Physical Chemistry Thermodynamics, Structure, and Change

Physical Chemistry Thermodynamics, Structure, and Change
Peter Atkins & Julio de Paula
Published in: W. H. Freeman and Company
Release Year: 2014
ISBN: 978-1-4292-9019-7
Pages: 1035
Edition: Tenth Edition
File Size: 46 MB
File Type: pdf
Language: English

Description of Physical Chemistry Thermodynamics, Structure, and Change

This new edition of Physical Chemistry Thermodynamics, Structure, and Change is the product of a thorough revision of content and its presentation. Our goal is to make the book Physical Chemistry Thermodynamics, Structure, and Change even more accessible to students and useful to instructors by enhancing its flexibility. We hope that both categories of the user will perceive and enjoy the renewed vitality of the text and the presentation of this demanding but engaging subject. 

The text is still divided into three parts, but each chapter is now presented as a series of short and more readily mastered Topics. For instance, Instead, students and instructors can match the choice of Topics to their learning objectives. We have been very careful not to presuppose or impose a particular sequence, except where it is demanded by common sense.

Content of Physical Chemistry Thermodynamics, Structure, and Change

Foundations 1
A Matter 2
A.1 Atoms 2
(a) The nuclear model 2
(b) The periodic table 2
(c) Ions 3
A.2 Molecules 3
(a) Lewis structures 3
(b) VSEPR theory 4
(c) Polar bonds 4
A.3 Bulk matter 5
(a) Properties of bulk matter 5
(b) The perfect gas equation 6
Checklist of concepts 7
Checklist of equations 8
B Energy 9
B.1 Force 9
(a) Momentum 9
(b) Newton’s second law of motion 10
B.2 Energy: a first look 11
(a) Work 11
(b) The definition of energy 11
(c) The Coulomb potential energy 12
(d) Thermodynamics 14
B.3 The relation between molecular and bulk properties 15
(a) The Boltzmann distribution 15
(b) Equipartition 17
Checklist of concepts 17
Checklist of equations 18
C Waves 19
C.1 Harmonic waves 19
C.2 The electromagnetic field 20
Checklist of concepts 22
Checklist of equations 22
Discussion questions and exercises 23

PART 1 Thermodynamics 27
CHAPTER 1 The properties of gases 29

Topic 1A The perfect gas 30
1A.1 Variables of state 30
(a) Pressure 30
(b) Temperature 31
1A.2 Equations of state 32
(a) The empirical basis 32
(b) Mixtures of gases 35
Checklist of concepts 36
Checklist of equations 36

Topic 1B The kinetic model 37
1B.1 The model 37
(a) Pressure and molecular speeds 37
(b) The Maxwell–Boltzmann distribution of speeds 39
(c) Mean values 40
1B.2 Collisions 42
(a) The collision frequency 42
(b) The mean free path 43
Checklist of concepts 44
Checklist of equations 44

Topic 1C Real gases 45
1C.1 Deviations from perfect behavior 45
(a) The compression factor 46
(b) Virial coefficients 47
(c) Critical constants 48
1C.2 The van der Waals equation 48
(a) Formulation of equation 48
(b) The features of the equation 50
(c) The principle of corresponding states 52
Checklist of concepts 53
Checklist of equations 53
Discussion questions, exercises, and problems 54
Mathematical background 1 Differentiation and
integration 59
CHAPTER 2 The First Law 63

Topic 2A Internal energy 64
2A.1 Work, heat, and energy 65
(a) Operational definitions 65
(b) The molecular interpretation of heat and work 66
2A.2 The definition of internal energy 66
(a) Molecular interpretation of internal energy 67
(b) The formulation of the First Law 67
2A.3 Expansion work 68
(a) The general expression for work 68
(b) Expansion against constant pressure 69
(c) Reversible expansion 70
(d) Isothermal reversible expansion 70
2A.4 Heat transactions 71
(a) Calorimetry 71
(b) Heat capacity 72
Checklist of concepts 74
Checklist of equations 74

Topic 2B Enthalpy 75
2B.1 The definition of enthalpy 75
(a) Enthalpy change and heat transfer 75
(b) Calorimetry 76
2B.2 The variation of enthalpy with temperature 77
(a) Heat capacity at constant pressure 77
(b) The relation between heat capacities 79
Checklist of concepts 79
Checklist of equations 79

Topic 2C Thermochemistry 80
2C.1 Standard enthalpy changes 80
(a) Enthalpies of physical change 81
(b) Enthalpies of chemical change 82
(c) Hess’s law 83
2C.2 Standard enthalpies of formation 84
(a) The reaction enthalpy in terms of enthalpies of formation 85
(b) Enthalpies of formation and molecular modeling 85
2C.3 The temperature dependence of reaction enthalpies 86
2C.4 Experimental techniques 87
(a) Differential scanning calorimetry 87
(b) Isothermal titration calorimetry 88
Checklist of concepts 88
Checklist of equations 89

Topic 2D State functions and exact differentials 90
2D.1 Exact and inexact differentials 90
2D.2 Changes in internal energy 91
(a) General considerations 91
(b) Changes in internal energy at constant pressure 93
2D.3 The Joule–Thomson effect 95
(a) Observation of the Joule–Thomson effect 95
(b) The molecular interpretation of the Joule–Thomson effect 98
Checklist of concepts 98
Checklist of equations 99

Topic 2E Adiabatic changes 100
2E.1 The change in temperature 100
2E.2 The change in pressure 101
Checklist of concepts 102
Checklist of equations 102
Discussion questions, exercises, and problems 103
Mathematical background 2 Multivariate calculus 109
CHAPTER 3 The Second and Third Laws 112

Topic 3A Entropy 113
3A.1 The Second Law 113
3A.2 The definition of entropy 115
(a) The thermodynamic definition of entropy 115
(b) The statistical definition of entropy 116
3A.3 The entropy as a state function 117
(a) The Carnot cycle 118
(b) The thermodynamic temperature of 120
(c) The Clausius inequality 120
3A.4 Entropy changes accompanying specific processes 121
(a) Expansion of 121
(b) Phase transitions 122
(c) Heating 123
(d) Composite processes 124
Checklist of concepts 124
Checklist of equations 125

Topic 3B The measurement of entropy 126
3B.1 The calorimetric measurement of entropy 126
3B.2 The Third Law 127
(a) The Nernst heat theorem 127
(b) Third-Law entropies 129
Checklist of concepts 130
Checklist of equations 130

Topic 3C Concentrating on the system 131
3C.1 The Helmholtz and Gibbs energies 131
(a) Criteria of spontaneity 131
(b) Some remarks on the Helmholtz energy 133
(c) Maximum work 133
(d) Some remarks on the Gibbs energy 134
(e) Maximum non-expansion work 135
3C.2 Standard molar Gibbs energies 136
(a) Gibbs energies of formation 136
(b) The Born equation 137
Checklist of concepts 138
Checklist of equations 138

Topic 3D Combining the First and Second Laws 140
3D.1 Properties of the internal energy 140
(a) The Maxwell relations 141
(b) The variation of internal energy with volume 141
3D.2 Properties of the Gibbs energy 142
(a) General considerations 142
(b) The variation of the Gibbs energy with temperature 144
(c) The variation of the Gibbs energy with pressure 144
(d) The fugacity 146
Checklist of concepts 148
Checklist of equations 148
Discussion questions, exercises, and problems 149
CHAPTER 4 Physical transformations of
pure substances 154

Topic 4A Phase diagrams of pure substances 155
4A.1 The stabilities of phases 155
(a) The number of phases 155
(b) Phase transitions 156
(c) Thermodynamic criteria of phase stability 156
4A.2 Phase boundaries 157
(a) Characteristic properties related to phase transitions 157
(b) The phase rule 159
4A.3 Three representative phase diagrams 160
(a) Carbon dioxide 160
(b) Water 161
(c) Helium 162
Checklist of concepts 162
Checklist of equations 163

Topic 4B Thermodynamic aspects of phase transitions 164
4B.1 The dependence of stability on the conditions 164
(a) The temperature dependence of phase stability 165
(b) The response of melting to applied pressure 165
(c) The vapor pressure of a liquid subjected to pressure 166
4B.2 The location of phase boundaries 167
(a) The slopes of the phase boundaries 167
(b) The solid–liquid boundary 168
(c) The liquid-vapor boundary 169
(d) The solid–vapor boundary 170
4B.3 The Ehrenfest classification of phase transitions 171
(a) The thermodynamic basis 171
(b) Molecular interpretation 172
Checklist of concepts 173
Checklist of equations 173
Discussion questions, exercises, and problems 174
CHAPTER 5 Simple mixtures 178

Topic 5A The thermodynamic description of mixtures 180
5A.1 Partial molar quantities 180
(a) Partial molar volume 181
(b) Partial molar Gibbs energies 182
(c) The wider significance of the chemical potential 183
(d) The Gibbs–Duhem equation 183
5A.2 The thermodynamics of mixing 184
(a) The Gibbs energy of mixing of perfect gases 185
(b) Other thermodynamic mixing functions 186
5A.3 The chemical potentials of liquids 187
(a) Ideal solutions 187
(b) Ideal–dilute solutions 188
Checklist of concepts 190
Checklist of equations 190

Topic 5B The properties of solutions 192
5B.1 Liquid mixtures 192
(a) Ideal solutions 192
(b) Excess functions and regular solutions 193
5B.2 Colligative properties 195
(a) The common features of colligative properties 195
(b) The elevation of boiling point 196
(c) The depression of freezing point 197
(d) Solubility 198
(e) Osmosis 199
Checklist of concepts 201
Checklist of equations 201

Topic 5C Phase diagrams of binary systems 202
5C.1 Vapour pressure diagrams 202
(a) The composition of the vapor 202
(b) The interpretation of the diagrams 203
(c) The lever rule 205
5C.2 Temperature–composition diagrams 206
(a) The distillation of mixtures 206
(b) Azeotropes 207
(c) Immiscible liquids 208
5C.3 Liquid-liquid phase diagrams 208
(a) Phase separation 208
(b) Critical solution temperatures 209
(c) The distillation of partially miscible liquids 211
5C.4 Liquid–solid-phase diagrams 212
(a) Eutectics 212
(b) Reacting systems 214
(c) Incongruent melting 214
Checklist of concepts 215
Checklist of equations 215

Topic 5D Phase diagrams of ternary systems 216
5D.1 Triangular phase diagrams 216
5D.2 Ternary systems 217
(a) Partially miscible liquids 217
(b) Ternary solids 218
Checklist of concepts 219

Topic 5E Activities 220
5E.1 The solvent activity 220
5E.2 The solute activity 221
(a) Ideal–dilute solutions 221
(b) Real solutes 221
(c) Activities in terms of molalities 222
(d) The biological standard state 222
5E.3 The activities of regular solutions 223
Checklist of concepts 224
Checklist of equations 225

Topic 5F The activities of ions 226
5F.1 Mean activity coefficients 226
(a) The Debye–Hückel limiting law 227
(b) Extensions of the limiting law 228
5F.2 The Debye–Hückel theory 229
(a) The work of charging 229
(b) The potential due to the charge distribution 229
(c) The activity coefficient 230
Checklist of concepts 232
Checklist of equations 232
Discussion questions, exercises, and problems 233
CHAPTER 6 Chemical equilibrium 244

Topic 6A The equilibrium constant 245
6A.1 The Gibbs energy minimum 245
(a) The reaction Gibbs energy 245
(b) Exergonic and endergonic reactions 246
6A.2 The description of equilibrium 247
(a) Perfect gas equilibria 247
(b) The general case of a reaction 248
(c) The relation between equilibrium constants 251
(d) Molecular interpretation of the equilibrium constant 251
Checklist of concepts 252
Checklist of equations 252

Topic 6B The response of equilibria to the conditions 254
6B.1 The response to pressure 254
6B.2 The response to temperature 255
(a) The van ’t Hoff equation 256
(b) The value of K at different temperatures 257
Checklist of concepts 258
Checklist of equations 258

Topic 6C Electrochemical cells 259
6C.1 Half-reactions and electrodes 259
6C.2 Varieties of cells 260
(a) Liquid junction potentials 261
(b) Notation 261
6C.3 The cell potential 261
(a) The Nernst equation 262
(b) Cells at equilibrium 264
6C.4 The determination of thermodynamic functions 264
Checklist of concepts 265
Checklist of equations 266

Topic 6D Electrode potentials 267
6D.1 Standard potentials 267
(a) The measurement procedure 268
(b) Combining measured values 269
6D.2 Applications of standard potentials 269
(a) The electrochemical series 269
(b) The determination of activity coefficients 270
(c) The determination of equilibrium constants 270
Checklist of concepts 271
Checklist of equations 271
Discussion questions, exercises, and problems 272

PART 2 Structure 279
CHAPTER 7 Introduction to quantum theory 281

Topic 7A The origins of quantum mechanics 282
7A.1 Energy quantization 282
(a) Black-body radiation 282
(b) Heat capacities 285
(c) Atomic and molecular spectra 286
7A.2 Wave–particle duality 287
(a) The particle character of electromagnetic radiation 287
(b) The wave character of particles 289
Checklist of concepts 290
Checklist of equations 291

Topic 7B Dynamics of microscopic systems 292
7B.1 The Schrödinger equation 292
7B.2 The Born interpretation of the wavefunction 293
(a) Normalization 295
(b) Constraints on the wavefunction 296
(c) Quantization 297
7B.3 The probability density 297
Checklist of concepts 298
Checklist of equations 298

Topic 7C The principles of quantum theory 299
7C.1 Operators 299
(a) Eigenvalue equations 299
(b) The construction of operators 300
(c) Hermitian operators 302
(d) Orthogonality 303
7C.2 Superpositions and expectation values 304
7C.3 The uncertainty principle 305
7C.4 The postulates of quantum mechanics 308
Checklist of concepts 308
Checklist of equations 308
Discussion questions, exercises, and problems 310
Mathematical background 3 Complex numbers 314
CHAPTER 8 The quantum theory of motion 316

Topic 8A Translation 317
8A.1 Free motion in one dimension 317
8A.2 Confined motion in one dimension 318
(a) The acceptable solutions 318
(b) The properties of the wavefunctions 320
(c) The properties of observables 321
8A.3 Confined motion in two or more dimensions 322
(a) Separation of variables 322
(b) Degeneracy 324
8A.4 Tunnelling 324
Checklist of concepts 327
Checklist of equations 328

Topic 8B Vibrational motion 329
8B.1 The harmonic oscillator 329
(a) The energy levels 330
(b) The wavefunctions 331
8B.2 The properties of oscillators 333
(a) Mean values 334
(b) Tunneling 335
Checklist of concepts 336
Checklist of equations 336

Topic 8C Rotational motion 337
8C.1 Rotation in two dimensions 337
(a) The qualitative origin of quantized rotation 337
(b) The solutions of the Schrödinger equation 338
(c) Quantization of angular momentum 340
8C.2 Rotation in three dimensions 342
(a) The wavefunctions 342
(b) The energies 344
(c) Angular momentum of 345
(d) Space quantization 345
(e) The vector model 346
Checklist of concepts 347
Checklist of equations 347
Discussion questions, exercises, and problems 349
Mathematical background 4 Differential equations 354
CHAPTER 9 Atomic structure and spectra 356

Topic 9A Hydrogenic atoms 357
9A.1 The structure of hydrogenic atoms 358
(a) The separation of variables 358
(b) The radial solutions 359
9A.2 Atomic orbitals and their energies 361
(a) The specification of orbitals 361
(b) The energy levels 362
(c) Ionization energies 362
(d) Shells and subshells 363
(e) s Orbitals 364
(f) Radial distribution functions 365
(g) p Orbitals 367
(h) d Orbitals 368
Checklist of concepts 368
Checklist of equations 369

Topic 9B Many-electron atoms 370
9B.1 The orbital approximation 370
(a) The helium atom 371
(b) Spin 371
(c) The Pauli principle 372
(d) Penetration and shielding 374
9B.2 The building-up principle 375
(a) Hund’s rules 376
(b) Ionization energies and electron affinities 377
9B.3 Self-consistent field orbitals 379
Checklist of concepts 380
Checklist of equations 380

Topic 9C Atomic spectra 381
9C.1 The spectra of hydrogenic atoms 381
9C.2 The spectra of complex atoms 382
(a) Singlet and triplet states 383
(b) Spin–orbit coupling 383
(c) Term symbols 386
(d) Hund’s rules 389
(e) Selection rules 389
Checklist of concepts 389
Checklist of equations 390
Discussion questions, exercises, and problems 391
Mathematical background 5 Vectors 395
CHAPTER 10 Molecular structure 398

Topic 10A Valence-bond theory 399
10A.1 Diatomic molecules 400
(a) The basic formulation of 400
(b) Resonance 401
10A.2 Polyatomic molecules 402
(a) Promotion 403
(b) Hybridization 403
Checklist of concepts 405
Checklist of equations 406

Topic 10B Principles of molecular orbital theory 407
10B.1 Linear combinations of atomic orbitals 407
(a) The construction of linear combinations 407
(b) Bonding orbitals 409
(c) Antibonding orbitals 411
10B.2 Orbital notation 412
Checklist of concepts 412
Checklist of equations 412

Topic 10C Homonuclear diatomic molecules 413
10C.1 Electron configurations 413
(a) σ Orbitals and π orbitals 413
(b) The overlap integral 415
(c) Period 2 diatomic molecules 416
10C.2 Photoelectron spectroscopy 418
Checklist of concepts 419
Checklist of equations 419

Topic 10D Heteronuclear diatomic molecules 420
10D.1 Polar bonds 420
(a) The molecular orbital formulation 420
(b) Electronegativity 421
10D.2 The variation principle 422
(a) Procedure 423
(b) The features of the solutions 424
Checklist of concepts 425
Checklist of equations 426

Topic 10E Polyatomic molecules 427
10E.1 The Hückel approximation 427
(a) An introduction to the method 428
(b) The matrix formulation of the method 428
10E.2 Applications 430
(a) Butadiene and π-electron binding energy 430
(b) Benzene and aromatic stability 431
10E.3 Computational chemistry 432
(a) Semi-empirical and ab initio methods 433
(b) Density functional theory 434
(c) Graphical representations 434
Checklist of concepts 435
Checklist of equations 435
Discussion questions, exercises, and problems 436
Mathematical background 6 Matrices 443
CHAPTER 11 Molecular symmetry 446

Topic 11A Symmetry elements 447
11A.1 Symmetry operations and symmetry elements 448
11A.2 The symmetry classification of molecules 449
(a) The groups C1, Ci, and Cs 450
(b) The groups Cn, Cnv, and Cnh 451
(c) The groups Dn, Dinh, and Dnd 452
(d) The groups Sn 452
(e) The cubic groups 453
(f) The full rotation group 454
11A.3 Some immediate consequences of symmetry 454
(a) Polarity 454
(b) Chirality 455
Checklist of concepts 455
Checklist of operations and elements 456

Topic 11B Group theory 457
11B.1 The elements of group theory 457
11B.2 Matrix representations 458
(a) Representatives of operations 459
(b) The representation of a group 459
(c) Irreducible representations 459
(d) Characters and symmetry species 460
11B.3 Character tables 461
(a) Character tables and orbital degeneracy 461
(b) The symmetry species of atomic orbitals 462
(c) The symmetry species of linear combinations of orbitals 463
Checklist of concepts 464
Checklist of equations 464

Topic 11C Applications of symmetry 465
11C.1 Vanishing integrals 465
(a) Integrals over the product of two functions 466
(b) Decomposition of a direct product 467
(c) Integrals over products of three functions 467
11C.2 Applications to orbitals 468
(a) Orbital overlap 468
(b) Symmetry-adapted linear combinations 468
11C.3 Selection rules 469
Checklist of concepts 470
Checklist of equations 470
Discussion questions, exercises, and problems 471
CHAPTER 12 Rotational and vibrational spectra 474

Topic 12A General features of molecular spectroscopy 476
12A.1 The absorption and emission of radiation 477
(a) Stimulated and spontaneous radiative processes 477
(b) Selection rules and transition moments 478
(c) The Beer–Lambert law 479
12A.2 Spectral linewidths 480
(a) Doppler broadening 481
(b) Lifetime broadening 482
12A.3 Experimental techniques 482
(a) Sources of radiation 482
(b) Spectral analysis 483
(c) Detectors 485
(d) Examples of spectrometers 485
Checklist of concepts 486
Checklist of equations 487

Topic 12B Molecular rotation 488
12B.1 Moments of inertia 488
12B.2 The rotational energy levels 490
(a) Spherical rotors 490
(b) Symmetric rotors 491
(c) Linear rotors 493
(d) Centrifugal distortion 493
Checklist of concepts 494
Checklist of equations 494

Topic 12C Rotational spectroscopy 495
12C.1 Microwave spectroscopy 495
(a) Selection rules 495
(b) The appearance of microwave spectra 497
12C.2 Rotational Raman spectroscopy 498
12C.3 Nuclear statistics and rotational states 500
Checklist of concepts 502
Checklist of equations 502

Topic 12D Vibrational spectroscopy of diatomic molecules 503
12D.1 Vibrational motion 503
12D.2 Infrared spectroscopy 505
12D.3 Anharmonicity 506
(a) The convergence of energy levels 506
(b) The Birge–Sponer plot 508
12D.4 Vibration–rotation spectra 509
(a) Spectral branches 509
(b) Combination differences 510
12D.5 Vibrational Raman spectra 511
Checklist of concepts 512
Checklist of equations 512

Topic 12E Vibrational spectroscopy of polyatomic molecules 514
12E.1 Normal modes 514
12E.2 Infrared absorption spectra 516
12E.3 Vibrational Raman spectra 518
(a) Depolarization 518
(b) Resonance Raman spectra 518
(c) Coherent anti-Stokes Raman spectroscopy 519
12E.4 Symmetry aspects of molecular vibrations 520
(a) The infrared activity of normal modes 520
(b) Raman activity of normal modes 521
Checklist of concepts 521
Checklist of equations 522
Discussion questions, exercises, and problems 523
CHAPTER 13 Electronic transitions 531

Topic 13A Electronic spectra 532
13A.1 Diatomic molecules 533
(a) Term symbols 533
(b) Selection rules 535
(c) Vibrational structure 536
(d) Rotational structure 538
13A.2 Polyatomic molecules 539
(a) d-Metal complexes 539
(b) π*←π and π*←n transitions 540
(c) Circular dichroism 541
Checklist of concepts 542
Checklist of equations 542

Topic 13B Decay of excited states 543
13B.1 Fluorescence and phosphorescence 543
13B.2 Dissociation and predissociation 545
Checklist of concepts 546

Topic 13C Lasers 547
13C.1 Population inversion 547
13C.2 Cavity and mode characteristics 549
13C.3 Pulsed lasers 550
13C.4 Time-resolved spectroscopy 552
13C.5 Examples of practical lasers 552
(a) Gas lasers 553
(b) Exciplex lasers 554
(c) Dye lasers 554
(d) Vibronic lasers 554
Checklist of concepts 555
Checklist of equations 555
Discussion questions, exercises, and problems 556
CHAPTER 14 Magnetic resonance 560

Topic 14A General principles 561
14A.1 Nuclear magnetic resonance 561
(a) The energies of nuclei in magnetic fields 561
(b) The NMR spectrometer 563
14A.2 Electron paramagnetic resonance 564
(a) The energies of electrons in magnetic fields 565
(b) The EPR spectrometer 566
Checklist of concepts 567
Checklist of equations 567

Topic 14B Features of NMR spectra 568
14B.1 The chemical shift 568
14B.2 The origin of shielding constants 570
(a) The local contribution 570
(b) Neighboring group contributions 571
(c) The solvent contribution 573
14B.3 The fine structure 573
(a) The appearance of the spectrum 573
(b) The magnitudes of coupling constants 575
(c) The origin of spin–spin coupling 576
(d) Equivalent nuclei 577
(e) Strongly coupled nuclei 579
14B.4 Conformational conversion and exchange processes 580
Checklist of concepts 581
Checklist of equations 581

Topic 14C Pulse techniques in NMR 582
14C.1 The magnetization vector 582
(a) The effect of the radiofrequency field 583
(b) Time- and frequency-domain signals 584
14C.2 Spin relaxation 585
(a) Longitudinal and transverse relaxation 585
(b) The measurement of T1 and T2 587
14C.3 Spin decoupling 588
14C.4 The nuclear Overhauser effect 589
14C.5 Two-dimensional NMR 590
14C.6 Solid-state NMR 592
Checklist of concepts 593
Checklist of equations 593

Topic 14D Electron paramagnetic resonance 594
14D.1 The g-value 594
14D.2 Hyperfine structure 595
(a) The effects of nuclear spin 595
(b) The McConnell equation 596
(c) The origin of the hyperfine interaction 597
Checklist of concepts 598
Checklist of equations 598
Discussion questions, exercises, and problems 599
CHAPTER 15 Statistical thermodynamics 604

Topic 15A The Boltzmann distribution 605
15A.1 Configurations and weights 605
(a) Instantaneous configurations 605
(b) The most probable distribution 607
(c) The relative population of states 608
15A.2 The derivation of the Boltzmann distribution 608
(a) The role of constraints 609
(b) The values of the constants 610
Checklist of concepts 611
Checklist of equations 611

Topic 15B Molecular partition functions 612
15B.1 The significance of the partition function 612
15B.2 Contributions to the partition function 614
(a) The translational contribution 615
(b) The rotational contribution of 616
(c) The vibrational contribution 620
(d) The electronic contribution 621
Checklist of concepts 622
Checklist of equations 622

Topic 15C Molecular energies 624
15C.1 The basic equations 624
15C.2 Contributions of the fundamental modes of motion 625
(a) The translational contribution 625
(b) The rotational contribution of 625
(c) The vibrational contribution 626
(d) The electronic contribution 627
(e) The spin contribution 628
Checklist of concepts 628
Checklist of equations 628

Topic 15D The canonical ensemble 630
15D.1 The concept of ensemble 630
(a) Dominating configurations 631
(b) Fluctuations from the most probable distribution 631
15D.2 The mean energy of a system 632
15D.3 Independent molecules revisited 633
15D.4 The variation of energy with volume 633
Checklist of concepts 635
Checklist of equations 635

Topic 15E The internal energy and the entropy 636
15E.1 The internal energy 636
(a) The calculation of internal energy 636
(b) Heat capacity 637
15E.2 The entropy 638
(a) Entropy and the partition function 638
(b) The translational contribution 640
(c) The rotational contribution of 641
(d) The vibrational contribution 642
(e) Residual entropies 642
Checklist of concepts 643
Checklist of equations 644

Topic 15F Derived functions 645
15F.1 The derivations 645
15F.2 Equilibrium constants 647
(a) The relation between K and the partition function 647
(b) A dissociation equilibrium 648
(c) Contributions to the equilibrium constant 648
Checklist of concepts 650
Checklist of equations 650
Discussion questions, exercises, and problems 651
CHAPTER 16 Molecular interactions 659

Topic 16A Electric properties of molecules 660
16A.1 Electric dipole moments 660
16A.2 Polarizabilities 663
16A.3 Polarization 664
(a) The frequency dependence of the polarization 664
(b) Molar polarization 665
Checklist of concepts 667
Checklist of equations 667

Topic 16B Interactions between molecules 668
16B.1 Interactions between partial charges 668
16B.2 The interactions of dipoles 669
(a) Charge–dipole interactions 669
(b) Dipole–dipole interactions 670
(c) Dipole–induced dipole interactions 673
(d) Induced dipole–induced dipole interactions 673
16B.3 Hydrogen bonding 674
16B.4 The hydrophobic interaction 675
16B.5 The total interaction 676
Checklist of concepts 678
Checklist of equations 678

Topic 16C Liquids 680
16C.1 Molecular interactions in liquids 680
(a) The radial distribution function 680
(b) The calculation of g(r) 681
(c) The thermodynamic properties of liquids 682
16C.2 The liquid-vapor interface 683
(a) Surface tension 683
(b) Curved surfaces 684
(c) Capillary action 685
16C.3 Surface films 686
(a) Surface pressure 686
(b) The thermodynamics of surface layers 687
16C.4 Condensation 689
Checklist of concepts 689
Checklist of equations 690
Discussion questions, exercises, and problems 691

CHAPTER 17 Macromolecules and
self-assembly 696

Topic 17A The structures of macromolecules 697
17A.1 The different levels of structure 697
17A.2 Random coils 698
(a) Measures of size 699
(b) Constrained chains 702
(c) Partly rigid coils 702
17A.3 Biological macromolecules 703
(a) Proteins 704
(b) Nucleic acids 705
Checklist of concepts 706
Checklist of equations 706

Topic 17B Properties of macromolecules 708
17B.1 Mechanical properties 708
(a) Conformational entropy 708
(b) Elastomers 709
17B.2 Thermal properties 710
17B.3 Electrical properties 712
Checklist of concepts 712
Checklist of equations 713

Topic 17C Self-assembly 714
17C.1 Colloids 714
(a) Classification and preparation 714
(b) Structure and stability 715
(c) The electrical double layer 715
17C.2 Micelles and biological membranes 717
(a) Micelle formation 717
(b) Bilayers, vesicles, and membranes 719
(c) Self-assembled monolayers 720
Checklist of concepts 720
Checklist of equations 721

Topic 17D Determination of size and shape 722
17D.1 Mean molar masses 722
17D.2 The techniques 724
(a) Mass spectrometry 724
(b) Laser light scattering 725
(c) Sedimentation 726
(d) Viscosity 728
Checklist of concepts 730
Checklist of equations 730
Discussion questions, exercises, and problems 731
CHAPTER 18 Solids 736

Topic 18A Crystal structure 737
18A.1 Periodic crystal lattices 737
18A.2 The identification of lattice planes 740
(a) The Miller indices 740
(b) The separation of planes 741
18A.3 X-ray crystallography 742
(a) X-ray diffraction 742
(b) Bragg’s law 744
(c) Scattering factors 745
(d) The electron density 745
(e) Determination of the structure 748
18A.4 Neutron and electron diffraction 749
Checklist of concepts 750
Checklist of equations 751

Topic 18B Bonding in solids 752
18B.1 Metallic solids 752
(a) Close packing 752
(b) Electronic structure of metals 754
18B.2 Ionic solids 756
(a) Structure 756
(b) Energetics 757
18B.3 Covalent and molecular solids 760
Checklist of concepts 761
Checklist of equations 761

Topic 18C Mechanical, electrical, and magnetic properties
of solids 762
18C.1 Mechanical properties 762
18C.2 Electrical properties 764
(a) Conductors 765
(b) Insulators and semiconductors 766
(c) Superconductivity 767
18C.3 Magnetic properties 768
(a) Magnetic susceptibility 768
(b) Permanent and induced magnetic moments 769
(c) Magnetic properties of superconductors 771
Checklist of concepts 771
Checklist of equations 772

Topic 18D The optical properties of solids 773
18D.1 Light absorption by excitons in molecular solids 773
18D.2 Light absorption by metals and semiconductors 775
18D.3 Light-emitting diodes and diode lasers 776
18D.4 Nonlinear optical phenomena 776
Checklist of concepts 776
Discussion questions, exercises, and problems 777
Mathematical background 7 Fourier series and
Fourier transforms 783

PART 3 Change 787
CHAPTER 19 Molecules in motion 789

Topic 19A Transport in gases 790
19A.1 The phenomenological equations 790
19A.2 The transport parameters 792
(a) The diffusion coefficient 793
(b) Thermal conductivity 794
(c) Viscosity 795
(d) Effusion 796
Checklist of concepts 796
Checklist of equations 797

Topic 19B Motion in liquids 798
19B.1 Experimental results 798
(a) Liquid viscosity 798
(b) Electrolyte solutions 799
19B.2 The mobilities of ions 800
(a) The drift speed 800
(b) Mobility and conductivity 802
(c) The Einstein relations 803
Checklist of concepts 804
Checklist of equations 804

Topic 19C Diffusion 805
19C.1 The thermodynamic view 805
19C.2 The diffusion equation 807
(a) Simple diffusion 807
(b) Diffusion with convection 808
(c) Solutions of the diffusion equation 809
19C.3 The statistical view 810
Checklist of concepts 811
Checklist of equations 811
Discussion questions, exercises, and problems 813
CHAPTER 20 Chemical kinetics 818

Topic 20A The rates of chemical reactions 820
20A.1 Monitoring the progress of a reaction 820
(a) General considerations 820
(b) Special techniques 821
20A.2 The rates of reactions 822
(a) The definition of rate 822
(b) Rate laws and rate constants 823
(c) Reaction order 824
(d) The determination of the rate law 824
Checklist of concepts 826
Checklist of equations 826

Topic 20B Integrated rate laws 827
20B.1 First-order reactions 827
20B.2 Second-order reactions 829
Checklist of concepts 831
Checklist of equations 832

Topic 20C Reactions approaching equilibrium 833
20C.1 First-order reactions approaching equilibrium 833
20C.2 Relaxation methods 834
Checklist of concepts 836
Checklist of equations 836

Topic 20D The Arrhenius equation 837
20D.1 The temperature dependence of reaction rates 837
20D.2 The interpretation of the Arrhenius parameters 839
(a) A first look at the energy requirements of reactions 839
(b) The effect of a catalyst on the activation energy 840
Checklist of concepts 841
Checklist of equations 841

Topic 20E Reaction mechanisms 842
20E.1 Elementary reactions 842
20E.2 Consecutive elementary reactions 843
20E.3 The steady-state approximation 844
20E.4 The rate-determining step 845
20E.5 Pre-equilibria 846
20E.6 Kinetic and thermodynamic control of reactions 847
Checklist of concepts 848
Checklist of equations 848

Topic 20F Examples of reaction mechanisms 849
20F.1 Unimolecular reactions 849
20F.2 Polymerization kinetics 850
(a) Stepwise polymerization 851
(b) Chain polymerization 852
Checklist of concepts 854
Checklist of equations 854

Topic 20G Photochemistry 855
20G.1 Photochemical processes 855
20G.2 The primary quantum yield 856
20G.3 Mechanism of decay of excited singlet states 857
20G.4 Quenching 858
20G.5 Resonance energy transfer 860
Checklist of concepts 861
Checklist of equations 862

Topic 20H Enzymes 863
20H.1 Features of enzymes 863
20H.2 The Michaelis–Menten mechanism 864
20H.3 The catalytic efficiency of enzymes 866
20H.4 Mechanisms of enzyme inhibition 866
Checklist of concepts 869
Checklist of equations 869
Discussion questions, exercises, and problems 870
CHAPTER 21 Reaction dynamics 879

Topic 21A Collision theory 881
21A.1 Reactive encounters 881
(a) Collision rates in gases 882
(b) The energy requirement 883
(c) The steric requirement 885
21A.2 The RRK model 886
Checklist of concepts 888
Checklist of equations 888

Topic 21B diffusion-controlled reactions 889
21B.1 Reactions in solution 889
(a) Classes of reaction 889
(b) Diffusion and reaction 890
21B.2 The material-balance equation 891
(a) The formulation of equation 891
(b) Solutions of equation 892
Checklist of concepts 892
Checklist of equations 893

Topic 21C Transition-state theory 894
21C.1 The Eyring equation 894
(a) The formulation of equation 894
(b) The rate of decay of the activated complex 895
(c) The concentration of the activated complex 896
(d) The rate constant 896
(e) Observation and manipulation of the activated complex 897
21C.2 Thermodynamic aspects 899
(a) Activation parameters 899
(b) Reactions between ions 900
21C.3 The kinetic isotope effect 901
Checklist of concepts 903
Checklist of equations 903

Topic 21D The dynamics of molecular collisions 904
21D.1 Molecular beams 904
(a) Techniques 904
(b) Experimental results 905
21D.2 Reactive collisions 907
(a) Probes of reactive collisions 907
(b) State-to-state reaction dynamics 907
21D.3 Potential energy surfaces 908
21D.4 Some results from experiments and calculations 910
(a) The direction of attack and separation 910
(b) Attractive and repulsive surfaces 911
(c) Classical trajectories 912
(d) Quantum mechanical scattering theory 912
Checklist of concepts 913
Checklist of equations 913

Topic 21E Electron transfer in homogeneous systems 914
21E.1 The electron transfer rate law 914
21E.2 The rate constant 915
(a) The role of electron tunneling 916
(b) The reorganization energy 917
Checklist of concepts 919
Checklist of equations 919

Topic 21F Processes at electrodes 920
21F.1 The electrode–solution interface 920
21F.2 The rate of electron transfer 921
(a) The Butler–Volmer equation 921
(b) Tafel plots 924
21F.3 Voltammetry 925
21F.4 Electrolysis 927
21F.5 Working galvanic cells 927
Checklist of concepts 928
Checklist of equations 929
Discussion questions, exercises, and problems 930
CHAPTER 22 Processes on solid surfaces 937

Topic 22A An introduction to solid surfaces 938
22A.1 Surface growth 938
22A.2 Physisorption and chemisorption 939
22A.3 Experimental techniques 940
(a) Microscopy 940
(b) Ionization techniques 942
(c) Diffraction techniques 942
(d) Determination of the extent and rates of adsorption
and desorption 944
Checklist of concepts 945
Checklist of equations 945

Topic 22B Adsorption and desorption 946
22B.1 Adsorption isotherms 946
(a) The Langmuir isotherm 946
(b) The isosteric enthalpy of adsorption 948
(c) The BET isotherm 949
(d) The Temkin and Freundlich isotherms 951
22B.2 The rates of adsorption and desorption 951
(a) The precursor state 951
(b) Adsorption and desorption at the molecular level 952
(c) Mobility on surfaces 953
Checklist of concepts 954
Checklist of equations 954

Topic 22C Heterogeneous catalysis 955
22C.1 Mechanisms of heterogeneous catalysis 955
(a) Unimolecular reactions 956
(b) The Langmuir–Hinshelwood mechanism 956
(c) The Eley–Rideal mechanism 956
22C.2 Catalytic activity at surfaces 957
Checklist of concepts 958
Checklist of equations 958
Discussion questions, exercises, and problems 959
Resource section 963
1 Common integrals 964
2 Units 965
3 Data 966
4 Character tables 996
Index 999

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