
Fundamental Concepts of Thermodynamics 


1  (12) 

What Is Thermodynamics and Why Is It Useful? 


1  (1) 

Basic Definitions Needed to Describe Thermodynamic Systems 


2  (2) 


4  (2) 

Equations of State and the Ideal Gas Law 


6  (3) 

A Brief Introduction to Real Gases 


9  (4) 

Heat, Work, Internal Energy, Enthalpy, and the First Law of Thermodynamics 


13  (26) 

The Internal Energy and the First Law of Thermodynamics 


13  (1) 


14  (2) 


16  (3) 


19  (3) 

State Functions and Path Functions 


22  (2) 

Equilibrium, Change, and Reversibility 


24  (1) 

Comparing Work for Reversible and Irreversible Processes 


25  (4) 

Determining ΔU and Introducing Enthalpy, a New State Function 


29  (1) 

Calculating q, w, ΔU, and ΔH for Processes Involving Ideal Gases 


30  (4) 

The Reversible Adiabatic Expansion and Compression of an Ideal Gas 


34  (5) 

The Importance of State Functions: Internal Energy and Enthalpy 


39  (24) 

The Mathematical Properties of State Functions 


39  (5) 

The Dependence of U on V and T 


44  (2) 

Does the Internal Energy Depend More Strongly on V or T? 


46  (4) 

The Variation of Enthalpy with Temperature at Constant Pressure 


50  (2) 

How Are CP and CV Related? 


52  (1) 

The Variation of Enthalpy with Pressure at Constant Temperature 


53  (2) 

The JouleThompson Experiment 


55  (3) 

Liquefying Gases Using an Isenthalpic Expansion 


58  (5) 


63  (16) 

Energy Stored in Chemical Bonds Is Released or Taken Up in Chemical Reactions 


63  (1) 

Internal Energy and Enthalpy Changes Associated with Chemical Reactions 


64  (4) 

Hess's Law Is Based on Enthalpy Being a State Function 


68  (2) 

The Temperature Dependence of Reaction Enthalpies 


70  (2) 

The Experimental Determination of ΔU and ΔH for Chemical Reactions 


72  (3) 

Differential Scanning Calorimetry 


75  (4) 

Entropy and the Second and Third Laws of Thermodynamics 


79  (34) 

The Universe Has a Natural Direction of Change 


79  (1) 

Heat Engines and the Second Law of Thermodynamics 


80  (5) 


85  (1) 

Calculating Changes in Entropy 


86  (4) 

Using Entropy to Calculate the Natural Direction of a Process in an Isolated System 


90  (2) 


92  (1) 

The Change of Entropy in the Surroundings and ΔS total = ΔS + ΔS surroundings 


93  (2) 

Absolute Entropies and the Third Law of Thermodynamics 


95  (4) 

Standard States in Entropy Calculations 


99  (1) 

Entropy Changes in Chemical Reactions 


99  (2) 

Refrigerators, Heat Pumps, and Real Engines 


101  (4) 

(Supplemental) Using the Fact that S Is a State Function to Determine the Dependence of S on V and T 


105  (1) 

(Supplemental) The Dependence of S on T and P 


106  (2) 

(Supplemental) The Thermodynamic Temperature Scale 


108  (5) 


113  (36) 

The Gibbs Energy and the Helmholtz Energy 


113  (4) 

The Differential Forms of U, H, A, and G 


117  (2) 

The Dependence of the Gibbs and Helmholtz Energies on P, V, and T 


119  (3) 

The Gibbs Energy of a Reaction Mixture 


122  (1) 

The Gibbs Energy of a Gas in a Mixture 


123  (1) 

Calculating the Gibbs Energy of Mixing for Ideal Gases 


124  (2) 

Expressing Chemical Equilibrium in an Ideal Gas Mixture in Terms of the μi 


126  (2) 

Calculating ΔG reaction and Introducing the Equilibrium Constant for a Mixture of Ideal Gases 


128  (2) 

Calculating the Equilibrium Partial Pressures in a Mixture of Ideal Gases 


130  (1) 

The Variation of Kp with Temperature 


131  (2) 

Equilibria Involving Ideal Gases and Solid or Liquid Phases 


133  (1) 

Expressing the Equilibrium Constant in Terms of Mole Fraction or Molarity 


134  (1) 

The Dependence of ξeq on T and P 


135  (1) 

(Supplemental) A Case Study: The Synthesis of Ammonia 


136  (5) 

(Supplemental) Expressing U and H and Heat Capacities Solely in Terms of Measurable Quantities 


141  (8) 

The Properties of Real Gases 


149  (18) 

Real Gases and Ideal Gases 


149  (1) 

Equations of State for Real Gases and Their Range of Applicability 


150  (4) 


154  (3) 

The Law of Corresponding States 


157  (3) 

Fugacity and the Equilibrium Constant for Real Gases 


160  (7) 

Phase Diagrams and the Relative Stability of Solids, Liquids, and Gases 


167  (26) 

What Determines the Relative Stability of the Solid, Liquid, and Gas Phases? 


167  (2) 

The PressureTemperature Phas Diagram 


169  (7) 

The PressureVolume and PressureVolumeTemperature Phase Diagrams 


176  (2) 

Providing a Theoretical Basis for the PT Phase Diagram 


178  (1) 

Using the Clapcyron Equation to Calculate Vapor Pressure as a Function of T 


179  (2) 

The Vapor Pressure of a Pure Substance Depends on the Applied Pressure 


181  (1) 


182  (3) 

Chemistry in Supercritical Fluids 


185  (1) 

Liquid Crystals and LCD Displays 


186  (7) 


193  (30) 

Defining the Ideal Solution 


193  (2) 

The Chemical Potential of a Component in the Gas and Solution Phases 


195  (1) 

Applying the Ideal Solution Model to Binary Solutions 


196  (4) 

The TemperatureComposition Diagram and Fractional Distillation 


200  (2) 


202  (2) 


204  (1) 

The Freezing Point Depression and Boiling Point Elevation 


204  (3) 


207  (1) 

Real Solutions Exhibit Deviations from Raoult's Law 


208  (3) 

The Ideal Dilute Solution 


211  (2) 

Activities Are Defined with Respect to Standard States 


213  (3) 

Henry's Law and the Solubility of Gases in a Solvent 


216  (2) 

Chemical Equilibrium in Solutions 


218  (5) 


223  (16) 

The Enthalpy, Entropy, and Gibbs Energy of Ion Formation in Solutions 


223  (3) 

Understanding the Thermodynamics of Ion Formation and Solvation 


226  (2) 

Activities and Activity Coefficients for Electrolyte Solutions 


228  (2) 

Calculating γ± Using the DebyeHuckel Theory 


230  (4) 

Chemical Equilibrium in Electrolyte Solutions 


234  (5) 

Electrochemical Cells, Batteries, and Fuel Cells 


239  (36) 

The Effect of an Electrical Potential on the Chemical Potential of Charged Species 


239  (2) 

Conventions and Standard States in Electrochemistry 


241  (3) 

Measurement of the Reversible Cell Potential 


244  (1) 

Chemical Reactions in Electrochemical Cells and the Nernst Equation 


245  (2) 

Combining Standard Electrode Potentials to Determine the Cell Potential 


247  (2) 

Obtaining Reaction Gibbs Energies and Reaction Entropies from Cell Potentials 


249  (1) 

The Relationship between the Cell EMF and the Equilibrium Constant 


249  (2) 

Determination of E° and Activity Coefficients Using an Electrochemical Cell 


251  (1) 

Cell Nomenclature and Types of Electrochemical Cells 


252  (1) 

The Electrochemical Series 


253  (1) 

Thermodynamics of Batteries and Fuel Cells 


254  (1) 

The Electrochemistry of Commonly Used Batteries 


254  (2) 


256  (3) 

(Supplemental) Electrochemistry at the Atomic Scale 


259  (7) 

(Supplemental) Using Electrochemistry for Nanoscale Machining 


266  (1) 

(Supplemental) Absolute HalfCell Potentials 


267  (8) 

From Classical to Quantum Mechanics 


275  (14) 

Why Study Quantum Mechanics? 


275  (1) 

Quantum Mechanics Arose Out of the Interplay of Experiments and Theory 


276  (1) 


277  (2) 


279  (2) 

Particles Exhibit WaveLike Behavior 


281  (1) 

Diffraction by a Double Slit 


281  (4) 


285  (4) 


289  (22) 

What Determines If a System Needs to Be Described Using Quantum Mechanics? 


289  (5) 

Classical Waves and the Nondispersive Wave Equation 


294  (3) 

Waves Are Conveniently Represented as Complex Functions 


297  (2) 

Quantum Mechanical Waves and the Schrodinger Equation 


299  (1) 

Solving the Schrodinger Equation: Operators, Observables, Eigenfunctions, and Eigenvalues 


300  (2) 

The Eigenfunctions of a Quantum Mechanical Operator Are Orthogonal 


302  (3) 

The Eigenfunctions of a Quantum Mechanical Operator Form a Complete Set 


305  (1) 

Summing Up the New Concepts 


306  (5) 

The Quantum Mechanical Postulates 


311  (8) 

The Physical Meaning Associated with the Wave Function 


311  (1) 

Every Observable Has a Corresponding Operator 


312  (1) 

The Result of an Individual Measurement 


313  (1) 


314  (3) 

The Evolution in Time of a Quantum Mechanical System 


317  (2) 

Using Quantum Mechanics on Simple Systems 


319  (18) 


319  (1) 

The Particle in a OneDimensional Box 


320  (5) 

Two and ThreeDimensional Boxes 


325  (2) 

Using the Postulates to Understand the Particle in the Box and Vice Versa 


327  (10) 

The Particle in the Box and the Real World 


337  (18) 

The Particle in the Finite Depth Box 


337  (1) 

Differences in Overlap between Core and Valence Electrons 


338  (1) 

Pi Electrons in Conjugated Molecules Can Be Treated as Moving Freely in a Box 


339  (1) 

Why Does Sodium Conduct Electricity and Why Is Diamond an Insulator? 


340  (1) 

Tunneling through a Barrier 


341  (1) 

The Scanning Tunneling Microscope 


342  (4) 

Tunneling in Chemical Reactions 


346  (1) 

(Supplemental) Quantum Wells and Quantum Dots 


347  (8) 

Commuting and Noncommuting Operators and the Surprising Consequences of Entanglement 


355  (22) 


355  (2) 

The SternGerlach Experiment 


357  (3) 

The Heisenberg Uncertainty Principle 


360  (4) 

(Supplemental) The Heisenberg Uncertainty Principle Expressed in Terms of Standard Deviations 


364  (2) 

(Supplemental) A Thought Experiment Using a Particle in a ThreeDimensional Box 


366  (2) 

(Supplemental) Entangled States, Teleportation, and Quantum Computers 


368  (9) 

A Quantum Mechanical Model for the Vibration and Rotation of Molecules 


377  (26) 

Solving the Schrodinger Equation for the Quantum Mechanical Harmonic Oscillator 


377  (5) 

Solving the Schrodinger Equation for Rotation in Two Dimensions 


382  (3) 

Solving the Schrodinger Equation for Rotation in Three Dimensions 


385  (3) 

The Quantization of Angular Momentum 


388  (2) 

The Spherical Harmonic Functions 


390  (2) 

(Optional Review) The Classical Harmonic Oscillator 


392  (4) 

(Optional Review) Angular Motion and the Classical Rigid Rotor 


396  (2) 

(Supplemental) Spatial Quantization 


398  (5) 

The Vibrational and Rotational Spectroscopy of Diatomic Molecules 


403  (32) 

An Introduction to Spectroscopy 


403  (3) 

Absorption, Spontaneous Emission, and Stimulated Emission 


406  (1) 

An Introduction to Vibrational Spectroscopy 


407  (3) 

The Origin of Selection Rules 


410  (2) 

Infrared Absorption Spectroscopy 


412  (4) 


416  (5) 

(Supplemental) Fourier Transform Infrared Spectroscopy 


421  (3) 

(Supplemental) Raman Spectroscopy 


424  (2) 

(Supplemental) How Does the Transition Rate between States Depend on Frequency? 


426  (9) 


435  (18) 

Formulating the Schrodinger Equation 


435  (1) 

Solving the Schrodinger Equation for the Hydrogen Atom 


436  (1) 

Eigenvalues and Eigenfunctions for the Total Energy 


437  (6) 

The Hydrogen Atom Orbitals 


443  (2) 

The Radial Probability Distribution Function 


445  (4) 

The Validity of the Shell Model of an Atom 


449  (4) 


453  (34) 

Helium: The Smallest ManyElectron Atom 


453  (2) 

Introducing Electron Spin 


455  (1) 

Wave Functions Must Reflect the Indistinguishability of Electrons 


456  (4) 

Using the Variational Method to Solve the Schrodinger Equation 


460  (1) 

The HartreeFock SelfConsistent Field Method 


461  (5) 

Understanding Trends in the Periodic Table from HartreeFock Calculations 


466  (3) 

Good Quantum Numbers, Terms, Levels, and States 


469  (2) 

The Energy of a Configuration Depends on Both Orbital and Spin Angular Momentum 


471  (7) 

SpinOrbit Coupling Breaks Up a Term into Levels 


478  (1) 

(Supplemental) Configurations with Paired and Unpaired Electron Spins Differ in Energy 


479  (8) 

Examples of Spectroscopy Involving Atoms 


487  (18) 

The Essentials of Atomic Spectroscopy 


487  (3) 

Analytical Techniques Based on Atomic Spectroscopy 


490  (3) 


493  (1) 


494  (4) 


498  (1) 

Auger Electron and XRay Photoelectron Spectroscopies 


498  (4) 

Selective Chemistry of Excited States: O(3P) and O(1D) 


502  (3) 

Chemical Bonding in H2+ and H2 


505  

Quantum Mechanics and the Chemical Bond 


505  (1) 

The Simplest OneElectron Molecule: H2+ 


505  (1) 

The Molecular Wave Function for GroundState H2+ 


506  (2) 

The Energy Corresponding to the Molecular Wave Functions ψg and ψu 


508  (4) 

A Closer Look at the Molecular Wave Functions ψg and ψu 


512  (2) 

The H2 Molecule: Molecular Orbital and Valence Bond Models 


514  (3) 

Comparing the Valence Bond and Molecular Orbital Models of the Chemical Bond 


517  

Chemical Bonding in Diatomic Molecules 


247  (298) 

Solving the Schrodinger Equation for ManyElectron Molecules 


521  (1) 

Expressing Molecular Orbitals as a Linear Combination of Atomic Orbitals 


522  (4) 

The Molecular Orbital Energy Diagram 


526  (2) 

Molecular Orbitals for Homonuclear Diatomic Molecules 


528  (4) 

The Electronic Structure of ManyElectron Molecules 


532  (3) 

Bond Order, Bond Energy, and Bond Length 


535  (2) 

Heteronuclear Diatomic Molecules 


537  (1) 

(Supplemental) The Molecular Electrostatic Potential 


538  (7) 

Molecular Structure and Energy Levels for Polyatomic Molecules 


545  (30) 

Lewis Structures and the VSEPR Model 


545  (3) 

Describing Localized Bonds Using Hybridization for Methane, Ethene, and Ethyne 


548  (3) 

Constructing Hybrid Orbitals for Nonequivalent Ligands 


551  (5) 

Using Hybridization to Describe Chemical Bonding 


556  (1) 

Predicting Molecular Structure Using Molecular Orbital Theory 


557  (4) 

How Different Are Localized and Delocalized Bonding Models? 


561  (2) 

Qualitative Molecular Orbital Theory for Conjugated and Aromatic Molecules: The Huckel Model 


563  (7) 


570  (1) 

Making Semiconductors Conductive at Room Temperature 


571  (4) 


575  (22) 

The Energy of Electronic Transitions 


575  (1) 


576  (2) 

Transitions Between Electronic States of Diatomic Molecules 


578  (2) 

The Vibrational Fine Structure of Electronic Transitions in Diatomic Molecules 


580  (2) 

UVVisible Light Absorption in Polyatomic Molecules 


582  (3) 

Transitions among the Ground and Excited States 


585  (1) 

SingletSinglet Transitions: Absorption and Fluorescence 


585  (2) 

Intersystem Crossing and Phosphorescence 


587  (1) 

Fluorescence Spectroscopy and Analytical Chemistry 


588  (2) 

Ultraviolet Photoelectron Spectroscopy 


590  (3) 

(Supplemental) Assigning + and  to Σ Terms of Diatomic Molecules 


593  (4) 


597  (60) 


The Promise of Computational Chemistry 


597  (1) 

Potential Energy Surfaces 


598  (4) 

HartreeFock Molecular Orbital Theory: A Direct Descendant of the Schrodinger Equation 


602  (2) 

Properties of Limiting HartreeFock Models 


604  (5) 

Theoretical Models and Theoretical Model Chemistry 


609  (1) 

Moving Beyond HartreeFock Theory 


610  (6) 


616  (2) 

Selection of a Theoretical Model 


618  (15) 


633  (9) 


642  (15) 


657  (30) 

Symmetry Elements, Symmetry Operations, and Point Groups 


657  (2) 

Assigning Molecules to Point Groups 


659  (2) 

The H2O Molecule and the C2v Point Group 


661  (5) 

Representations of Symmetry Operators, Bases for Representations, and the Character Table 


666  (3) 

The Dimension of a Representation 


669  (4) 

Using the C2v Representations to Construct Molecular Orbitals for H2O 


673  (2) 

The Symmetries of the Normal Modes of Vibration of Molecules 


675  (5) 

Selection Rules and Infrared versus Raman Activity 


680  (1) 

(Supplemental) Using the Projection Operator Method to Generate MOs That Are Bases for Irreducible Representations 


681  (6) 

Nuclear Magnetic Resonance Spectroscopy 


687  (34) 

Intrinsic Nuclear Angular Momentum and Magnetic Moment 


687  (1) 

The Energy of Nuclei of Nonzero Nuclear Spin in a Magnetic Field 


688  (3) 

The Chemical Shift for an Isolated Atom 


691  (1) 

The Chemical Shift for an Atom Embedded in a Molecule 


692  (1) 

Electronegativity of Neighboring Groups and Chemical Shifts 


693  (1) 

Magnetic Fields of Neighboring Groups and Chemical Shifts 


694  (1) 

Multiplet Splitting of NMR Peaks Arises through SpinSpin Coupling 


695  (5) 

Multiplet Splitting When More Than Two Spins Interact 


700  (3) 

Peak Widths in NMR Spectroscopy 


703  (1) 


704  (1) 


705  (1) 

(Supplemental) The NMR Experiment in the Laboratory and Rotating Frames 


706  (2) 

(Supplemental) Fourier Transform NMR Spectroscopy 


708  (4) 

(Supplemental) TwoDimensional NMR 


712  (9) 


721  (24) 


721  (1) 


722  (8) 


730  (1) 

Probability Distribution Functions 


731  (3) 

Probability Distributions Involving Discrete and Continuous Variables 


734  (2) 

Characterizing Distribution Functions 


736  (9) 

The Boltzmann Distribution 


745  (22) 

Microstates and Configurations 


745  (6) 

Derivation of the Boltzmann Distribution 


751  (5) 

Dominance of the Boltzmann Distribution 


756  (2) 

Physical Meaning of the Boltzmann Distribution Law 


758  (2) 


760  (7) 

Ensemble and Molecular Partition Functions 


767  (32) 


767  (2) 

Relating Q to q for an Ideal Gas 


769  (2) 


771  (1) 

Translational Partition Function 


772  (2) 

Rotational Partition Function: Diatomics 


774  (8) 

Rotational Partition Function: Polyatomics 


782  (2) 

Vibrational Partition Function 


784  (6) 

The Equipartition Theorem 


790  (1) 

Electronic Partition Function 


791  (4) 


795  (4) 

Statistical Thermodynamics 


799  (32) 


799  (4) 

Energy and Molecular Energetic Degrees of Freedom 


803  (5) 


808  (4) 


812  (5) 


817  (1) 

Other Thermodynamic Functions 


818  (4) 


822  (9) 


831  (22) 

Kinetic Theory of Gas Motion and Pressure 


831  (3) 

Velocity Distribution in One Dimension 


834  (4) 

The Maxwell Distribution of Molecular Speeds 


838  (2) 

Comparative Values for Speed Distribution: νave, νmp, and νrms 


840  (2) 


842  (3) 


845  (3) 


848  (5) 


853  (34) 


853  (2) 

Mass Transport: Diffusion 


855  (3) 

The Time Evolution of a Concentration Gradient 


858  (2) 

(Supplemental) Statistical View of Diffusion 


860  (2) 


862  (4) 


866  (3) 


869  (2) 

Diffusion in Liquids and Viscosity of Liquids 


871  (2) 

(Supplemental) Sedimentation and Centrifugation 


873  (3) 


876  (11) 

Elementary Chemical Kinetics 


887  (44) 


887  (1) 


888  (2) 


890  (6) 


896  (1) 

Integrated Rate Law Expressions 


897  (5) 

(Supplemental) Numerical Approaches 


902  (1) 

Sequential FirstOrder Reactions 


903  (5) 


908  (2) 

Temperature Dependence of Rate Constants 


910  (2) 

Reversible Reactions and Equilibrium 


912  (4) 

(Supplemental) PerturbationRelaxation Methods 


916  (2) 

(Supplemental) The Autoionization of Water: A TJump Example 


918  (1) 

Potential Energy Surfaces 


919  (2) 


921  (10) 

Complex Reaction Mechanisms 


931  (40) 

Reaction Mechanisms and Rate Laws 


931  (2) 

The Preequilibrium Approximation 


933  (2) 


935  (2) 


937  (12) 


949  (3) 

RadicalChain Polymerization 


952  (1) 


953  (2) 


955  (16) 
Appendix A Math Supplement 

971  (22) 
Appendix B Data Tables 

993  (22) 
Appendix C Point Group Character Tables 

1015  (8) 
Appendix D Answers to Selected EndofChapter Problems 

1023  (16) 
Index 

1039  