University of California, Davis

John D. Simon

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 sigma_{p}sigma_{x}*>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*E*_{v }=*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*^{2}*J(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.*H_{2}^{+}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 H_{2}^{+}Yields a Bonding Orbital and an Antibonding Orbital*9-6.*A Simple Molecular-Orbital Treatment of H_{2}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 BeH_{2}Linear and H_{2}O 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 H_{2}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 C_{3V}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*E*_{j}*(N,V)*Is Proportional to*e*^{-Ej(N,V)/k}_{B}^{T}*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*mk*_{B}T /h^{2})^{3/2}V*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 delta_{r}H 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 q_{rev}, 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 = k_{B}_{ }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 = k*_{B}in*W*is Analogous to the Thermodynamic Formula*dS*= delta*q*_{rev}/*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.*delta_{trs}S = delta_{trs}H / T_{trs}at a Phase Transition*21-4.*The Third Law of Thermodynamics Asserts That C_{P}-> 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.**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 delta_{r}G And Not That of delta_{r }G^{o}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) +D_{2 }(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) + D_{2}(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 Fundamental 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 H_{2}(g) and N_{2}(g) to Make NH_{3 }(g) Can Be Surface Catalyzed- Problems

**Answers to the Numerical Problems****lllustration Credits****Index**