfunctions of Quantum Mechanical Operators Are Orthogonal

4-6. The Physical Quantities Corresponding to Operators That Commute Can Be Measured Simultaneously to Any Precision

Problems

MathChapter D / Spherical Coordinates

**Chapter 5. The Harmonic Oscillator and the Rigid Rotator : Two Spectroscopic Models **

5-1. A Harmonic Oscillator Obeys Hooke's Law

5-2. The Equation for a Harmonic-Oscillator Model of a Diatomic Molecule Contains the Reduced Mass of the Molecule

5-3. The Harmonic-Oscillator Approximation Results from the Expansion of an Internuclear Potential Around its Minimum

5-4. The Energy Levels of a Quantum-Mechanical Harmonic Oscillator Are Ev = hw(v + 1/2) with v= 0,1,2...

5-5. The Harmonic Oscillator Accounts for the Infrared Spectrum of a Diatomic Molecule

5-6. The Harmonic-Oscillator Wave Functions Involve Hermite Polynomials

5-7. Hermite Polynomials Are Either Even or Odd Functions

5-8. The Energy Levels of a Rigid Rotator Are E = h 2J(J+1)/2I

5-9. The Rigid Rotator Is a Model for a Rotating Diatomic Molecule

Problems

**Chapter 6. The Hydrogen Atom **

6-1. The Schrodinger Equation for the Hydrogen Atom Can Be Solved Exactly

6-2. The Wave Functions of a Rigid Rotator Are Called Spherical Harmonics

6-3. The Precise Values of the Three Components of Angular Momentum Cannot Be Measured Simultaneously

6-4. Hydrogen Atomic Orbitals Depend upon Three Quantum Numbers

6-5. s Orbitals Are Spherically Symmetric

6-6. There Are Three p Orbitals for Each Value of the Principle Quantum Number, n>= 2

6-7. The Schrodinger Equation for the Helium Atom Cannot Be Solved Exactly

Problems

MathChapter E / Determinants

**Chapter 7. Approximation Methods **

7-1. The Variational Method Provides an Upper Bound to the Ground-State Energy of a System

7-2. A Trial Function That Depends Linearly on the Variational Parameters Leads to a Secular Determinant

7-3. Trial Functions Can Be Linear Combinations of Functions That Also Contain Variational Parameters

7-4. Perturbation Theory Expresses the Solution to One Problem in Terms of Another Problem Solved Previously

Problems

**Chapter 8. Multielectron Atoms **

8-1. Atomic and Molecular Calculations Are Expressed in Atomic Units

8-2. Both Pertubation Theory and the Variational Method Can Yield Excellent Results for Helium

8-3. Hartree-Fock Equations Are Solved by the Self-Consistent Field Method

8-4. An Electron Has An Intrinsic Spin Angular Momentum

8-5. Wave Functions Must Be Antisymmetric in the Interchange of Any Two Electrons

8-6. Antisymmetric Wave Functions Can Be Represented by Slater Determinants

8-7. Hartree-Fock Calculations Give Good Agreement with Experimental Data

8-8. A Term Symbol Gives a Detailed Description of an Electron Configuration

8-9. The Allowed Values of J are L+S, L+S-1, .....,|L-S|

8-10. Hund's Rules Are Used to Determine the Term Symbol of the Ground Electronic State

8-11. Atomic Term Symbols Are Used to Describe Atomic Spectra

Problems

**Chapter 9. The Chemical Bond : Diatomic Molecules **

9-1. The Born-Oppenheimer Approximation Simplifies the Schrodinger Equation for Molecules

9-2. H2+ Is the Prototypical Species of Molecular-Orbital Theory

9-3. The Overlap Integral Is a Quantitative Measure of the Overlap of Atomic Orbitals Situated on Different Atoms

9-4. The Stability of a Chemical Bond Is a Quantum-Mechanical Effect

9-5. The Simplest Molecular Orbital Treatment of H2+ Yields a Bonding Orbital and an Antibonding Orbital

9-6. A Simple Molecular-Orbital Treatment of H2 Places Both Electrons in a Bonding Orbital

9-7. Molecular Orbitals Can Be Ordered According to Their Energies

9-8. Molecular-Orbital Theory Predicts that a Stable Diatomic Helium Molecule Does Not Exist

9-9. Electrons Are Placed into Moleular Orbitals in Accord with the Pauli Exclusion Principle

9-10. Molecular-Orbital Theory Correctly Predicts that Oxygen Molecules Are Paramagnetic

9-11. Photoelectron Spectra Support the Existence of Molecular Orbitals

9-12. Molecular-Orbital Theory Also Applies to Heteronuclear Diatomic Molecules

9-13. An SCF-LCAO-MO Wave Function Is a Molecular Orbital Formed from a Linear Combination of Atomic Orbitals and Whose Coefficients Are Determined Self-Consistently

9-14. Electronic States of Molecules Are Designated by Molecular Term Symbols

9-15. Molecular Term Symbols Designate the Symmetry Properties of Molecular Wave Functions

9-16. Most Molecules Have Excited Electronic States

Problems

**Chapter 10. Bonding in Polyatomic Molecules **

10-1. Hybrid Orbitals Account for Molecular Shape

10-2. Different Hybrid Orbitals Are Used for the Bonding Electrons and the Lone Pair Electrons in Water

10-3. Why is BeH2 Linear and H2O Bent?

10-4. Photoelectron Spectroscopy Can Be Used to Study Molecular Orbitals

10-5. Conjugated Hydrocarbons and Aromatic Hydrocarbons Can Be Treated by a Pi-Electron Approximation

10-6. Butadiene is Stabilized by a Delocalization Energy

Problems

**Chapter 11. Computational Quantum Chemistry **

11-1. Gaussian Basis Sets Are Often Used in Modern Computational Chemistry

11-2. Extended Basis Sets Account Accurately for the Size and Shape of Molecular Charge Distributions

11-3. Asterisks in the Designation of a Basis Set Denote Orbital Polarization Terms

11-4. The Ground-State Energy of H2 can be Calculated Essentially Exactly

11-5. Gaussian 94 Calculations Provide Accurate Information About Molecules

Problems

MathChapter F / Matrices

**Chapter 12. Group Theory : The Exploitation of Symmetry **

12-1. The Exploitation of the Symmetry of a Molecule Can Be Used to Significantly Simplify Numerical Calculations

12-2. The Symmetry of Molecules Can Be Described by a Set of Symmetry Elements

12-3. The Symmetry Operations of a Molecule Form a Group

12-4. Symmetry Operations Can Be Represented by Matrices

12-5. The C3V Point Group Has a Two-Dimenstional Irreducible Representation

12-6. The Most Important Summary of the Properties of a Point Group Is Its Character Table

12-7. Several Mathematical Relations Involve the Characters of Irreducible Representations

12-8. We Use Symmetry Arguments to Prediect Which Elements in a Secular Determinant Equal Zero

12-9. Generating Operators Are Used to Find Linear Combinations of Atomic Orbitals That Are Bases for Irreducible Representations

Problems

**Chapter 13. Molecular Spectroscopy **

13-1. Different Regions of the Electromagnetic Spectrum Are Used to Investigate Different Molecular Processes

13-2. Rotational Transitions Accompany Vibrational Transitions

13-3. Vibration-Rotation Interaction Accounts for the Unequal Spacing of the Lines in the P and R Branches of a Vibration-Rotation Spectrum

13-4. The Lines in a Pure Rotational Spectrum Are Not Equally Spaced

13-5. Overtones Are Observed in Vibrational Spectra

13-6. Electronic Spectra Contain Electronic, Vibrational, and Rotational Information

13-7. The Franck-Condon Principle Predicts the Relative Intensities of Vibronic Transitions

13-8. The Rotational Spectrum of a Polyatomic Molecule Depends Upon the Principal Moments of Inertia of the Molecule

13-9. The Vibrations of Polyatomic Molecules Are Represented by Normal Coordinates

13-10. Normal Coordinates Belong to Irreducible Representation of Molecular Point Groups

13-11. Selection Rules Are Derived from Time-Dependent Perturbation Theory

13-12. The Selection Rule in the Rigid Rotator Approximation Is Delta J = (plus or minus) 1

13-13. The Harmonic-Oscillator Selection Rule Is Delta v = (plus or minus) 1

13-14. Group Theory Is Used to Determine the Infrared Activity of Normal Coordinate Vibrations

Problems

**Chapter 14. Nuclear Magnetic Resonance Spectroscopy **

14-1. Nuclei Have Intrinsic Spin Angular Momenta

14-2. Magnetic Moments Interact with Magnetic Fields

14-3. Proton NMR Spectrometers Operate at Frequencies Between 60 MHz and 750 MHz

14-4. The Magnetic Field Acting upon Nuclei in Molecules Is Shielded

14-5. Chemical Shifts Depend upon the Chemical Environment of the Nucleus

14-6. Spin-Spin Coupling Can Lead to Multiplets in NMR Spectra

14-7. Spin-Spin Coupling Between Chemically Equivalent Protons Is Not Observed

14-8. The n+1 Rule Applies Only to First-Order Spectra

14-9. Second-Order Spectra Can Be Calculated Exactly Using the Variational Method

Problems

**Chapter 15. Lasers, Laser Spectroscopy, and Photochemistry **

15-1. Electronically Excited Molecules Can Relax by a Number of Processes

15-2. The Dynamics of Spectroscopic Transitions Between the Electronic States of Atoms Can Be Modeled by Rate Equations

15-3. A Two-Level System Cannot Achieve a Population Inversion

15-4. Population Inversion Can Be Achieved in a Three-Level System

15-5. What is Inside a Laser?

15-6. The Helium-Neon Laser is an Electrical-Discharge Pumped, Continuous-Wave, Gas-Phase Laser

15-7. High-Resolution Laser Spectroscopy Can Resolve Absorption Lines that Cannot be Distinguished by Conventional Spectrometers

15-8. Pulsed Lasers Can by Used to Measure the Dynamics of Photochemical Processes

Problems

MathChapter G / Numerical Methods

**Chapter 16. The Properties of Gases **

16-1. All Gases Behave Ideally If They Are Sufficiently Dilute

16-2. The van der Waals Equation and the Redlich-Kwong Equation Are Examples of Two-Parameter Equations of State

16-3. A Cubic Equation of State Can Describe Both the Gaseous and Liquid States

16-4. The van der Waals Equation and the Redlich-Kwong Equation Obey the Law of Corresponding States

16-5. The Second Virial Coefficient Can Be Used to Determine Intermolecular Potentials

16-6. London Dispersion Forces Are Often the Largest Contributer to the r-6 Term in the Lennard-Jones Potential

16-7. The van der Waals Constants Can Be Written in Terms of Molecular Parameters

Problems

**Chapter 17. The Boltzmann Factor And Partition Functions **

17-1. The Boltzmann Factor Is One of the Most Important Quantities in the Physical Sciences

17-2. The Probability That a System in an Ensemble Is in the State j with Energy Ej (N,V) Is Proportional to e-Ej(N,V)/kBT

17-3. We Postulate That the Average Ensemble Energy Is Equal to the Observed Energy of a System

17-4. The Heat Capacity at Constant Volume Is the Temperature Derivative of the Average Energy

17-5. We Can Express the Pressure in Terms of a Partition Function

17-6. The Partition Function of a System of Independent, Distinguishable Molecules Is the Product of Molecular Partition Functions

17-7. The Partition Function of a System of Independent, Indistinguishable Atoms or Molecules Can Usually Be Written as [q(V,T)]N/N!

17-8. A Molecular Partition Function Can Be Decomposed into Partition Functions for Each Degree of Freedom

Problems

MathChapter I / Series and Limits

**Chapter 18. Partition Functions And Ideal Gases **

18-1. The Translational Partition Function of a Monatomic Ideal Gas is (2pi mkBT /h2) 3/2V

18-2. Most Atoms Are in the Ground Electronic State at Room Temperature

18-3. The Energy of a Diatomic Molecule Can Be Approximated as a Sum of Separate Terms

18-4. Most Molecules Are in the Ground Vibrational State at Room Temperature

18-5. Most Molecules Are in Excited Rotational States at Ordinary Temperatures

18-6. Rotational Partition Functions Contain a Symmetry Number

18-7. The Vibrational Partition Function of a Polyatomic Molecule Is a Product of Harmonic Oscillator Partition Functions for Each Normal Coordinate

18-8. The Form of the Rotational Partition Function of a Polyatomic Molecule Depends Upon the Shape of the Molecule

18-9. Calculated Molar Heat Capacities Are in Very Good Agreement with Experimental Data

Problems

**Chapter 19. The First Law of Thermodynamics **

19-1. A Common Type of Work is Pressure-Volume Work

19-2. Work and Heat Are Not State Functions, but Energy is a State Function

19-3. The First Law of Thermodynamics Says the Energy Is a State Function

19-4. An Adiabatic Process Is a Process in Which No Energy as Heat Is Transferred

19-5. The Temperature of a Gas Decreases in a Reversible Adiabatic Expansion

19-6. Work and Heat Have a Simple Molecular Interpretation

19-7. The Enthalpy Change Is Equal to the Energy Transferred as Heat in a Constant-Pressure Process Involving Only P-V Work

19-8. Heat Capacity Is a Path Function

19-9. Relative Enthalpies Can Be Determined from Heat Capacity Data and Heats of Transition

19-10. Enthalpy Changes for Chemical Equations Are Additive

19-11. Heats of Reactions Can Be Calculated from Tabulated Heats of Formation

19-12. The Temperature Dependence of deltarH is Given in Terms of the Heat Capacities of the Reactants and Products

Problems

MathChapter J / The Binomial Distribution and Stirling's Approximation

**Chapter 20. Entropy and The Second Law of Thermodynamics **

20-1. The Change of Energy Alone Is Not Sufficient to Determine the Direction of a Spontaneous Process

20-2. Nonequilibrium Isolated Systems Evolve in a Direction That Increases Their Disorder

20-3. Unlike qrev, Entropy Is a State Function

20-4. The Second Law of Thermodynamics States That the Entropy of an Isolated System Increases as a Result of a Spontaneous Process

20-5. The Most Famous Equation of Statistical Thermodynamics is S = kB ln W

20-6. We Must Always Devise a Reversible Process to Calculate Entropy Changes

20-7. Thermodynamics Gives Us Insight into the Conversion of Heat into Work

20-8. Entropy Can Be Expressed in Terms of a Partition Function

20-9. The Molecular Formula S = kB in W is Analogous to the Thermodynamic Formula dS = deltaqrev/T

Problems

**Chapter 21. Entropy And The Third Law of Thermodynamics **

21-1. Entropy Increases With Increasing Temperature

21-2. The Third Law of Thermodynamics Says That the Entropy of a Perfect Crystal is Zero at 0 K

21-3. deltatrsS = deltatrsH / Ttrs at a Phase Transition

21-4. The Third Law of Thermodynamics Asserts That CP -> 0 as T -> 0

21-5. Practical Absolute Entropies Can Be Determined Calorimetrically

21-6. Practical Absolute Entropies of Gases Can Be Calculated from Partition Functions

21-7. The Values of Standard Entropies Depend Upon Molecular Mass and Molecular Structure

21-8. The Spectroscopic Entropies of a Few Substances Do Not Agree with the Calorimetric Entropies

21-9. Standard Entropies Can Be Used to Calculate Entropy Changes of Chemical Reactions

Problems

**Chapter 22. Helmholtz and Gibbs Energies **

22-1. The Sign of the Helmholtz Energy Change Determines the Direction of a Spontaneous Process in a System at Constant Volume and Temperature

22-2. The Gibbs Energy Determines the Direction of a Spontaneous Process for a System at Constant Pressure and Temperature

22-3. Maxwell Relations Provide Several Useful Thermodynamic Formulas

22-4. The Enthalpy of an Ideal Gas Is Independent of Pressure

22-5. The Various Thermodynamic Functions Have Natural Independent Variables

22-6. The Standard State for a Gas at Any Temperature Is the Hypothetical Ideal Gas at One Bar

22-7. The Gibbs-Helmholtz Equation Describes the Temperature Dependance of the Gibbs Energy

22-8. Fugacity Is a Measure of the Nonideality of a Gas

Problems

**Chapter 23. Phase Equilibria **

23-1. A Phase Diagram Summarizes the Solid-Liquid-Gas Behavior of a Substance

23-2. The Gibbs Energy of a Substance Has a Close Connection to Its Phase Diagram

23-3. The Chemical Potentials of a Pure Substance in Two Phases in Equilibrium Are Equal

23-4. The Clausius-Clapeyron Equation Gives the Vapor Pressure of a Substance As a Function of Temperature

23-5. Chemical Potential Can be Evaluated From a Partition Function

Problems

**Chapter 24. Solutions I: Liquid-Liquid Solutions**

24-1. Partial Molar Quantities Are Important Thermodynamic Properites of Solutions

24-2. The Gibbs-Duhem Equation Relates the Change in the Chemical Potential of One Component of a Solution to the Change in the Chemical Potential of the Other

24-3. The Chemical Potential of Each Component Has the Same Value in Each Phase in Which the Component Appears

24-4. The Components of an Ideal Solution Obey Raoult's Law for All Concentrations

24-5. Most Solutions are Not Ideal

24-6. The Gibbs-Duhem Equation Relats the Vapor Pressures of the Two Components of a Volatile Binary Solution

24-7. The Central Thermodynamic Quantity for Nonideal Solutions is the Activity

24-8. Activities Must Be Calculated with Respect to Standard States

24-9. We Can Calculate the Gibbs Energy of Mixing of Binary Solutions in Terms of the Activity Coefficient

Problems

**Chapter 25. Solutions II: Solid-Liquid Solutions**

25-1. We Use a Raoult's Law Standard State for the Solvent and a Henry's Law Standard State for the Solute for Solutionsof Solids Dissolved in Liquids

25-2. The Activity of a Nonvolatile Solute Can Be Obtained from the Vapor Pressure of the Solvent

25-3. Colligative Properties Are Solution Properties That Depend Only Upon the Number Density of Solute Particles

25-4. Osmotic Pressure Can Be Used to Determine the Molecular Masses of Polymers

25-5. Solutions of Electrolytes Are Nonideal at Relatively Low Concentrations

25-6. The Debye-Hukel Theory Gives an Exact Expression of 1n gamma(plus or minus) For Very Dilute Solutions

25-7. The Mean Spherical Approximation Is an Extension of the Debye-Huckel Theory to Higher Concentrations

Problems

**Chapter 26. Chemical Equilibrium **

26-1. Chemical Equilibrium Results When the Gibbs Energy Is a Minimun with Respect to the Extent of Reaction

26-2. An Equilibrium Constant Is a Function of Temperature Only

26-3. Standard Gibbs Energies of Formation Can Be Used to Calculate Equilibrium Constants

26-4. A Plot of the Gibbs Energy of a Reaction Mixture Against the Extent of Reaction Is a Minimum at Equilibrium

26-5. The Ratio of the Reaction Quotient to the Equilibrium Constant Determines the Direction in Which a Reaction Will Proceed

26-6. The Sign of deltar G And Not That of deltar Go Determines the Direction of Reaction Spontaneity

26-7. The Variation of an Equilibrium Constant with Temperature Is Given by the Van't Hoff Equation

26-8. We Can Calculate Equilibrium Constants in Terms of Partition Functions

26-9. Molecular Partition Functions and Related Thermodynamic Data Are Extensively Tabulated

26-10. Equilibrium Constants for Real Gases Are Expressed in Terms of Partial Fugacities

26-11. Thermodynamic Equilibrium Constants Are Expressed in Terms of Activities

26-12. The Use of Activities Makes a Significant Difference in Solubility Calculations Involving Ionic Species

Problems

**Chapter 27. The Kinetic Theory of Gases **

27-1. The Average Translational Kinetic Energy of the Molecules in a Gas Is Directly Proportional to the Kelvin Temperature

27-2. The Distribution of the Components of Molecular Speeds Are Described by a Gaussian Distribution

27-3. The Distribution of Molecular Speeds Is Given by the Maxwell-Boltzmann Distribution

27-4. The Frequency of Collisions that a Gas Makes with a Wall Is Proportional to its Number Density and to the Average Molecular Speed

27-5. The Maxwell-Boltzmann Distribution Has Been Verified Experimentally

27-6. The Mean Free Path Is the Average Distance a Molecule Travels Between Collisions

27-7. The Rate of a Gas-Phase Chemical Reaction Depends Upon the Rate of Collisions in Which the Relative Kinetic Energy Exceeds Some Critical Value

Problems

**Chapter 28. Chemical Kinetics I : Rate Laws **

28-1. The Time Dependence of a Chemical Reaction Is Described by a Rate Law

28-2. Rate Laws Must Be Determined Experimentally

28-3. First-Order Reactions Show an Exponential Decay of Reactant Concentration with Time

28-4. The Rate Laws for Different Reaction Orders Predict Different Behaviors for the Time-Dependent Reactant Concentration

28-5. Reactions Can Also Be Reversible

28-6. The Rate Constants of a Reversible Reaction Can Be Determined Using Relaxation Techniques

28-7. Rate Constants Are Usually Strongly Temperature Dependent

28-8. Transition-State Theory Can Be Used to Estimate Reaction Rate Constants

Problems

**Chapter 29. Chemical Kinetics II : Reaction Mechanisms **

29-1. A Mechanism is a Sequence of Single-Step Chemical Reactions called Elementary Reactions

29-2. The Principle of Detailed Balance States that when a Complex Reaction is at Equilibrium, the Rate of the Forward Process is Equal to the Rate of the Reverse Process for Each and Every Step of the Reaction Mechanism

29-3. When Are Consecutive and Single-Step Reactions Distinguishable?

29-4. The Steady-State Approximation Simplifies Rate Expressions yy Assuming that d[I]/dt=0, where I is a Reaction Intermediate

29-5. The Rate Law for a Complex Reaction Does Not Imply a Unique Mechanism

29-6. The Lindemann Mechanism Explains How Unimolecular Reactions Occur

29-7. Some Reaction Mechanisms Involve Chain Reactions

29-8. A Catalyst Affects the Mechanism and Activation Energy of a Chemical Reaction

29-9. The Michaelis-Menten Mechanism Is a Reaction Mechanism for Enzyme Catalysis

Problems

**Chapter 30. Gas-Phase Reaction Dynamics **

30-1. The Rate of Bimolecular Gas-Phase Reaction Can Be Calculated Using Hard-Sphere Collision Theory and an Energy-Dependent Reaction Cross Section

30-2. A Reaction Cross Section Depends Upon the Impact Parameter

30-3. The Rate Constant for a Gas-Phase Chemical Reaction May Depend on the Orientations of the Colliding Molecules

30-4. The Internal Energy of the Reactants Can Affect the Cross Section of a Reaction

30-5. A Reactive Collision Can Be Described in a Center-of-Mass Coordinate System

30-6. Reactive Collisions Can be Studied Using Crossed Molecular Beam Machines

30-7. The Reaction F(g) +D2 (g) => DF(g) + D(g) Can Produce Vibrationally Excited DF(g) Molecules

30-8. The Velocity and Angular Distribution of the Products of a Reactive Collision Provide a Molecular Picture of the Chemical Reaction

30-9. Not All Gas-Phase Chemical Reactions Are Rebound Reactions

30-10. The Potential-Energy Surface for the Reaction F(g) + D2(g) => DF(g) + D(g) Can Be Calculated Using Quantum Mechanics

Problems

**Chapter 31. Solids and Surface Chemistry **

31-1. The Unit Cell Is the Funamental Building Block of a Crystal

31-2. The Orientation of a Lattice Plane Is Described by its Miller Indices

31-3. The Spacing Between Lattice Planes Can Be Determined from X-Ray Diffraction Measurements

31-4. The Total Scattering Intensity Is Related to the Periodic Structure of the Electron Density in the Crystal

31-5. The Structure Factor and the Electron Density Are Related by a Fourier Transform

31-6. A Gas Molecule Can Physisorb or Chemisorb to a Solid Surface

31-7. Isotherms Are Plots of Surface Coverage as a Function of Gas Pressure at Constant Temperature

31-8. The Langmuir Isotherm Can Be Used to Derive Rate Laws for Surface-Catalyzed Gas-Phase Reactions

31-9. The Structure of a Surface is Different from that of a Bulk Solid

31-10. The Reaction Between H2(g) and N 2(g) to Make NH3 (g) Can Be Surface Catalyzed

Problems

Answers to the Numerical Problems

llustration Credits

Index