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Edition: 97

Copyright: 1997

Publisher: University Science Books

Published: 1997

International: No

Copyright: 1997

Publisher: University Science Books

Published: 1997

International: No

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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

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