Rent 9780805338423 | Physical Chemistry | Engel, Thomas; Reid, Philip @knetbooks.com

Summary Table of Contents

Physical Chemistry is a groundbreaking new 4-color text that explains core topics in depth with a focus on basic principles, applications, and modern research. the authors hone in on key concepts and cover them thoroughly and in detail - as opposed to the general, encyclopedic approach competing textbooks take. Excessive math formalism is avoided to keep students focused on the most important concepts and to provide greater clarity. Applications woven throughout each chapter demonstrate to students how chemical theories are used to solve real-world chemical problems in biology, environmental science, and material science. Extensive coverage of modern research and new developments in the field get students excited about this dynamic branch of science. The text has been designed in such a way that it can be used for either "Quantum first" or "Thermo first" courses. the combined text is arranged for a traditional "Thermo first" course; the split texts are organized to facilitate "Quantum first" courses. The online Chemistry Place for Physical Chemistry features interactive problems and simulations that reinforce and build upon material included in the book.

Fundamental Concepts of Thermodynamics

(12)

What Is Thermodynamics and Why Is It Useful?

(1)

Basic Definitions Needed ... MORE

(2)

Thermometry

(2)

Equations of State and the Ideal Gas Law

(3)

A Brief Introduction to Real Gases

(4)

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

(26)

The Internal Energy and the First Law of Thermodynamics

(1)

Work

(2)

Heat

(3)

Heat Capacity

(3)

State Functions and Path Functions

(2)

Equilibrium, Change, and Reversibility

(1)

Comparing Work for Reversible and Irreversible Processes

(4)

Determining ΔU and Introducing Enthalpy, a New State Function

(1)

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

(4)

The Reversible Adiabatic Expansion and Compression of an Ideal Gas

(5)

The Importance of State Functions: Internal Energy and Enthalpy

(24)

The Mathematical Properties of State Functions

(5)

The Dependence of U on V and T

(2)

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

(4)

The Variation of Enthalpy with Temperature at Constant Pressure

(2)

How Are CP and CV Related?

(1)

The Variation of Enthalpy with Pressure at Constant Temperature

(2)

The Joule-Thompson Experiment

(3)

Liquefying Gases Using an Isenthalpic Expansion

(5)

Thermochemistry

(16)

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

(1)

Internal Energy and Enthalpy Changes Associated with Chemical Reactions

(4)

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

(2)

The Temperature Dependence of Reaction Enthalpies

(2)

The Experimental Determination of ΔU and ΔH for Chemical Reactions

(3)

Differential Scanning Calorimetry

(4)

Entropy and the Second and Third Laws of Thermodynamics

(34)

The Universe Has a Natural Direction of Change

(1)

Heat Engines and the Second Law of Thermodynamics

(5)

Introducing Entropy

(1)

Calculating Changes in Entropy

(4)

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

(2)

The Clausius Inequality

(1)

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

(2)

Absolute Entropies and the Third Law of Thermodynamics

(4)

Standard States in Entropy Calculations

(1)

Entropy Changes in Chemical Reactions

(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)

Chemical Equilibrium

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)

The Compression Factor

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 Pressure-Temperature Phas Diagram

169

(7)

The Pressure-Volume and Pressure-Volume-Temperature Phase Diagrams

176

(2)

Providing a Theoretical Basis for the P--T 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)

Surface Tension

182

(3)

Chemistry in Supercritical Fluids

185

(1)

Liquid Crystals and LCD Displays

186

(7)

Ideal and Real Solutions

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 Temperature-Composition Diagram and Fractional Distillation

200

(2)

The Gibbs-Duhem Equation

202

(2)

Colligative Properties

204

(1)

The Freezing Point Depression and Boiling Point Elevation

204

(3)

The Osmotic Pressure

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)

Electrolyte Solutions

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 Debye-Huckel 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)

Fuel Cells

256

(3)

(Supplemental) Electrochemistry at the Atomic Scale

259

(7)

(Supplemental) Using Electrochemistry for Nanoscale Machining

266

(1)

(Supplemental) Absolute Half-Cell 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)

Blackbody Radiation

277

(2)

The Photoelectric Effect

279

(2)

Particles Exhibit Wave-Like Behavior

281

(1)

Diffraction by a Double Slit

281

(4)

Atomic Spectra

285

(4)

The Schrodinger Equation

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)

The Expectation Value

314

(3)

The Evolution in Time of a Quantum Mechanical System

317

(2)

Using Quantum Mechanics on Simple Systems

319

(18)

The Free Particle

319

(1)

The Particle in a One-Dimensional Box

320

(5)

Two- and Three-Dimensional 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)

Commutation Relations

355

(2)

The Stern-Gerlach 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 Three-Dimensional 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)

Rotational Spectroscopy

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)

The Hydrogen Atom

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)

Many-Electron Atoms

453

(34)

Helium: The Smallest Many-Electron 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 Hartree-Fock Self-Consistent Field Method

461

(5)

Understanding Trends in the Periodic Table from Hartree-Fock 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)

Spin-Orbit 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)

The Doppler Effect

493

(1)

The Helium-Neon Laser

494

(4)

Laser Isotope Separation

498

(1)

Auger Electron and X-Ray 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 One-Electron Molecule: H2+

505

(1)

The Molecular Wave Function for Ground-State 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 Many-Electron 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 Many-Electron 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)

From Molecules to Solids

570

(1)

Making Semiconductors Conductive at Room Temperature

571

(4)

Electronic Spectroscopy

575

(22)

The Energy of Electronic Transitions

575

(1)

Molecular Term Symbols

576

(2)

Transitions Between Electronic States of Diatomic Molecules

578

(2)

The Vibrational Fine Structure of Electronic Transitions in Diatomic Molecules

580

(2)

UV-Visible Light Absorption in Polyatomic Molecules

582

(3)

Transitions among the Ground and Excited States

585

(1)

Singlet-Singlet 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)

Computational Chemistry

597

(60)

Warren Hehre

The Promise of Computational Chemistry

597

(1)

Potential Energy Surfaces

598

(4)

Hartree-Fock Molecular Orbital Theory: A Direct Descendant of the Schrodinger Equation

602

(2)

Properties of Limiting Hartree-Fock Models

604

(5)

Theoretical Models and Theoretical Model Chemistry

609

(1)

Moving Beyond Hartree-Fock Theory

610

(6)

Gaussian Basis Sets

616

(2)

Selection of a Theoretical Model

618

(15)

Graphical Models

633

(9)

Conclusion

642

(15)

Molecular Symmetry

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 Spin-Spin Coupling

695

(5)

Multiplet Splitting When More Than Two Spins Interact

700

(3)

Peak Widths in NMR Spectroscopy

703

(1)

Solid-State NMR

704

(1)

NMR Imaging

705

(1)

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

706

(2)

(Supplemental) Fourier Transform NMR Spectroscopy

708

(4)

(Supplemental) Two-Dimensional NMR

712

(9)

Probability

721

(24)

Why Probability?

721

(1)

Basic Probability Theory

722

(8)

Stirling's Approximation

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)

The Definition of β

760

(7)

Ensemble and Molecular Partition Functions

767

(32)

The Canonical Ensemble

767

(2)

Relating Q to q for an Ideal Gas

769

(2)

Molecular Energy Levels

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)

Review

795

(4)

Statistical Thermodynamics

799

(32)

Energy

799

(4)

Energy and Molecular Energetic Degrees of Freedom

803

(5)

Heat Capacity

808

(4)

Entropy

812

(5)

Residual Entropy

817

(1)

Other Thermodynamic Functions

818

(4)

Chemical Equilibrium

822

(9)

Kinetic Theory of Gases

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)

Gas Effusion

842

(3)

Molecular Collisions

845

(3)

The Mean Free Path

848

(5)

Transport Phenomena

853

(34)

What Is Transport?

853

(2)

Mass Transport: Diffusion

855

(3)

The Time Evolution of a Concentration Gradient

858

(2)

(Supplemental) Statistical View of Diffusion

860

(2)

Thermal Conduction

862

(4)

Viscosity of Gases

866

(3)

Measuring Viscosity

869

(2)

Diffusion in Liquids and Viscosity of Liquids

871

(2)

(Supplemental) Sedimentation and Centrifugation

873

(3)

Ionic Conduction

876

(11)

Elementary Chemical Kinetics

887

(44)

Introduction to Kinetics

887

(1)

Reaction Rates

888

(2)

Rate Laws

890

(6)

Reaction Mechanisms

896

(1)

Integrated Rate Law Expressions

897

(5)

(Supplemental) Numerical Approaches

902

(1)

Sequential First-Order Reactions

903

(5)

Parallel Reactions

908

(2)

Temperature Dependence of Rate Constants

910

(2)

Reversible Reactions and Equilibrium

912

(4)

(Supplemental) Perturbation-Relaxation Methods

916

(2)

(Supplemental) The Autoionization of Water: A T-Jump Example

918

(1)

Potential Energy Surfaces

919

(2)

Activated Complex Theory

921

(10)

Complex Reaction Mechanisms

931

(40)

Reaction Mechanisms and Rate Laws

931

(2)

The Preequilibrium Approximation

933

(2)

The Lindemann Mechanisms

935

(2)

Catalysis

937

(12)

Radical-Chain Reactions

949

(3)

Radical-Chain Polymerization

952

(1)

Explosions

953

(2)

Photochemistry

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 End-of-Chapter Problems

1023

(16)

Index

1039

RENT TEXTBOOKS

Physical Chemistry

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