Physical Chemistry كتاب الكيمياء الفيزيائية

كتاب الكيمياء الفيزيائية

Physical Chemistry

David W. Ball (Cleveland State University)

1 Gases and the Zeroth Law of Thermodynamics 1

1.1 Synopsis 1

1.2 System, Surroundings, and State 2

1.3 The Zeroth Law of Thermodynamics 3

1.4 Equations of State 5

1.5 Partial Derivatives and Gas Laws 8

1.6 Nonideal Gases 10

1.7 More on Derivatives 18

1.8 A Few Partial Derivatives Defined 20

1.9 Summary 21

Exercises 22

2 The First Law of Thermodynamics 24

2.1 Synopsis 24

2.2 Work and Heat 24

2.3 Internal Energy and the First Law of Thermodynamics 32

2.4 State Functions 33

2.5 Enthalpy 36

2.6 Changes in State Functions 38

2.7 Joule-Thomson Coefficients 42

2.8 More on Heat Capacities 46

2.9 Phase Changes 50

2.10 Chemical Changes 53

2.11 Changing Temperatures 58

2.12 Biochemical Reactions 60

2.13 Summary 62

Exercises 63

3 The Second and Third Laws of Thermodynamics 66

3.1 Synopsis 66

3.2 Limits of the First Law 66

3.3 The Carnot Cycle and Efficiency 68

3.4 Entropy and the Second Law of Thermodynamics 72

3.5 More on Entropy 75

3.6 Order and the Third Law of Thermodynamics 79

3.7 Entropies of Chemical Reactions 81

3.8 Summary 85

Exercises 86

4 Free Energy and Chemical Potential 89

4.1 Synopsis 89

4.2 Spontaneity Conditions 89

4.3 The Gibbs Free Energy and the Helmholtz Energy 92

4.4 Natural Variable Equations and Partial Derivatives 96

4.5 The Maxwell Relationships 99

4.6 Using Maxwell Relationships 103

4.7 Focusing on G 105

4.8 The Chemical Potential and Other Partial Molar

Quantities 108

4.9 Fugacity 110

4.10 Summary 114

Exercises 115

5 Introduction to Chemical Equilibrium 118

5.1 Synopsis 118

5.2 Equilibrium 119

5.3 Chemical Equilibrium 121

5.4 Solutions and Condensed Phases 129

5.5 Changes in Equilibrium Constants 132

5.6 Amino Acid Equilibria 135

5.7 Summary 136

Exercises 138

6 Equilibria in Single-Component Systems 141

6.1 Synopsis 141

6.2 A Single-Component System 145

6.3 Phase Transitions 145

6.4 The Clapeyron Equation 148

6.5 The Clausius-Clapeyron Equation 152

6.6 Phase Diagrams and the Phase Rule 154

6.7 Natural Variables and Chemical Potential 159

6.8 Summary 162

Exercises 163

7 Equilibria in Multiple-Component Systems 166

7.1 Synopsis 166

7.2 The Gibbs Phase Rule 167

7.3 Two Components: Liquid/Liquid Systems 169

7.4 Nonideal Two-Component Liquid Solutions 179

7.5 Liquid/Gas Systems and Henry’s Law 183

7.6 Liquid/Solid Solutions 185

7.7 Solid/Solid Solutions 188

7.8 Colligative Properties 193

7.9 Summary 201

Exercises 203

8 Electrochemistry and Ionic Solutions 206

8.1 Synopsis 206

8.2 Charges 207

8.3 Energy and Work 210

8.4 Standard Potentials 215

8.5 Nonstandard Potentials and Equilibrium Constants 218

8.6 Ions in Solution 225

8.7 Debye-Hückel Theory of Ionic Solutions 230

8.8 Ionic Transport and Conductance 234

8.9 Summary 237

Exercises 238

9 Pre-Quantum Mechanics 241

9.1 Synopsis 241

9.2 Laws of Motion 242

9.3 Unexplainable Phenomena 248

9.4 Atomic Spectra 248

9.5 Atomic Structure 251

9.6 The Photoelectric Effect 253

9.7 The Nature of Light 253

9.8 Quantum Theory 257

9.9 Bohr’s Theory of the Hydrogen Atom 262

9.10 The de Broglie Equation 267

9.11 Summary: The End of Classical Mechannics 269

Exercises 271

10 Introduction to Quantum Mechanics 273

10.1 Synopsis 273

10.2 The Wavefunction 274

10.3 Observables and Operators 276

10.4 The Uncertainty Principle 279

10.5 The Born Interpretation of the Wavefunction;

Probabilities 281

10.6 Normalization 283

10.7 The Schrödinger Equation 285

10.8 An Analytic Solution: The Particle-in-a-Box 288

10.9 Average Values and Other Properties 293

10.10 Tunneling 296

10.11 The Three-Dimensional Particle-in-a-Box 299

10.12 Degeneracy 303

10.13 Orthogonality 306

10.14 The Time-Dependent Schrödinger Equation 308

10.15 Summary 309

Exercises 311

11 Quantum Mechanics: Model Systems and the

Hydrogen Atom 315

11.1 Synopsis 315

11.2 The Classical Harmonic Oscillator 316

11.3 The Quantum-Mechanical Harmonic Oscillator 318

11.4 The Harmonic Oscillator Wavefunctions 324

11.5 The Reduced Mass 330

11.6 Two-Dimensional Rotations 333

11.7 Three-Dimensional Rotations 341

11.8 Other Observables in Rotating Systems 347

11.9 The Hydrogen Atom: A Central Force Problem 352

11.10 The Hydrogen Atom: The Quantum-Mechanical Solution 353

11.11 The Hydrogen Atom Wavefunctions 358

11.12 Summary 365

Exercises 367

12 Atoms and Molecules 370

12.1 Synopsis 370

12.2 Spin 371

12.3 The Helium Atom 374

12.4 Spin Orbitals and the Pauli Principle 377

12.5 Other Atoms and the Aufbau Principle 382

12.6 Perturbation Theory 386

12.7 Variation Theory 394

12.8 Linear Variation Theory 398

12.9 Comparison of Variation and Perturbation Theories 402

12.10 Simple Molecules and the Born-Oppenheimer

Approximation 403

12.11 Introduction to LCAO-MO Theory 405

12.12 Properties of Molecular Orbitals 409

12.13 Molecular Orbitals of Other Diatomic Molecules 410

12.14 Summary 413

Exercises 416

10.6 Normalization 283

10.7 The Schrödinger Equation 285

10.8 An Analytic Solution: The Particle-in-a-Box 288

10.9 Average Values and Other Properties 293

10.10 Tunneling 296

10.11 The Three-Dimensional Particle-in-a-Box 299

10.12 Degeneracy 303

10.13 Orthogonality 306

10.14 The Time-Dependent Schrödinger Equation 308

10.15 Summary 309

Exercises 311

11 Quantum Mechanics: Model Systems and the

Hydrogen Atom 315

11.1 Synopsis 315

11.2 The Classical Harmonic Oscillator 316

11.3 The Quantum-Mechanical Harmonic Oscillator 318

11.4 The Harmonic Oscillator Wavefunctions 324

11.5 The Reduced Mass 330

11.6 Two-Dimensional Rotations 333

11.7 Three-Dimensional Rotations 341

11.8 Other Observables in Rotating Systems 347

11.9 The Hydrogen Atom: A Central Force Problem 352

11.10 The Hydrogen Atom: The Quantum-Mechanical Solution 353

11.11 The Hydrogen Atom Wavefunctions 358

11.12 Summary 365

Exercises 367

12 Atoms and Molecules 370

12.1 Synopsis 370

12.2 Spin 371

12.3 The Helium Atom 374

12.4 Spin Orbitals and the Pauli Principle 377

12.5 Other Atoms and the Aufbau Principle 382

12.6 Perturbation Theory 386

12.7 Variation Theory 394

12.8 Linear Variation Theory 398

12.9 Comparison of Variation and Perturbation Theories 402

12.10 Simple Molecules and the Born-Oppenheimer

Approximation 403

12.11 Introduction to LCAO-MO Theory 405

12.12 Properties of Molecular Orbitals 409

12.13 Molecular Orbitals of Other Diatomic Molecules 410

12.14 Summary 413

Exercises 416

13 Introduction to Symmetry in Quantum Mechanics 419

13.1 Synopsis 419

13.2 Symmetry Operations and Point Groups 419

13.3 The Mathematical Basis of Groups 423

13.4 Molecules and Symmetry 427

13.5 Character Tables 430

13.6 Wavefunctions and Symmetry 437

13.7 The Great Orthogonality Theorem 438

13.8 Using Symmetry in Integrals 441

13.9 Symmetry-Adapted Linear Combinations 443

13.10 Valence Bond Theory 446

13.11 Hybrid Orbitals 450

13.12 Summary 456

Exercises 457

14 Rotational and Vibrational Spectroscopy 461

14.1 Synopsis 461

14.2 Selection Rules 462

14.3 The Electromagnetic Spectrum 463

14.4 Rotations in Molecules 466

14.5 Selection Rules for Rotational Spectroscopy 471

14.6 Rotational Spectroscopy 473

14.7 Centrifugal Distortions 479

14.8 Vibrations in Molecules 481

14.9 The Normal Modes of Vibration 483

14.10 Quantum-Mechanical Treatment of Vibrations 484

14.11 Selection Rules for Vibrational Spectroscopy 487

14.12 Vibrational Spectroscopy of Diatomic and Linear

Molecules 491

14.13 Symmetry Considerations for Vibrations 496

14.14 Vibrational Spectroscopy of Nonlinear Molecules 498

14.15 Nonallowed and Nonfundamental Vibrational Transitions 503

14.16 Fingerprint Regions 504

14.17 Rotational-Vibrational Spectroscopy 506

14.18 Raman Spectroscopy 511

14.19 Summary 514

Exercises 515

15 Introduction to Electronic Spectroscopy and Structure 519

15.1 Synopsis 519

15.2 Selection Rules 520

15.3 The Hydrogen Atom 520

15.4 Angular Momenta: Orbital and Spin 522

15.5 Multiple Electrons: Term Symbols and Russell-Saunders

Coupling 526

15.6 Electronic Spectra of Diatomic Molecules 534

15.7 Vibrational Structure and the Franck-Condon Principle 539

15.8 Electronic Spectra of Polyatomic Molecules 541

15.9 Electronic Spectra of Electron Systems:

Hückel Approximations 543

15.10 Benzene and Aromaticity 546

15.11 Fluorescence and Phosphorescence 548

15.12 Lasers 550

15.13 Summary 556

Exercises 558

16 Introduction to Magnetic Spectroscopy 560

16.1 Synopsis 560

16.2 Magnetic Fields, Magnetic Dipoles, and Electric Charges 561

16.3 Zeeman Spectroscopy 564

16.4 Electron Spin Resonance 567

16.5 Nuclear Magnetic Resonance 571

16.6 Summary 582

Exercises 584

17 Statistical Thermodynamics: Introduction 586

17.1 Synopsis 586

17.2 Some Statistics Necessities 587

17.3 The Ensemble 590

17.4 The Most Probable Distribution: Maxwell-Boltzmann

Distribution 593

17.5 Thermodynamic Properties from Statistical Thermodynamics 600

17.6 The Partition Function: Monatomic Gases 604

17.7 State Functions in Terms of Partition Functions 608

17.8 Summary 613

Exercises 614

18 More Statistical Thermodynamics 616

18.1 Synopsis 617

18.2 Separating q: Nuclear and Electronic Partition Functions 617

18.3 Molecules: Electronic Partition Functions 621

18.4 Molecules: Vibrations 623

18.5 Diatomic Molecules: Rotations 628

18.6 Polyatomic Molecules: Rotations 634

18.7 The Partition Function of a System 636

18.8 Thermodynamic Properties of Molecules from Q 637

18.9 Equilibria 640

18.10 Crystals 644

18.11 Summary 648

Exercises 649