atkins' physical chemistryatkins' physical chemistry ( eleventh edition ) peter atkins fellow of...

Atkins' PHYSICAL CHEMISTRY

( Eleventh edition )

Peter Atkins Fellow of Lincoln College, University of Oxford, Oxford, UK

Julio de Paula Professor of Chemistry, Lewis & Clark College, Portland, Oregon, USA

James Keeler Senior Lecturer in Chemistry and Fellow of Selwyn College, University of Cambridge, Cambridge, UK

OXFORD UNIVERSITY PRESS

FULL CONTENTS

Conventions XXV (a) Operational definltlons 34

List of tables xxvi (b) The molecular Interpretation of heat and work 36

List of The chemist's toolkits xxviii 2A.2 The definition of internal energy 37 (a) Molecular Interpretation of Interna! energy 37

List of material provided as A deeper Jook xxix (b) The formulation of the First Law 38 List of Impacts XXX 2A.3 Expansion work 38

(a) The general exi:;resslon for work 39

(b) Expansion agalnst constant pressure 39 PROLOGUE Energy, temperature, (c) Reversible expanslon 40 and chemistry 1 (d) lsothermal reversible expanslon of a perfect gas 41

2A.4 Heat transactlons 42 FOCUS 1 The properties of gases 3 (a) Calorimetry 42

(b) Heat capaclty 43 TOPIC 1A The perfect gas 4

Checklist of concepts 4S 1A.1 Variables ofstate 4

Checklist of equations 4S (a) Pressure 4

(b) Temperature 5 TOPIC 28 Enthalpy 46 1A.2 Equations of state 6 28.1 The definition of enthalpy 46 (a) The emplrlcal basls 7

(a) Enthalpy change and heat transfer 46 (b) Mlxtures of gases 9

(b) Calorlmetry 47 Checklist of concepts 10 28.2 The varlatlon of enthalpy wlth temperature 48 Checklist of equations 10 (a) Heat capaclty at constant pressure 48

(b) The relatlon between heat capacltles 49 TOPIC 18 The kinetic model 11

Checklist of concepts so 18.1 The model 11

Checklist of equations so (a) Pressure and molecular speeds 12

(b) The Maxwell- Boltzmann distributlon of speeds 13 TOPIC 2C Thermochemistry 51 (c) Mean values 15

2C.1 Standard enthalpy changes Sl 18.2 Colllsions 17

(a) Enthalpies of physlcal change 51 (a) The collislon frequency 17

(b) Enthalples of chemical change 52 (b) The mean free path 18

(c) Hess's law 53 Checklist of concepts 18 2C.2 Standard enthalples of formation S4 Checklist of equatlons 18 2C.3 The temperature dependence of reactlon enthalples ss

19 2C.4 Experimental techniques S6 TOPIC 1C Real gases (a) Differential scannlng calorlmetry 56

1C.1 Oeviations from perfect behaviour 19 (b) lsothermal titration caiorimetry 57

(a) The compresslon factor 20 S7 Checklist of concepts (b) Vlrlal coefficlents 20

(c) Crltlcal constants 22 Checklist of equations S8

1c.2 The van der Waals equation 23 TOPIC 20 State functions and exact differentials 59 (a) Formulatlon of the equatlon 23

20.1 Exact and lnexact differentials S9 (b) The features of the equatlon 24

(c) The prlnclple of corresponding states 26 20.2 Changes in Interna! energy 60

Checklist of concepts 27 (a) General consideratlons 60 62 (b) Changes In Interna! energy at constant pressure

Checklist of equations 27 20.3 Changes in enthalpy 63

20.4 The Joule-Thomson effect 64 FOCUS 2 The First Law 33 (a) The observatlon of the Joule- Thomson effect 64

(b) The molecular Interpretation of the Joule-Thomson effect 65 TOPIC 2A Interna! energy 34 Checklist of concepts 66 2A.1 Work, heat, and energy 34

66 Checklist of equations

xvi Full Content5

TOPIC 2E Adiabatic changes 67 3E.2 Properties ofthe Gibbs energy 106 2E.1 The change in temperature 67 (a) General conslderatlons 106

(b) The variation of the Gibbs energy wlth temperature 108 2E.2 The change in pressure 68

(c) The variation of the Glbbs energy wlth pressure 108 Checklist of concepts 69

Checklist of concepts 110 Checklist of equations 69

110 Checklist of equations

FOCUS 3 The Second and Third Laws 77 FOCUS 4 Physical transformations of TOPIC 3A Entropy 78 pure substances 119

3A.1 The Second Law 78 TOPIC 4A Phase diagrams of pure substances 120 3A.2 The definition of entropy 80

4A. 1 The stabilities of phases 120 (a) The thermodynamlc definltlon of entropy 80

(a) The number of phases 120 (b) The statlstlcal definitlon of entropy 81

(b) Phase transltions 120 3A.3 The entropy as a state functlon 82 (c) Thermodynamic criteria of phase stablllty 121 (a) The Ca rnot cycle 82

4A.2 Phase boundaries . 122 (b) The thermodynamlc temperature 85

(a) Characterlstlc properties related to phase transltlons 122 (c) The Clauslus lnequality 85

(b) The phase rule 123 Checklist of concepts 86

4A.3 Three representative phase dlagrams 125 Checklist of equations 87 (a) Carbon dioxide 125

TOPIC 38 Entropy changes accompanying (b) Water 125

specific processes 88 (c) Helium 126

Checklist of concepts 127 38.1 Expansion 88

Checklist of equations 127 38.2 Phase transitions 89

38.3 Heating 90 TOPIC 48 Thermodynamic aspects of phase 38.4 Composlte processes 90 transitions 128

Checklist of concepts 91 48.1 The dependence of stabllity on the conditions 128

Checklist of equations 91 (a) The temperature dependence of phase stablllty 128

(b) The response of melting to applled pressure 129 TOPIC 3C The measurement of entropy 92 (c) The vapour pressure of a liquid subjected to pressure 130

3C. 1 The calorimetrlc measurement of entropy 92 48.2 The location of phase boundaries 131

3C.2 The Third Law 93 (a) The slopes of the phase boundaries 131

(a) The Nernst heat theorem 93 (b) The solid-liquid boundary 132

(b) Thlrd-Law entroples 94 (c) The liquid-vapour boundary 132

(c) The temperature dependence of reaction entropy 95 (d) The solld-vapour boundary 134

Checklist of concepts 96 Checklist of concepts 134

Checklist of equations 96 Checklist of equations 134

TOPIC 30 Concentrating on the system 97 FOCUS 5 Simple mixtures 141 30.1 The Helmholtz and Gibbs energies 97

(a) Crlterla of spontanelty 97 TOPIC SA The thermodynamic description (b) Some remarks on the Helmholtz energy 98 of mixtures 143 (c) Maximum work 98 5A.1 Partial molar quantities 143 (d) Some remarks on the Gibbs energy 99 (a) Partial molarvolume 143 (e) Maximum non-expanslon work 100 (b) Partial molar Glbbs energles 145 30.2 Standard molar Glbbs energles 100 (c) The wider slgnlfic~nce ofthe chemlcal potential 146 (a) Glbbs energles of formatlon 101 (d) The Glbbs-Duhem equation 146 (b) The Born equatlon 102 5A.2 The thermodynamics of mixing 147

Checklist of concepts 103 (a) The Glbbs energy of mlxing of perfect gases 147 Checklist of equations 103 (b) Other thermodynamic mlxing functlons 149

TOPIC 3E Combining the First and Second Laws 5A.3 The chemical potentials of liqulds 150

104 (a) Ideal solutlons 150

3E.1 Properties ofthe Interna! energy 104 (b) ldeal-dllute solutlons 152 (a) The Maxwell relatlons 104

Checklist of concepts 153 (b) The varlatlon of Interna! energy wlth volume 106

Checklist of equations 154

TOPIC SB The properties of solutions 58.1 Liquid mixtures (a) Ideal solutlons

(b) Excess functlons and regular solutlons

58.2 Colligative properties (a) The common features of colligative propertles

(b) The elevatlon of boiling polnt

(c) The depresslon of freezlng point

(d) Solublllty

(e) Osmosls

Checklist of concepts

Checklist of equations

TOPIC SC Phase diagrams of binary systems:

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liquids 166 SC.1 Vapour pressure diagrams 166

SC.2 Temperature-composition diagrams 168 (a) The constructlon of the dlagrams 168

(b) The Interpretation of the diagrams 169

SC.3 Distillation 170 (a) Simple and fractional dlstillation 170

(b) Azeotropes 171

(c) lmmlsclble liqulds 172

SC.4 Liquid-liquid phase diagrams 172 (a) Phase Separation 172

(b) Critlcal solutlon temperatures 173

(c) The dlstlllatlon of partlally miscible liquids 175

Checklist of concepts 176


TOPIC SO Phase diagrams of binary systems: solids 177 SO. 1 Eutectlcs 177

50.2 Reacting systems 178

50.3 lncongruent melting 179


TOPIC SE Phase diagrams of ternary systems 180 SE.1 Trlangular phase diagrams 180

SE.2 Ternary systems 181 (a) Partlally mlscible llqulds 181

(b) Ternary solids 182


TOPIC SF Activities 183 SF.1 The solvent actlvity 183

SF.2 The solute activlty (a) ldeal-dllute solutlons

(b) Real solutes

(c) Actlvltles In terms of molalltles

SF.3 The activities of regular solutions

SF.4 The activities of Ions (a) Mean actlvlty coefficlents

(b) The Oebye- Hückel llmlting law

(c) Extensions of the llmlting law



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Full Content5 XVii

FOCUS 6 Chemical equilibrium

TOPIC 6A The equilibrium constant 6A.1 The Glbbs energy minimum (a) The reactlon Glbbs energy

(b) Exergonlc and endergonlc reactlons

6A.2 The description of equilibrium (a) Perfect gas equlllbrla

(b) The general case of a reaction

(c) The relation between equllibrium constants

(d) Molecular Interpretation of the equillbrlum constant



TOPIC 68 The response of equilibria to the conditions 68.1 The response to pressure

68.2 The response to temperature (a) The van 't Hoff equatlon

(b) The value of Kat different temperatures



TOPIC 6C Electrochemical cells 6C.1 Half-reactions and electrodes

6C.2 Varieties of cells (a) Liquid junctlon potentlals

(b) Notation

6C.3 The cell potential (a) The Nernst equation

(b) Cells at equillbrlum

6C.4 The determinatlon of thermodynamlc functions



TOPIC 60 Electrode potentials 60.1 Standardpotentials (a) The measurement procedure

(b) Comblnlng measured values

60.2 Applications of standard potentials (a) The electrochemical serles

(b) The determlnation of actlvlty coefficlents

(c) The determlnation of equillbrium constants


Checklist of equatlons

FOCUS 7 Quantum theory

TOPIC 7A The origins of quantum mechanics 7A.1 Energy quantization (a) Black-body radlatlon

(b) Heat capaclty

(c) Atomlc and molecular spectra

7A.2 Wave-particle duallty (a) The partlcle character of electromagnetlc radlatlon

(b) The wave character of partlcles

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TOPIC 78 Wavefunctions 246 78.1 The Schrödinger equation 246 FOCUS 8 Atomic structure and spectra 303

78.2 The Born interpretation 247 TOPIC 8A Hydrogenic atoms 304 (a) Normallzatlon 248 8A.1 The structure of hydrogenic atoms 304 (b) Constralnts on the wavefunction 249 (a) The separatlon of variables 304 (c) Quantlzatlon 250 (b) The radial solutions 305

Checklist of concepts 250 8A.2 Atomic orbitals and thelr energies 308 Checklist of equations 250 (a) The specification of orbitals 308

TOPIC 7C Operators and observables 251 (b) The energy levels 308

(c) lonlzatlon energles 309 7C.1 Operators 251 (d) Shells and subshells 309 (a) Elgenvalue equatlons 251 (e) s Orbitals 310 (b) The constructlon of operators 252 (f) Radial dlstribution functlons 311 (c) Hermltlan operators 253 (g) p Orbitals 313 (d) Orthogonallty 254 (h) d Orbitals 314

7C.2 Superpositions and expectation values 255 Checklist of concepts 314

7C.3 The uncertalnty principle 257 Checklist of equations 315

7C.4 The postulates of quantum mechanics 259

Checklist of concepts 260 TOPIC 88 Many-electron atoms 316 Checklist of equations 260 88.1 The orbital approxlmation 316

88.2 The Pauli excluslon prlnclple 317

TOPIC 70 Translational motion 261 (a) Spin 317 70.1 Free motlon in one dlmension 261 (b) The Pauli prlnciple 318

70.2 Confined motlon in one dlmension 262 88.3 The bullding-up prlnclple 319

(a) The acceptable solutions 263 (a) Penetration and shleldlng 319

(b) The propertles of the wavefunctions 264 (b) Hund's rules 321

(c) The propertles of the energy 265 (c) Atomlc and lonic radll 323

70.3 Confined motlon in two and more dimensions 266 (d) lonlzatlon energles and electron affinltles 324

(a) Energy levels and wavefunctlons 266 88.4 Self-consistent field orbltals 325

(b) De9eneracy 267 Checklist of concepts 325

70.4 Tunnelling 268 Checklist of equations 326


Checklist of equatlons 272 TOPIC 8C Atomic spectra 327

8C.1 The spectra of hydrogenlc atoms 327

TOPIC 7E Vibrational motion 273 8C.2 The spectra of many-electron atoms 328 7E.1 The harmonlc oscillator 273 (a) Slnglet and trlplet terms 328

(a) The energy levels 274 (b) Spin-orblt coupling 329

(b) The wavefunctlons 275 (c) Term symbols 332

7E.2 Propertles of the harmonlc oscillator 277 (d) Hund's rules 335

(a) Mean values 277 (e) Selectlon rules 335

(b) Tunnelllng 278 Checklist of concepts 336



TOPIC 7F Rotational motion 281 FOCUS 9 Molecular structure 341

7F.1 Rotation In two dimenslons 281 PROLOGUE The Born- Oppenheimer approxlmation 343

(a) The solutlons of the Schrödinger equatlon 283 TOPIC 9A Valence-bond theory

(b) Quantlzatlon of angular momentum 284 344

7F.2 Rotation in three dimenslons 285 9A.1 Oiatomic molecules 344

(a) The wavefunctlons and energy levels 285 9A.2 Resonance 346

(b) Angular momentum 288 9A.3 Polyatomlc molecules 346

(c) The vector model 288 (a) Promotion 347

(b) Hybrldlzatlon 347

Futl Contents >ÖX

Checklist of concepts 350 (e) The cubic groups 393

Checklist of equations 350 (f) The full rotation group 394

lOA.3 Some immediate consequences of symmetry 394 TOPIC 98 Molecular orbital theory: (a) Polarlty 394

the hydrogen molecule-ion 351 (b) Chirallty 395 98.1 Linear combinatlons of atomlc orbitals 351 Checklist of concepts 395 (a) The construction of linear comblnatlons 351 Checklist of operations and elements 396 (b) Bonding orbitals 353

(c) Antibonding orbitais 354 TOPIC 108 Group theory 397 98.2 Orbital notation 356 108.1 The elements of group theory 397

Checklist of concepts 356 108.2 Matrix representations 398

Checklist of equatlons 356 (a) Representatlves of operatlons 398 (b) The representation of a group 399

TOPIC 9C Molecular orbital theory: homonuclear (c) lrreducible representations 400 diatomic molecules 357 (d) Characters 401 9C.1 Electron configurations 357 108.3 Character tables 401 (a) a Orbitals and 1t orbitals 357 (a) The symmetry specles of atomic orbitals 402 (b) The overlap integral 359 (b) The symmetry species of linear combinations of orbitals 403

(c) Period 2 diatomic molecules 360 (c) Character tables and degeneracy 404

9C.2 Photoelectron spectroscopy 362 Checklist of concepts 405


Checklist of equations 364 TOPIC 10C Applications of symmetry 406

TOPIC 90 Molecular orbital theory: heteronuclear lOC.1 Vanishing Integrals 406 diatomic molecules 365 (a) Integrals of the product of functions 407 90.1 Polarbondsand electronegatlvity 365 (b) Oecompositlon of a representation 408

90.2 The varlation prlnclple 366 lOC.2 Applications to molecular orbital theory 409

(a) The procedure 367 (a) Orbital overlap 409

(b) The features of the solutions 369 (b) Symmetry-adapted linear combinations 409

Checklist of concepts 370 lOC.3 Selection rules 411

Checklist of equations 370 Checklist of concepts 411

TOPIC 9E Molecular orbital theory: polyatomic Checklist of equations 411

molecules 371 9E.1 The Hückel approximation 371 FOCUS 11 Molecular spectroscopy 417 (a) An introduction to the method 371 TOPIC 11A General features of molecular (b) The matrix formulation of the method 372 spectroscopy 419 9E.2 Applicatlons 375

11A.1 The absorption and emlssion of radiatlon 420 (a) 1t-Electron binding energy 375

(a) Stimulated and spontaneous radiative processes 420 (b) Aromatic stablllty 376

(b) Selectlon rules and transitlon moments 421 9E.3 Computational chemistry 377 (c) The Beer-Lambert law 421 (a) Semi-empirlcal and ab lnltlo methods 378

11A.2 Spectral linewidths 423 (b) Density functlonal theory 379

(a) Doppler broadening 423 (c) Graphical representatlons 379

(b) Llfetime broadening 425 Checklist of concepts 380

11A.3 Experimental techniques 425 Checklist of equations 380 (a) Sources of radiation 426

(b) Spectral analysis 426

FOCUS 10 Molecular symmetry 387 (c) Oetectors 428

TOPIC 10A Shape and symmetry 388 (d) Examples of spectrometers 428 Checklist of concepts 429

lOA.1 Symmetry operations and symmetry elements 388 Checklist of equations 429

lOA.2 The symmetry ciassification of molecules 390 (a) The groups c,, C

1, and C, 392 TOPIC 118 Rotational spectroscopy 430

(b) The groups C_, c,.., and C.., 392 118.1 Rotational energy levels 430 (c) ThegroupsD_,D„,andD„ 393

(a) Spherical rotors 432 (d) The groups s. 393

XX Full Contents

(b) Symmetrie rotors 432 TOPIC 11G Decay of excited states 470 (c) Linear rotors 434 11G.1 Fluorescence and phosphorescence 470 (d) Centrlfugal dlstortlon 434

11G.2 Oissociation and predlssociatlon 472 118.2 Microwave spectroscopy 435

11G.3 Lasers 473 (a) Selectlon rules 435

(b) The appearance of mlcrowave spectra 436 Checklist of concepts 474

118.3 Rotational Raman spectroscopy 437

118.4 Nuclear statistlcs and rotatlonal states 439 FOCUS12 Magnetic resonance 487 Checklist of concepts 441 TOPIC 12A General principles 488 Checklist of equatlons 441

12A.1 Nuclear magnetic resonance 488

TOPIC 11C Vibrational spectroscopy of diatomic (a) The energles of nuclel In magnetlc fields 488

molecules 442 (b) The NMR spectrometer 490

11C.1 Vibratlonal motion 442 12A.2 Electron paramagnetic resonance 491

(a) The energles of electrons In magnetlc fields 491 11C.2 lnfrared spectroscopy 443

(b) The EPR spectrometer 492 11C.3 Anharmonlcity 444

Checklist of concepts 493 (a) The conver9ence of energy levels 444

Checklist of equations 493 (b) The Blr9e-Sponer plot 445

11C.4 Vibratlon-rotation spectra 446 TOPIC 128 Features of NMR spectra 494 (a) Spectral branches 447 128.1 The chemical shift 494 (b) Comblnatlon differences 448

128.2 The origin of shielding constants 496 11C.5 Vibrational Raman spectra 448

(a) The local contrlbutlon 496 Checklist of concepts 449 (b) Nelghbourlng group contrlbutlons 497 Checklist of equations 450 (c) The solvent contrlbutlon 498

TOPIC 110 Vibrational spectroscopy of polyatomic 128.3 The fine structure 499

(a) The appearance of the spectrum 499 molecules 451 (b) The magnitudes of coupllng constants 501 110.1 Normal modes 451 (c) The orlgln of spln-spln coupllng 502 110.2 lnfrared absorption spectra 452 (d) Equlvalent nuclei 503

110.3 Vibrational Raman spectra 453 (e) Strongly coupled nuclel 504

Checklist of concepts 454 128.4 Exchange processes 505

Checklist of equations 454 128.5 5olid-state NMR 506

Checklist of concepts 507 TOPIC 11E Symmetry analysis of vibrational

Checklist of equations 508 spectra 455 11 E.1 Classification of normal modes according to symmetry 455 TOPIC 12C Pulse techniques in NMR 509 11 E.2 Symmetry of vibrat ional wavefunctions 457 12C.1 The magnetization vector 509

(a) lnfrared actlvlty of normal modes 457 (a) The effect of the radlofrequency field 510

(b) Raman actlvlty of normal modes 458 (b) Time- and frequency-dornain slgnals 511 (c) The symmetry basls of the excluslon rule 458 12C.2 Spin relaxation 513

Checklist of concepts 458 (a) The mechanlsm of relaxatlon 513

(b) The measurement of T, and T, 514 TOPIC 11F Electronic spectra 459 12C.3 Spin decoupling 515

11F.1 Olatomic molecules 459 12C.4 The nuclear Overhauser effect 516

(a) Term symbols 459 Checklist of concepts 518

(b) Selectlon rules 461

(c) Vlbratlonal fine structure 462 Checklist of equations 518

(d) Rotatlonal fine structure 465 TOPIC 120 Electron paramagnetic resonance 519 11f.2 Polyatomlc molecules 466

120.1 The g-value 519 (a) d-Metal complexes 467

(b) lt" +-1' and lt"+- n transltions 468 120.2 Hyperfine structure 520

(a) The effects of nuclear spln 520 Checklist of concepts 469

(b) The McConnell equatlon 521 Checklist of equations 469 (c) The orlgln of the hyperfine lnteractlon 522

Full Contents xxi

Checklist of concepts 523 (e) Residual entroples 565

Checklist of equations 523 Checklist of concepts 566


FOCUS 13 Statistical thermodynamics 531 TOPIC 13F Derived functions 567 TOPIC 13A The Boltzmann distribution 532 13F.1 The derivations 567

13A.1 Configuratlons and welghts 532 13F.2 Equillbrium constants 570

(a) lnstantaneous conli9uratlons 532 (a) The relation between K and the partltlon functlon 570

(b) The most probable distrlbutlon 533 (b) A dissociation equlllbrlum 570

(c) The values of the constants 535 (c) Contributions to the equilibrlum constant 571

13A.2 The relative population of states 536 Checklist of concepts 573



TOPIC 138 Molecular partition functions 538 FOCUS 14 Molecular interactions 583

138.1 The significance of the partition function 538 TOPIC 14A The electric properties of molecules 585 138.2 Contributions to the partition function 540 14A.1 Electric dipole moments 585

(a) The translatlonal contrlbutlon 540 14A.2 Polarizabilities 587

(b) The rotatlonal contrlbutlon 542 14A.3 Polarization 588 (c) The vlbratlonal contrlbutlon 546 (a) The frequency dependence of the polarlzatlon 588 (d) The electronlc contributlon 547 (b) Molar polarization 590



TOPIC 13C Molecular energies 549 TOPIC 148 lnteractions between molecules 593 13C.1 The baslc equations 549 148.1 The interactions of dlpoles 593

13C.2 Contributions of the fundamental modes of motion 550 (a) Char9e-dlpole interactlons 593

(a) The translational contrlbutlon 550 (b) Dipole-dipole lnteractions 594

(b) The rotatlonal contributlon 550 (c) Dipole-induced dlpole interactlons 597

(c) The vlbratlonal contrlbutlon 551 (d) lnduced dlpole-induced dlpole lnteractlons 597

(d) The electronlc contrlbutlon 552 148.2 Hydrogen bonding 598 (e) The spln contrlbutlon 552 148.3 The total interaction 599

Checklist of concepts 553 Checklist of concepts 601 Checklist of equations 553 Checklist of equations 601

TOPIC 130 The canonical ensemble 554 TOPIC 14C Liquids 602 130.1 The concept of ensemble 554 14C.1 Molecular interactions in liquids 602 (a) Domlnatlng confi9uratlons 555 (a) The radial dlstrlbution functlon 602 (b) Fluctuatlons from the most probable dlstrlbutlon 555 (b) The calculation of g(r) 603 130.2 The mean energy of a system 556 (c) The thermodynamic properties ofllqulds 604

130.3 Independent molecules revisited 556 14C.2 The liquid- vapour interface 605

130.4 The variation of the energy with volume 557 (a) Surface tenslon 605

Checklist of concepts 558 (b) Curved surfaces 606

Checklist of equations 558 (c) Caplllary actlon 606

14C.3 Surfacefilms 608 TOPIC 13E The internal energy and the entropy 559 (a) Surface pressure 608

13E.1 The internal energy 559 (b) The thermodynamlcs of surface layers 609

(a) The calculation of Interna! ener9y 559 14C.4 Condensation 611 (b) Heat capaclty 560 Checklist of concepts 612 13E.2 The entropy 561 Checklist of equations 612 (a) Entropy and the partltlon functlon 561

(b) The translatlonal contrlbutlon 563 TOPIC 140 Macromolecules 613 (c) The rotatlonal contrlbutlon 563 140.1 Average molar masses 613 (d) The vlbrational contrlbutlon 564 140.2 The different levels of structure 614

xxii Full Content5

140.3 Random colls

(a) Measures of size

(b) Constralned chains

(c) Partly rigid colls

140.4 Mechanical properties

(a) Conformational entropy

(b) Elastomers

140.5 Thermal properties



TOPIC 14E Self-assembly 14E.1 Colloids

(a) Classificatlon and preparation

(b) Structure an

(c) The electrical double layer

14E.2 Micelles and biological membranes

(a) The hydrophobic interaction

(b) Miceile formatlon

(c) Bilayers, vesicles, and membranes



FOCUS 15 Solids

TOPIC 15A Crystal structure 15A.1 Periodic crystal lattices

15A.2 The ldentification of lattice planes

(a) The Milier Indices

(b) The separatlon of neighbouring planes



TOPIC 158 Diffraction techniques 158.1 X-ray crystallography

(a) X-ray diffraction

(b) Bragg's law

(c) Scattering factors

(d) The eiectron density

(e) The determlnatlon of structure

158.2 Neutron and electron diffraction



TOPIC 15C Bonding in solids 15C.1 Metals

(a) Close packing

(b) Electronlc structure of metals

15C.2 lonic sollds

(a) Structure

(b) Energetics

15C.3 Covalent and molecular solids



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TOPIC 150 The mechanical properties of solids Checklist of concepts


TOPIC 15E The electrical properties of solids 15E.1 Metallic conductors

15E.2 lnsulators and semiconductors

15E.3 Superconductors



TOPIC 15F The magnetic properties of solids 15F.1 Magnetic susceptibility

1SF.2 Permanent and induced magnetic moments

15F.3 Magnetic properties of superconductors



TOPIC 15G The optical properties of solids 15G.1 Excitons

15G.2 Metals and semiconductors

(a) Light absorptlon

(b) Llght-emlttlng diodes and dlode lasers

1SG.3 Nonlinear optical phenomena


FOCUS 16 Molecules in motion

TOPIC 16A Transport properties of a perfect gas 16A.1 The phenomenological equations

16A.2 The transport parameters

(a) The diffusion coefficient

(b) Thermal conductlvity

(c) Vlscoslty

(d) Effusion



TOPIC 168 Motion in liquids 168.1 Experimental results

(a) Liquid viscosity

(b) Electrolyte solutions

168.2 The mobilities of Ions

(a) The drlft speed

(b) Mobility and conductivlty

(c) The Einstein relations



FOCUS 16( Diffusion 16C.1 The thermodynamic view

16C.2 The diffusion equation

(a) Simple diffusion

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Full Contents X:Xfü

(b) Diffusion with convectlon 710 (a) Stepwise polymerizatlon 755

(c) Solutlons of the diffusion equatlon 710 (b) Chaln polymerlzatlon 756

16C.3 The statistical view 712 17F.3 Enzyme-catalysed reactlons 758



Chemical kinetics TOPIC 17G Photochemistry 762

FOCUS17 721 17G.1 Photochemical processes 762 TOPIC 17A The rates of chemical reactions 723 17G.2 The prlmary quantum yleld 763

17A.1 Monitoring the progress of a reaction 723 17G.3 Mechanism of decay of excited singlet states 764

(a) General conslderatlons 723 17G.4 Quenching 765

(b) Special technlques 724 17G.5 Resonance energy transfer 767

17A.2 The rates of reactions 725 Checklist of conc~pts 768 (a) The definitlon of rate 725 Checklist of equatlons 768 (b) Rate laws and rate constants 726

(c) Reactlon order 727

(d) The determlnatlon of the rate law 728 FOCUS18 Reaction dynamics 779 Checklist of concepts 729 TOPIC 18A Collision theory 780 Checklist of equations 730 18A.1 Reactive encounters 780

TOPIC 178 lntegrated rate laws 731 (a) Colllsion rates In gases 781 (b) The energy requlrement 781

178.1 Zeroth-order reactions 731 (c) The steric requirement 784

178.2 Flrst-order reactions 731 18A.2 The RRK model 785

178.3 5econd-order reactions 733 Checklist of concepts 786 Checklist of concepts 736 Checklist of equations 786 Checklist of equations 736

TOPIC 188 Diffusion-controlled reactions 787 TOPIC 17C Reactions approaching equilibrium 737 188.1 Reactions in solution 787

17C.1 First-order reactions approaching equilibrium 737 (a) Classes of reaction 787 17C.2 Relaxation methods 738 (b) Diffusion and reactlon 788

Checklist of concepts 740 188.2 The material-balance equation 789

Checklist of equations 740 (a) The formulatlon of the equatlon 789

(b) Solutlons of the equatlon 790 TOPIC 170 The Arrhenius equation 741 Checklist of concepts 790

170.1 The temperature dependence of reaction rates 741 Checklist of equations 791 170.2 The Interpretation ofthe Arrhenius parameters 742

(a) A first look at the energy requirements of reactlons 743 TOPIC 18C Transition-state theory 792 (b) The effect of a catalyst on the actlvatlon energy 744 18C.1 The Eyring equation 792

Checklist of concepts 745 (a) Theformulatlon ofthe equatlon 792

Checklist of equatlons 745 (b) The rate of decay of the actlvated complex 793

(c) The concentration of the activated complex 793

TOPIC 17E Reaction mechanisms 746 (d) The rate constant 794 17E.1 Elementary reactlons 746 18C.2 Thermodynamic aspects 795

17E.2 Consecutive elementary reactlons 747 (a) Actlvatlon parameters 795

17E.3 The steady-state approximation 748 (b) Reactlons between Ions 797

17E.4 The rate-determlnlng step 749 18C.3 The kinetic isotope effect 798

17E.5 Pre-equilibrla 750 Checklist of concepts 800

17E.6 Kinetic and thermodynamlc control of reactions 752 Checklist of equations 800

Checklist of concepts 752 TOPIC 180 The dynamics of molecular collisions 801 Checklist of equatlons 752

180.1 Molecular beams 801

TOPIC 17F Examples of reaction mechanisms 753 (a) Technlques 801

17F.1 Unimolecular reactions 753 (b) Experimental results 802

17F.2 Polymerlzatlon klnetlcs 180.2 Reactive collislons 804

754 (a) Probes of reactive colllsions 804

XXiV Full Contents

(b) State-to-state reactlon dynamics 804

180.3 Potential energy surfaces 805

180.4 Some results from experiments and calculations 806

(a) The dlrectlon of attack and separatlon 807

(b) Attractlve and repulsive surfaces 808

(c) Quantum mechanlcal scatterlng theory 808



TOPIC 18E Electron transfer in homogeneous systems 810 18E.1 The rate law 810

18E.2 The role of electron tunnelling 811

18E.3 The rate constant 812

18E.4 Experimental tests of the theory 813



FOCUS 19 Processes at solid surfaces 823

TOPIC 19A An introduction to solid surfaces 824 19A.1 Surface growth 824

19A.2 Physisorption and chemisorption 825

19A.3 Experimental techniques 826

(a) Mlcroscopy 827

(b) lonlzatlon technlques 828

(c) Dlffractlon technlques 829

(d) Determination of the extent and rates of adsorption and desorption 830



TOPIC 198 Adsorption and desorption 832 198.1 Adsorption isotherms

(a) The Langmulr Isotherm

(b) The lsosterlc enthalpy of adsorptlon

(c) The BET Isotherm

832

832

834

835

(d) The Temkln and Freundlich lsotherms

198.2 The rates of adsorption and desorption

(a) The precursor state

(b) Adsorption and desorptlon at the molecular level

(c) Mobility on surfaces



TOPIC 19C Heterogeneous catalysis 19C.1 Mechanisms of heterogeneous catalysis

(a) Unlmolecular reactlons

(b) The Langmulr-Hlnshelwood mechanlsm

(c) The Eley-Rideal mechanlsm

19C.2 Cataiytic activity at surfaces



TOPIC 190 Processes at electrodes 190.1 The electrode-solutlon Interface

190.2 The current density at an electrode (a) The Butler-Volmer equatlon

(b) Tafel plots

190.3 Voltammetry

190.4 Electrolysis

190.5 Working galvanic cells



Resource section 1 Common integrals

2 Units

3

4

Index

Data

Character tables

837

837

837

838

839

840

840

841 841

841

842

843

843

844

844

845 845

846

846

850

850

852

853

854

854

861

862

864

865

895

899

atkins' physical chemistryatkins' physical chemistry ( eleventh edition ) peter atkins fellow of...

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