Principles of physical chemistry / 2nd ed.

Contents
1 WAVE-PARTICLEDUALITY 3
1.1 Overall Look on QuantumMechanics . . . . . . . . . . . . . 3
1.1.1 Historical Highlights . . . . . . . . . . . . . . . . . . 3
1.1.2 Our Present Approach to Quantum Mechanics . . . 5
1.2 Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.1 Particle Nature of Light: Photoelectric Effect . . . . 6
1.2.2 Wave Nature of Light: Diffraction . . . . . . . . . . 8
1.2.3 Interpretation of the Experiments . . . . . . . . . . 11
1.3 Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.1 Particle Nature of Electrons . . . . . . . . . . . . . . 12
1.3.2 Wave Nature of Electrons . . . . . . . . . . . . . . . 13
1.3.3 Interpretation of the Experiments . . . . . . . . . . 14
1.3.4 Formal Similarity Between Electron and Photon . . 15
1.4 Questions Arising About Wave-Particle Duality . . . . . . . 16
1.4.1 Single Event: Probability Statement; Collective Behavior:
Definite Statement . . . . . . . . . . . . . . . 16
1.4.2 Wave-Particle Duality and the Need to Abandon Familiar
Ways of Thinking . . . . . . . . . . . . . . . . 17
1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.6 Problems and Exercises . . . . . . . . . . . . . . . . . . . . 19
1.6.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 19
1.6.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . 22
1.7 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 28
1.8 Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 28
2 Essential Aspects of Structure and Bonding 35
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.2 Distinct Energy States . . . . . . . . . . . . . . . . . . . . . 36
2.2.1 Atomic Spectra . . . . . . . . . . . . . . . . . . . . . 36
2.2.2 Franck-Hertz Experiment . . . . . . . . . . . . . . . 37
2.3 StandingWaves . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.3.1 Particle Between ParallelWalls . . . . . . . . . . . . 38
2.3.2 Ill-Posed Questions . . . . . . . . . . . . . . . . . . . 42
2.3.3 Electron in a Cubic Box . . . . . . . . . . . . . . . . 43
2.4 Ground State H-Atom . . . . . . . . . . . . . . . . . . . . . 43
2.4.1 Result of Rigorous Treatment (see Chapter 3) . . . . 44
2.4.2 Box Model for H Atom and the Variational Principle 45
2.5 Ground State H+2 . . . . . . . . . . . . . . . . . . . . . . . . 48
2.5.1 Forming H+2 from an H Atom and a Proton . . . . . 48
2.5.2 Box Test Functions for H+2 . . . . . . . . . . . . . . 49
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.7 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 51
2.8 Problems and Exercises . . . . . . . . . . . . . . . . . . . . 51
2.8.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 51
2.8.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . 54
2.9 Boxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.9.1 Box 2.1. H Atom: Energy for Particle in a Box Trial
Function . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.9.2 Box 2.2. H+2 Ground State Energy from Particle in a
Box Trial Functions . . . . . . . . . . . . . . . . . . 58
2.10 Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 60
3 SCHR¿DINGER EQUATION AND THE H-ATOM 67
I Part 3/I: Schr¿dinger Equation 68
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.2 Wave Equation and Schr¿dinger Equation . . . . . . . . . . 69
3.2.1 Wave Equation . . . . . . . . . . . . . . . . . . . . . 69
3.2.2 One-Dimensional Schr¿dinger Equation . . . . . . . 72
3.2.3 Three-Dimensional Schr¿dinger Equation . . . . . . 77
3.3 Normalized Wavefunction: ? = ?2 . . . . . . . . . . . . . . . 80
3.4 Orthogonality of the Wavefunctions . . . . . . . . . . . . . 83
3.4.1 Non-Degenerate Wavefunctions . . . . . . . . . . . . 83
3.4.2 DegenerateWavefunctions . . . . . . . . . . . . . . . 84
3.4.3 Degeneracy Removed in an Electric Field . . . . . . 85
3.5 Bohr Correspondence Principle and Generalized Form of
QuantumMechanics . . . . . . . . . . . . . . . . . . . . . . 86
3.5.1 Bohr Correspondence Principle . . . . . . . . . . . . 86
3.5.2 pop? of a Free Electron and Eigenvalue Equations . 87
3.5.3 ElectronMoving on a Circle . . . . . . . . . . . . . . 89
3.5.4 Degeneracy Removed by Magnetic Field . . . . . . . 90
3.5.5 Operator for Angular Momentum . . . . . . . . . . . 91
3.5.6 Operator i}?/?t and the Time-Dependent Schr¿dinger
Equation . . . . . . . . . . . . . . . . . . . . . . . . 91
3.5.7 Relation Between Time-Independent and Time-Dependent
Schr¿dinger Equation . . . . . . . . . . . . . . . . . 93
3.5.8 Average Values of an Observable (also Called Expectation
Value) . . . . . . . . . . . . . . . . . . . . . . 94
3.6 Heisenberg Uncertainty Principle . . . . . . . . . . . . . . . 95
3.7 Summary of Postulates of Quantum Mechanics . . . . . . . 96
3.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
II Part 3/II: Hydrogen Atom 98
3.9 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
3.10 H Atomin theGround State . . . . . . . . . . . . . . . . . 99
3.10.1 Wavefunction . . . . . . . . . . . . . . . . . . . . . . 99
3.10.2 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.10.3 Radial Probability Distribution of Electron . . . . . 101
3.10.4 Most Probable Distance and Average Distance . . . 102
3.10.5 Average Potential Energy and Virial Theorem . . . 104
3.11 H Atomin Excited States . . . . . . . . . . . . . . . . . . . 105
3.11.1 Energies . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.11.2 Wavefunctions . . . . . . . . . . . . . . . . . . . . . 105
3.11.3 Radial Probability Distribution and Average Distance 109
3.11.4 Emission Spectra . . . . . . . . . . . . . . . . . . . . 110
3.11.5 Degeneracy of H-atom Orbitals Can Be Removed by
aMagnetic Field . . . . . . . . . . . . . . . . . . . . 111
3.12 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.13 Problems and Exercises . . . . . . . . . . . . . . . . . . . . 113
3.13.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 113
3.13.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . 116
3.14 Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . 119
3.14.1 Foundation 3.1. Electron in a PotentialWell of Finite
Depth . . . . . . . . . . . . . . . . . . . . . . . . . . 119
3.14.2 Foundation 3.2: Orthogonality . . . . . . . . . . . . 124
3.14.3 Foundation 3.3. H Atom: Solution of the Schr¿dinger
Equation . . . . . . . . . . . . . . . . . . . . . . . . 125
3.14.4 Supplement 3.1: H Atom: Angular and Radial Wavefunctions
. . . . . . . . . . . . . . . . . . . . . . . . 129
3.14.5 Supplement 3.2 Uncertainty Principle. . . . . . . . . 135
3.15 Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 139
4 ATOMS AND VARIATION PRINCIPLE 153
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
4.2 Variation Principle . . . . . . . . . . . . . . . . . . . . . . . 153
4.2.1 Justification of the Variation Principle . . . . . . . . 154
4.3 He-Atom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
4.3.1 Ground State of He . . . . . . . . . . . . . . . . . . 158
4.3.2 Indistinguishability of Electrons . . . . . . . . . . . . 160
4.3.3 Excited States of He . . . . . . . . . . . . . . . . . . 160
4.4 Electron Spin and Pauli Exclusion Principle . . . . . . . . 161
4.4.1 Energy Splitting in a Magnetic Field, Electron Paramagnetic
Resonance . . . . . . . . . . . . . . . . . . 161
4.4.2 Spin Variables . . . . . . . . . . . . . . . . . . . . . 163
4.4.3 Antisymmetry Postulate and Pauli Exclusion Principle.164
4.4.4 Singlet-Triplet Splitting - Magnetic Forces Negligible 166
4.5 Many-Electron Atoms . . . . . . . . . . . . . . . . . . . . . 167
4.5.1 Atomic Number Z and Ionization Energy . . . . . . 167
4.5.2 Electronic Structure of the First Three Elements . . 168
4.5.3 Aufbau Principle and Periodic Table . . . . . . . . . 171
4.5.4 Periodic Properties of the Elements . . . . . . . . . 174
4.6 Spin-Orbit Interactions of Electrons in Atoms . . . . . . . . 176
4.6.1 Angular Momentum and Vector Model of Atoms . . 176
4.6.2 Atomic TermSymbols . . . . . . . . . . . . . . . . . 178
4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
4.8 Problems and Exercises . . . . . . . . . . . . . . . . . . . . 180
4.8.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 180
4.8.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . 182
4.9 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 184
4.10 FOUNDATIONS . . . . . . . . . . . . . . . . . . . . . . . . 184
4.10.1 Foundation 4.1. Proof of Variation Principle . . . . . 184
4.10.2 Foundation 4.2. He Atom: Energy in the Ground State186
4.10.3 Foundation 4.3 The Self-Consistent Field approximation
. . . . . . . . . . . . . . . . . . . . . . . . . . 188
4.10.4 Supplement 4.1: Atomic Term Symbols . . . . . . . 190
4.11 Boxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
4.11.1 Box 4.1. Perturbation Theory . . . . . . . . . . . . . 194
4.11.2 Box 4.2. Current Loop in a Magnetic Field (Bohr
Magneton) . . . . . . . . . . . . . . . . . . . . . . . 195
4.11.3 Box 4.3. The Electron Spin Postulate . . . . . . . . 196
4.11.4 Box 4.4: SlaterWavefunctions . . . . . . . . . . . . . 197
4.12 Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 198
5 A QUANTITATIVE VIEW OF CHEMICAL BONDING 209
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
5.2 H+2 Molecule Ion . . . . . . . . . . . . . . . . . . . . . . . . 210
5.2.1 Electron Described by Exact Wavefunction . . . . . 210
5.2.2 Electron Density and the Chemical Bond . . . . . . 212
5.2.3 Electron Described by LCAO Wavefunction . . . . . 214
5.2.4 Comparison of Box Model (Chapter 2) and LCAO
Method . . . . . . . . . . . . . . . . . . . . . . . . . 217
5.2.5 Excited State of H+2 : Bonding and Antibonding Orbitals
. . . . . . . . . . . . . . . . . . . . . . . . . . 218
5.3 H2: A Two Electron System . . . . . . . . . . . . . . . . . . 219
5.3.1 Rigorous Treatment . . . . . . . . . . . . . . . . . . 219
5.3.2 Product of One-Electron Wavefunctions . . . . . . . 221
5.3.3 Indistinguishability of Electrons . . . . . . . . . . . 223
5.3.4 Pauli Exclusion Principle: Electronic Wavefunctions
Must be Antisymmetric. . . . . . . . . . . . . . . . . 224
5.4 Tunneling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
5.4.1 Electron Oscillating Between Protons a and b . . . . 225
5.4.2 Tunneling Barrier and Frequency of Oscillation . . . 226
5.4.3 Importance of Tunneling in Redox Chemistry . . . . 226
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
5.6 Problems and Exercises . . . . . . . . . . . . . . . . . . . . 227
5.6.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 227
5.6.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . 228
5.7 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 231
5.8 Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
5.8.1 Foundation 5.1. H+2 Ion: ExactWavefunction and Energy
. . . . . . . . . . . . . . . . . . . . . . . . . . . 231
5.8.2 Foundation 5.2. Evaluation of LCAO Integrals in H+2 233
5.8.3 Foundation 5.3 Calculation of Evasion Energy (H2
Ground State) . . . . . . . . . . . . . . . . . . . . . 236
5.8.4 Foundation 5.4. Oscillation of Electron between Protons
at Distance d (Tunneling). . . . . . . . . . . . . 237
5.9 Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 241
6 BONDING DESCRIBED BY ELECTRON PAIRS AND
MOLECULAR ORBITALS 251
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
6.2 Electron Pair Bonds . . . . . . . . . . . . . . . . . . . . . . 252
6.2.1 Connectivity of Atoms in Three-Atom Molecules . . 252
6.2.2 Geometries for Electron Pair Bonds . . . . . . . . . 255
6.2.3 Limitations of Electron Pair Model . . . . . . . . . . 259
6.3 Molecular Orbitals . . . . . . . . . . . . . . . . . . . . . . . 260
6.3.1 Homonuclear Diatomics . . . . . . . . . . . . . . . . 260
6.3.2 Heteronuclear Diatomics . . . . . . . . . . . . . . . . 265
6.3.3 Triatomics (H2O) . . . . . . . . . . . . . . . . . . . . 267
6.3.4 Polyatomics . . . . . . . . . . . . . . . . . . . . . . . 270
6.4 Polarity, Bond length, Elasticity . . . . . . . . . . . . . . . 274
6.4.1 Polarity of Bonds and Electronegativity . . . . . . . 274
6.4.2 Covalent Radii and Van der Waals Radii . . . . . . . 276
6.4.3 Stretching, Bending, and Torsion of Bonds . . . . . 279
6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
6.6 Boxes and Foundations . . . . . . . . . . . . . . . . . . . . . 283
6.6.1 Box 6.1 Tetrahedral Hybrid Function . . . . . . . . . 283
6.6.2 Foundation 6.1. LCAO-Treatment of Heteronuclear
DiatomicMolecules. . . . . . . . . . . . . . . . . . . 284
6.7 Problems and Exercises . . . . . . . . . . . . . . . . . . . . 287
6.7.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 287
6.7.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . 289
6.8 Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 290
7 MOLECULES WITH PI-ELECTRON SYSTEMS 311
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
7.2 Bonding Properties of ã Electrons . . . . . . . . . . . . . . 312
7.2.1 Sigma-Bonded Molecular Skeleton and ã-Electrons . 312
7.2.2 ã-Electrons Described as Electrons in an Effective
Potential V (s) . . . . . . . . . . . . . . . . . . . . . 314
7.3 Free Electron Molecular Orbital (FEMO) Model . . . . . . 315
7.3.1 Ethene, Butadiene, Amidinium. ã-Electron Chains. . 315
7.3.2 Benzene. A ã-Electron Ring . . . . . . . . . . . . . . 317
7.3.3 Charge Density dQ/ds . . . . . . . . . . . . . . . . . 319
7.3.4 BranchedMolecules . . . . . . . . . . . . . . . . . . 321
7.4 Bondlength ConsistentWith Total ã Electron DensityMethod
(BCD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
7.5 Principles of Density Functional Theory (DFT) . . . . . . . 325
7.6 HMOModel . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
7.6.1 Wavefunctions and Energies . . . . . . . . . . . . . . 326
7.6.2 Application of the HMOMethod to ã-Electron Chains
328
7.6.3 Bond Length and HMOBond Order . . . . . . . . . 331
7.7 Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
7.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
7.9 Exercises and Problems . . . . . . . . . . . . . . . . . . . . 334
7.9.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 334
7.9.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . 336
7.10 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 338
7.11 Boxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338
7.11.1 Box 7.1: Neglect of the Overlap Integral Sab in HMO 338
7.11.2 Foundation 7.1: Free-Electron Model . . . . . . . . . 339
7.11.3 Foundation 7.2: Self-consistency in Bond Alternation 341
7.11.4 Supplement 7.1: Construction of V (s) in Figure 7.3 . 344
7.11.5 Supplement 7.2: Free-Electron Model, Representation
by Determinants . . . . . . . . . . . . . . . . . 347
7.11.6 Supplement 7.3: HMO Model . . . . . . . . . . . . . 351
7.11.7 Supplement 7.4: Bond Lengths in Fullerene . . . . . 357
7.12 Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 357
8 ABSORPTION AND EMISSION OF LIGHT 371
III Part 8/I: Absorption of Light 372
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
8.2 Excitation of ã Electron Systems . . . . . . . . . . . . . . . 373
8.2.1 Basic Experimental Facts . . . . . . . . . . . . . . . 373
8.2.2 AbsorptionMaxima of Dyes . . . . . . . . . . . . . . 378
8.2.3 Strength and Polarization of Absorption Bands . . . 382
8.2.4 Hetero-Atoms as Probes for Electron Distribution . 386
8.2.5 HOMO-LUMO Gap by Bond Alternation . . . . . . 390
8.2.6 Cyclic ã-Systems . . . . . . . . . . . . . . . . . . . . 392
8.2.7 Coupling of ã Electrons . . . . . . . . . . . . . . . . 397
8.3 Optical Activity . . . . . . . . . . . . . . . . . . . . . . . . 399
8.3.1 Rotatory Dispersion . . . . . . . . . . . . . . . . . . 399
8.3.2 Ellipticity and Circular Dichroism . . . . . . . . . . 401
8.3.3 Anisotropy Factor g for Model in Figure 8.24 . . . . 402
8.3.4 Absolute Configuration of Chiral Molecules. . . . . . 404
8.3.5 Circular Dichroism of Spirobisanthracene . . . . . . 404
8.3.6 Circular Dichroism of Chiral Cyanine Dye . . . . . . 407
8.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 408
IV Part 8/II: Emission of Light 410
8.5 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 411
8.6 Spontaneous Emission . . . . . . . . . . . . . . . . . . . . . 411
8.6.1 Fluorescence . . . . . . . . . . . . . . . . . . . . . . 412
8.6.2 Phosphorescence and Triplet States . . . . . . . . . 415
8.6.3 Relation Between Fluorescence, Phosphorescence, and
Absorption . . . . . . . . . . . . . . . . . . . . . . . 418
8.6.4 Quenching of Fluorescence. . . . . . . . . . . . . . . 420
8.6.5 Absorption fromExcited States . . . . . . . . . . . . 421
8.7 Stimulated Emission and Laser Action . . . . . . . . . . . . 422
8.7.1 Inversion of Population . . . . . . . . . . . . . . . . 423
8.7.2 Dye Laser Operation . . . . . . . . . . . . . . . . . . 424
8.7.3 Excimer and Exciplex Laser . . . . . . . . . . . . . . 426
8.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 426
8.9 Problems and Exercises . . . . . . . . . . . . . . . . . . . . 427
8.9.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 427
8.9.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . 429
8.10 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 432
8.11 Boxes and Foundations . . . . . . . . . . . . . . . . . . . . . 432
8.11.1 Box 8.1. Law of Lambert-Beer . . . . . . . . . . . . 432
8.11.2 Box 8.2. Derivation of Equation () in Section 8.3.3 . 432
8.11.3 Box 8.3. Relation Between Ellipticity é and ?î . . . 433
8.11.4 Box 8.4 Einstein Coefficients . . . . . . . . . . . . . 434
8.11.5 Foundation 8.1. Integrated Absorption: Classical Oscillator
. . . . . . . . . . . . . . . . . . . . . . . . . . 436
8.11.6 Foundation 8.2. Oscillator Strength: Quantum Mechanical
Treatment . . . . . . . . . . . . . . . . . . . 442
8.11.7 Foundation 8.3. Coupling Transitions with Parallel
TransitionMoments . . . . . . . . . . . . . . . . . . 444
8.11.8 Foundation 8.4. Normal Modes of Coupled Oscillators.447
8.11.9 Foundation 8.5. Fluorescence Life Time . . . . . . . 451
8.11.10Foundation 8.7 Calculation of Repulsion Integrals . 453
8.11.11 Supplement 8.1. Classical and Quantum Mechanical
Description of Light Absorption. . . . . . . . . . . . 455
8.12 Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 460
9 Nuclei: Particle and Wave Properties and Nuclear Spin 483
V Part 9/I: Nuclei: Particle and Wave Properties 484
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
9.2 RotationalMotion ofMolecules . . . . . . . . . . . . . . . . 486
9.2.1 Diatomic Quantum-Mechanical Rotator . . . . . . . 486
9.2.2 PolyatomicMolecules . . . . . . . . . . . . . . . . . 489
9.2.3 Rotational Spectra . . . . . . . . . . . . . . . . . . . 491
9.3 VibrationalMotion ofMolecules . . . . . . . . . . . . . . . 497
9.3.1 Classical Oscillator . . . . . . . . . . . . . . . . . . . 497
9.3.2 Quantum-Mechanical Harmonic Oscillator . . . . . . 499
9.3.3 Vibrational-Rotational Spectra . . . . . . . . . . . . 502
9.3.4 Quantum-Mechanical Anharmonic Oscillator . . . . 509
9.4 Raman Spectra . . . . . . . . . . . . . . . . . . . . . . . . . 513
9.4.1 Rayleigh Scattering . . . . . . . . . . . . . . . . . . 513
9.4.2 Raman Spectroscopy . . . . . . . . . . . . . . . . . . 514
9.4.3 Rotational Raman Spectra of Heteronuclear Diatomic
Molecules . . . . . . . . . . . . . . . . . . . . . . . . 515
9.4.4 Raman Spectra of Polyatomics . . . . . . . . . . . . 518
9.5 Vibrational Structure of Electronic Spectra . . . . . . . . . 519
9.5.1 Franck-Condon Principle . . . . . . . . . . . . . . . 520
9.5.2 Photoelectron Spectroscopy . . . . . . . . . . . . . . 522
9.5.3 PolyatomicMolecules . . . . . . . . . . . . . . . . . 524
9.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 528
VI Part 9/II: Nuclear Spin 529
9.7 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 530
9.8 Nuclear Spin: Fundamentals . . . . . . . . . . . . . . . . . 530
9.8.1 Spin of Protons in H2 . . . . . . . . . . . . . . . . . 530
9.8.2 Antisymmetry of Total Wavefunction of a Molecule
Including Electrons and Nuclei . . . . . . . . . . . . 531
9.8.3 Nuclei With Half-Integer Spin (Antisymmetric Total
Wavefunction), Nuclei With Integral Spin (Symmetric
Total Wavefunction) . . . . . . . . . . . . . . . . 533
9.9 NuclearMagnetic Resonance . . . . . . . . . . . . . . . . . 535
9.9.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . 536
9.9.2 Chemical Shift . . . . . . . . . . . . . . . . . . . . . 537
9.9.3 Fine Structure of NMR Spectra . . . . . . . . . . . . 539
9.9.4 NMR Spectroscopy for Determination of Protein Structures
in Solution . . . . . . . . . . . . . . . . . . . . 541
9.9.5 Magnetic Resonance Imaging (MRI) . . . . . . . . . 541
9.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 541
9.11 Problems and Exercises . . . . . . . . . . . . . . . . . . . . 541
9.11.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 541
9.11.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . 543
9.12 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 548
9.13 Boxes and Foundations . . . . . . . . . . . . . . . . . . . . 548
9.13.1 Box 9.1. Rotator: ReducedMass . . . . . . . . . . . 548
9.13.2 Box 9.2. Classical Oscillator: Frequency ?0 . . . . . 549
9.13.3 Box 9.3. Oscillator: Reduced Mass of Diatomic Molecules
. . . . . . . . . . . . . . . . . . . . . . . . . . . 550
9.13.4 Foundation 9.1. Selection Rules for Rotation of LinearMolecules
(Absorption Spectra) . . . . . . . . . . 550
9.13.5 Foundation 9.2. Centrifugal Effect on Energy of Diatomic
Rotator . . . . . . . . . . . . . . . . . . . . . 552
9.13.6 Foundation 9.3. Selection Rules for Vibration (Absorption
Spectra) . . . . . . . . . . . . . . . . . . . . 554
9.13.7 Foundation 9.4. Oscillator: Normal Modes of a Triatomic
LinearMolecule . . . . . . . . . . . . . . . . 555
9.13.8 Foundation 9.5. Selection Rules for Rotation of LinearMolecules
(Raman Spectra) . . . . . . . . . . . . 558
9.13.9 Foundation 9.6. Selection Rules for Vibration of DiatomicMolecules
(Raman Spectra) . . . . . . . . . . 560
9.13.10 Supplement 9.1. Rotator: Solution of the Schr¿dinger
Equation . . . . . . . . . . . . . . . . . . . . . . . . 561
9.13.11 Supplement 9.2. Quantum-Mechanical Treatment of
the Harmonic Oscillator . . . . . . . . . . . . . . . . 564
9.14 Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 569
10 Solids and Intermolecular Forces 603
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 603
10.2 Ionic Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . 604
10.2.1 Bond Energy of an Ion Pair . . . . . . . . . . . . . . 604
10.2.2 Lattice Types . . . . . . . . . . . . . . . . . . . . . . 605
10.3 Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608
10.3.1 Free Electron Model for Conduction Electrons . . . 608
10.3.2 Cohesion Energy ofMetals . . . . . . . . . . . . . . 611
10.3.3 Quantum Wires and Nanostructure . . . . . . . . . . 613
10.4 Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . 616
10.4.1 Soliton Conductors: Polyacetylene . . . . . . . . . . 616
10.4.2 Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . 617
10.4.3 Semiconductor Bandgap . . . . . . . . . . . . . . . . 617
10.4.4 Semiconductor quantumdots . . . . . . . . . . . . . 619
10.5 Molecular Crystals and Intermolecular Forces . . . . . . . . 621
10.5.1 Electrostatic Forces, the Dipole . . . . . . . . . . . . 622
10.5.2 Hydrogen Bonds . . . . . . . . . . . . . . . . . . . . 625
10.5.3 Induction Forces . . . . . . . . . . . . . . . . . . . . 627
10.5.4 Dispersion Forces . . . . . . . . . . . . . . . . . . . . 629
10.5.5 Crystal Packing and Lattice Energy . . . . . . . . . 632
10.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 632
10.7 Problems and Exercises . . . . . . . . . . . . . . . . . . . . 633
10.7.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 633
10.7.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . 635
10.8 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 637
10.9 Boxes and Foundations . . . . . . . . . . . . . . . . . . . . . 637
10.9.1 Box 10.1:Madelung Constant . . . . . . . . . . . . . 637
10.9.2 Box 10.2 Properties of a Metal?s Electron Gas . . . . 638
10.9.3 Box 10.3 Dipole and Induction Energies . . . . . . . 641
10.9.4 Box 10.4 Vibrations of H-Bond Aggregates . . . . . 641
10.9.5 Supplement 10.1 Some Features of Crystal Structures
and Lattices . . . . . . . . . . . . . . . . . . . . . . . 642
10.10Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 644
11 THERMAL MOTION OF MOLECULES 661
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 661
11.2 Kinetic Gas Theory and Temperature . . . . . . . . . . . . 661
11.2.1 ThermalMotion and Pressure . . . . . . . . . . . . . 662
11.2.2 Avogadro?s Law . . . . . . . . . . . . . . . . . . . . 666
11.2.3 Thermal Equilibration and Heat . . . . . . . . . . . 668
11.2.4 Ideal Gas Law and the Definition of Absolute Temperature
. . . . . . . . . . . . . . . . . . . . . . . . . 669
11.2.5 Law of Partial Pressures . . . . . . . . . . . . . . . . 672
11.3 Speed and Collisions of Gas Molecules . . . . . . . . . . . . 672
11.3.1 Average Speed ofMolecules in a Gas . . . . . . . . . 672
11.3.2 Mean Free Path and Number of Collisions . . . . . . 675
11.3.3 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . 678
11.3.4 Viscosity Arising from Collisions of Molecules . . . . 689
11.4 ThermalMotion in Liquids . . . . . . . . . . . . . . . . . . 693
11.4.1 Collisions in Liquids . . . . . . . . . . . . . . . . . . 693
11.4.2 Diffusion Coefficient D of a Liquid . . . . . . . . . . 694
11.4.3 Viscosity of a Liquid . . . . . . . . . . . . . . . . . . 695
11.4.4 Stokes-Einstein Equation . . . . . . . . . . . . . . . 695
11.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 697
11.6 Problems and Exercises . . . . . . . . . . . . . . . . . . . . 697
11.6.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 697
11.6.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . 699
11.7 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 702
11.8 Boxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702
11.8.1 Box 11.1.Molar Quantities . . . . . . . . . . . . . . 702
11.8.2 Box 11.2. Pressure on the Wall of a Container and
Number of Collisions with aWall . . . . . . . . . . . 703
11.8.3 Box 11.3. Averaging the Displacement x2 . . . . . . 705
11.8.4 Box 11.4. Averaging the Free Path ? . . . . . . . . . 705
11.8.5 Box 11.5. Atmospheric Distribution . . . . . . . . . 706
11.8.6 Box 11.6. Derivation of the Stokes-Einstein Equation 707
11.8.7 Foundation 11.1 The RandomWalk in Three Dimensions
. . . . . . . . . . . . . . . . . . . . . . . . . . . 707
11.8.8 Foundation 11.2. Intermolecular Forces Affecting the
Mean Free Path . . . . . . . . . . . . . . . . . . . . 709
11.8.9 Supplement 11.1. Law of Hagen-Poiseuille . . . . . . 710
11.9 Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 713
12 Energy Distribution in Molecular Assemblies 727
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 727
12.2 The Boltzmann Distribution Law . . . . . . . . . . . . . . . 728
12.2.1 System Consisting of Two Quantum States . . . . . 728
12.2.2 Systems Consisting of Many Quantum States . . . . 729
12.2.3 Internal Energy U . . . . . . . . . . . . . . . . . . . 731
12.3 Electronic Energy . . . . . . . . . . . . . . . . . . . . . . . . 733
12.4 Vibrational Energy . . . . . . . . . . . . . . . . . . . . . . . 734
12.4.1 Population Number Nn of Harmonic Oscillator . . . 734
12.4.2 Internal Energy Uvib of Diatomic Molecules . . . . . 737
12.4.3 Internal Energy Uvib of Polyatomic Molecules . . . . 738
12.5 Rotational Energy . . . . . . . . . . . . . . . . . . . . . . . 739
12.5.1 Population Number NJ of Rigid Rotator (HeteronuclearMolecules)
. . . . . . . . . . . . . . . . . . . . 739
12.5.2 Internal Energy Urot of Rotation (HeteronuclearMolecules)
. . . . . . . . . . . . . . . . . . . . . . . . . . 741
12.5.3 Homonuclear Diatomic Molecules: Ortho- and Para-
Hydrogen . . . . . . . . . . . . . . . . . . . . . . . . 743
12.6 Translational Energy . . . . . . . . . . . . . . . . . . . . . . 745
12.6.1 Internal Energy Utrans of Translation According to
QuantumMechanics . . . . . . . . . . . . . . . . . . 745
12.6.2 Maxwell-Boltzmann Distribution of Speeds . . . . . 747
12.7 Characteristic Temperature . . . . . . . . . . . . . . . . . . 751
12.8 Proving the Boltzmann Distribution for Distinguishable Particles
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752
12.8.1 Treatment Using Numerical Examples . . . . . . . . 752
12.8.2 Rigorous Treatment . . . . . . . . . . . . . . . . . . 755
12.9 Proving the Boltzmann Distribution for Indistinguishable
Particles (High Temperature) . . . . . . . . . . . . . . . . . 758
12.10Energy Distribution of Fermions and Bosons Among QuantumStates
. . . . . . . . . . . . . . . . . . . . . . . . . . . 761
12.11Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 764
12.12Problems and Exercises . . . . . . . . . . . . . . . . . . . . 764
12.12.1Exercises . . . . . . . . . . . . . . . . . . . . . . . . 764
12.12.2Problems . . . . . . . . . . . . . . . . . . . . . . . . 768
12.13 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 770
12.14 Boxes and Foundations . . . . . . . . . . . . . . . . . . . . 770
12.14.1Box 12.1. Equipartition Principle in the Classical Limit770
12.14.2Box12.2.Molecular Partition Function Ztrans of Translation
. . . . . . . . . . . . . . . . . . . . . . . . . . 772
12.14.3Box 12.3 Canonical and Microcanonical Ensembles . 773
12.14.4Foundation 12.1 Energy Distribution of Fermions and
Bosons. . . . . . . . . . . . . . . . . . . . . . . . . . 774
12.14.5 Supplement 12.1. Classical Derivation of the One-
DimensionalMaxwell-Boltzmann Distribution of Speeds778
12.14.6Mathematical Appendix: Stirling?s Formula: lnN! =
N ú lnN ? N . . . . . . . . . . . . . . . . . . . . . . 780
12.15 Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 780
13 WORK w, HEAT q, and INTERNAL ENERGY U 795
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 795
13.2 Thermodynamic Systems . . . . . . . . . . . . . . . . . . . 796
13.2.1 Defining System and Surroundings . . . . . . . . . . 796
13.2.2 Defining Thermodynamic States . . . . . . . . . . . 796
13.2.3 Change of State . . . . . . . . . . . . . . . . . . . . 797
13.3 Change of State at Constant Volume (Isochoric Process) . . 799
13.3.1 Change of Internal Energy ?U and the Heat q . . . 799
13.3.2 Heat Capacity CV: Definition . . . . . . . . . . . . . 800
13.3.3 Translational Contribution to CV of a Gas . . . . . 802
13.3.4 Rotational and Vibrational Contributions to CV of a
Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . 802
13.3.5 Ortho- and Para-H2: Fascinating Quantum Effects
on CV . . . . . . . . . . . . . . . . . . . . . . . . . . 805
13.3.6 Electronic Contribution to CV (CV,el) . . . . . . . . 805
13.3.7 Heat Capacity and Characteristic Temperature . . . 806
13.3.8 CV of Solids . . . . . . . . . . . . . . . . . . . . . . . 807
13.4 Change of State at Constant Pressure (Isobaric Process) . . 809
13.4.1 Change of Internal Energy ?U; Heat q and work w 809
13.4.2 Enthalpy H and Heat Capacity CP: Definition . . . 811
13.5 Heat Exchange and Chemical Reactions . . . . . . . . . . . 815
13.5.1 Reaction at Constant Volume: ?U . . . . . . . . . . 815
13.5.2 Reaction at Constant Pressure: ?H . . . . . . . . . 817
13.5.3 Temperature Dependence of ?U and ?H . . . . . . 818
13.5.4 Molar Enthalpies of Formation from Elements ?fH¦ 820
13.5.5 Molar Enthalpy of Reaction ?rH¦ . . . . . . . . . . 821
13.5.6 Bond Enthalpies and Bond Dissociation Energies . . 822
13.5.7 Enthalpies and Reaction Cycles . . . . . . . . . . . . 824
13.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 825
13.7 Problems and Exercises . . . . . . . . . . . . . . . . . . . . 826
13.7.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 826
13.7.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . 828
13.8 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 830
13.9 Boxes and Foundations . . . . . . . . . . . . . . . . . . . . . 830
13.9.1 Box 13.1. ?U, q, and w in a Change of State . . . . 830
13.9.2 Box 13.2 Temperature of a Flame . . . . . . . . . . 831
13.9.3 Foundation 13.1. How to Calculate
Z T2
T1
?C¦P,múdT . 832
13.9.4 Supplement 13.1. Deriving the Debye Function (CV
of Solids) . . . . . . . . . . . . . . . . . . . . . . . . 835
13.10Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 838
14 REVERSIBLEWORK wrev, REVERSIBLE HEAT qrev, and
ENTROPY S 853
14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 853
14.2 Irreversible and Reversible Changes of State . . . . . . . . . 854
14.2.1 Irreversible Changes . . . . . . . . . . . . . . . . . . 854
14.2.2 Reversible Changes . . . . . . . . . . . . . . . . . . . 855
14.3 Counting the Number of Representations of a Thermodynamic
State, ê . . . . . . . . . . . . . . . . . . . . . . . . . 862
14.3.1 Distribution Possibilities . . . . . . . . . . . . . . . . 862
14.3.2 Number of Representations ê of an Atomic Gas in a
Given Thermodynamic State . . . . . . . . . . . . . 865
14.4 The Entropy: S = k ln ê . . . . . . . . . . . . . . . . . . . . 868
14.4.1 Entropy of Subsystems . . . . . . . . . . . . . . . . . 868
14.4.2 Entropy of Atomic Gas: Sackur-Tetrode Equation . 869
14.5 Entropy Change ?S . . . . . . . . . . . . . . . . . . . . . . 870
14.5.1 Temperature Equilibration: Entropy Increase . . . . 871
14.5.2 Mixing: Entropy Increase . . . . . . . . . . . . . . . 872
14.5.3 Entropy Cannot Decrease for an Isolated System . . 873
14.5.4 Entropy Can Decrease in Closed Systems . . . . . . 874
14.6 Heat and Entropy Change . . . . . . . . . . . . . . . . . . . 874
14.6.1 Analysis for an Ideal Gas . . . . . . . . . . . . . . . 874
14.6.2 Cyclic Processes (?S = 0) and Processes in Isolated
Systems (?S ò 0) . . . . . . . . . . . . . . . . . . . 878
14.6.3 Heat and Change of Entropy in Arbitrary Processes 878
14.7 Thermodynamic Temperature Scale and Cooling . . . . . . 879
14.7.1 Thermodynamic Temperature Scale . . . . . . . . . 879
14.7.2 How Low Can Temperature Go? . . . . . . . . . . . 880
14.8 Entropies of Substances . . . . . . . . . . . . . . . . . . . . 881
14.8.1 Entropy of an Atomic Gas . . . . . . . . . . . . . . . 881
14.8.2 Entropy of Diatomic Gases . . . . . . . . . . . . . . 883
14.8.3 Entropy of PolyatomicGases . . . . . . . . . . . . . 886
14.8.4 Entropy of Different Substances . . . . . . . . . . . . 887
14.9 Laws of Thermodynamics . . . . . . . . . . . . . . . . . . . 890
14.10Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 892
14.11Problems and Exercises . . . . . . . . . . . . . . . . . . . . 893
14.11.1Exercises . . . . . . . . . . . . . . . . . . . . . . . . 893
14.11.2Problems . . . . . . . . . . . . . . . . . . . . . . . . 895
14.12Boxes and Foundations . . . . . . . . . . . . . . . . . . . . . 899
14.12.1Box 14.1. Derivation of Equation (14.34) . . . . . . . 899
14.12.2Box 14.2. Indistinguishable Particles: Change of ?S
when Dividing a System into Subsystems . . . . . . 900
14.12.3Box 14.3. Proof of Proposal 1:
14.12.4Box 14.4. Proof of Proposal 2:
14.12.5Foundation 14.1. Number of Representations ê from
Molecular Partition Function Z . . . . . . . . . . . . 906
14.12.6Foundation 14.2 Entropy of Homonuclear Diatomic
Gases . . . . . . . . . . . . . . . . . . . . . . . . . . 909
14.13Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 911
14.14Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 911
15 General Conditions for Sponataneity and its Application
to Equilibria of Ideal Gases and Dilute Solutions 923
15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 923
15.2 General Conditions for Spontaneity . . . . . . . . . . . . . . 924
15.2.1 Helmholtz Energy A . . . . . . . . . . . . . . . . . . 926
15.2.2 Gibbs Energy G . . . . . . . . . . . . . . . . . . . . 927
15.3 ?G and its Dependence on Temperature . . . . . . . . . . . 928
15.3.1 Molar Gibbs Energy of Formation from Elements
?fG¦ . . . . . . . . . . . . . . . . . . . . . . . . . . 928
15.3.2 Molar Gibbs Energy of Reaction ?rG¦ . . . . . . . 929
15.3.3 Temperature Dependence of ?G¦ . . . . . . . . . . 930
15.4 Pressure Dependence of ?G In Ideal Gases . . . . . . . . . 932
15.4.1 Vapor Pressure (Clausius-Clapeyron Equation) . . . 933
15.4.2 Chemical Evolution of a Gas . . . . . . . . . . . . . 935
15.5 ?G and Chemical Equilibrium in Ideal Gases . . . . . . . . 936
15.5.1 Formal Derivation of Mass Action Law . . . . . . . . 937
15.5.2 Mass Action Law - A Direct Consequence of the Relation
BetweenWork and Heat . . . . . . . . . . . . 939
15.5.3 Applying the Mass Action Law . . . . . . . . . . . . 942
15.5.4 Temperature Dependence of K . . . . . . . . . . . . 946
15.5.5 Pressure Changes and Equilibrium . . . . . . . . . . 948
15.5.6 Reactions Involving Gases and Immiscible Condensed
Species . . . . . . . . . . . . . . . . . . . . . . . . . 950
15.5.7 Equilibrium Constant from Molecular Properties . . 951
15.6 ?G and Equilibrium in Dilute Solution . . . . . . . . . . . 954
15.6.1 Osmotic Pressure and Concentration . . . . . . . . . 954
15.6.2 Depression of Vapor Pressure (Raoult?s law) . . . . . 957
15.6.3 Elevation of Boiling Point and Depression of Melting
Point . . . . . . . . . . . . . . . . . . . . . . . . . . 959
15.6.4 Mass Action Law (Solutions of Neutral Particles) . . 962
15.6.5 Mass Action Law (Solutions of Charged Particles) . 964
15.6.6 Gibbs Energy of Formation in Aqueous Solution . . 964
15.6.7 Part of Reactants or Products in Condensed or Gaseous
State . . . . . . . . . . . . . . . . . . . . . . . . . . . 967
15.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 967
15.8 Problems and Exercises . . . . . . . . . . . . . . . . . . . . 968
15.8.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 968
15.8.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . 972
15.9 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 977
15.10Boxes and Foundations . . . . . . . . . . . . . . . . . . . . . 977
15.10.1Box 15.1 Temperature Dependence of ?G . . . . . . 977
15.10.2Box 15.2 Temperature Dependence of the EquilibriumConstant
. . . . . . . . . . . . . . . . . . . . . 978
15.10.3Box 15.3 Raoult?s Law . . . . . . . . . . . . . . . . . 978
15.10.4Box 15.4. How to Obtain ?fG¦aq from ?fG¦ . . . . 979
15.10.5Foundation 15.1. How to Calculate ?GT2 from ?GT1 980
15.10.6Foundation 15.2. Relationship between theMolecular
Partition Function and the Equilibrium Constant . . 981
15.10.7Foundation 15.3. How to Determine ?G¦ for Ions . 983
15.10.8 Supplement 15.1 Isotope Exchange Equilibrium . . . 985
15.11Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 987
16 Classical Thermodynamics in Terms of Differential Calculus,
Phase Equilibria, Real Gases and Solutions 997
VII Part 16/I: Formal Thermodynamics its Application
to Phase Equilibria 998
16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 999
16.2 Internal Energy, Enthalpy,Work, and Heat . . . . . . . . . 999
16.2.1 Work . . . . . . . . . . . . . . . . . . . . . . . . . . 1000
16.2.2 Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . 1001
16.2.3 Relating U and H to Measurable Quantities . . . . . 1002
16.2.4 Maxwell Relations . . . . . . . . . . . . . . . . . . . 1005
16.2.5 An Important Application: Calculating CP ? CV . . 1006
16.3 Spontaneity and Free Energy . . . . . . . . . . . . . . . . . 1008
16.3.1 Helmholtz Energy A . . . . . . . . . . . . . . . . . . 1009
16.3.2 Gibbs Energy G . . . . . . . . . . . . . . . . . . . . 1010
16.4 Phase Equilibria and Phase Transitions . . . . . . . . . . . 1012
xviii
16.4.1 Solid-Liquid Equilibria . . . . . . . . . . . . . . . . . 1013
16.4.2 Liquid-Gas and Solid-Gas Equilibria . . . . . . . . . 1015
16.4.3 Phase Diagrams and Phase Rule . . . . . . . . . . . 1017
16.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 1020
16.6 Problems and Exercises . . . . . . . . . . . . . . . . . . . . 1020
16.6.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 1020
16.6.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . 1024
VIII Part 16/II: Real Gases 1028
16.7 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1029
16.8 ?G for Real Gases and the Fugacity . . . . . . . . . . . . . 1029
16.9 Equations of State for Real Gases . . . . . . . . . . . . . . . 1031
16.9.1 Hard Sphere Gas . . . . . . . . . . . . . . . . . . . . 1032
16.9.2 Van derWaals Equation . . . . . . . . . . . . . . . . 1033
16.9.3 Critical Point and Van der Waals Constants . . . . . 1034
16.9.4 Virial Equation of State . . . . . . . . . . . . . . . . 1036
16.10Change of State of Real Gases . . . . . . . . . . . . . . . . . 1038
16.10.1Adiabatic Expansion into Vacuum . . . . . . . . . . 1038
16.10.2 Joule-Thomson Effect . . . . . . . . . . . . . . . . . 1040
16.11Chemical Equilibria Involving Real Gases . . . . . . . . . . 1043
16.12Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 1045
16.13Problems and Exercises . . . . . . . . . . . . . . . . . . . . 1046
16.13.1Exercises . . . . . . . . . . . . . . . . . . . . . . . . 1046
16.13.2Problems . . . . . . . . . . . . . . . . . . . . . . . . 1050
IX Part 16/III: Real Solutions 1057
16.14Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1058
16.15Partial Molar Quantities and Thermodynamics of Multicomponent
Systems . . . . . . . . . . . . . . . . . . . . . . . . . 1058
16.15.1PartialMolar Volume . . . . . . . . . . . . . . . . . 1058
16.15.2Chemical Potential . . . . . . . . . . . . . . . . . . . 1060
16.15.3Thermodynamic Relations . . . . . . . . . . . . . . . 1061
16.16Activities and Activity Coefficient for Real Solutions . . . . 1063
16.16.1Activity from Vapor Pressure Above a Solution . . . 1063
16.16.2Activity from Osmotic Pressure . . . . . . . . . . . . 1065
16.17Phase Transitions of Solutions . . . . . . . . . . . . . . . . . 1067
16.17.1Elevation of Boiling Point and Depression of Melting
Point. . . . . . . . . . . . . . . . . . . . . . . . . . . 1067
16.17.2 Solutions with Two Volatile Components . . . . . . 1070
16.18Mass Action Law For Reactions in Solution . . . . . . . . . 1071
16.19Electrolyte Solutions and the Debye-H¿ckel Theory . . . . . 1074
16.19.1Debye-H¿ckel Theory for Electrolytes . . . . . . . . 1074
16.20Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 1077
xix
16.21Problems and Exercises . . . . . . . . . . . . . . . . . . . . 1078
16.21.1Exercises . . . . . . . . . . . . . . . . . . . . . . . . 1078
16.21.2Problems . . . . . . . . . . . . . . . . . . . . . . . . 1083
16.22Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 1088
16.23Boxes and Foundations . . . . . . . . . . . . . . . . . . . . . 1088
16.23.1Box 16.1 Partial and Total Differentials . . . . . . . 1088
16.23.2Box 16.2. Derivation of Equation (16.21). . . . . . . 1090
16.23.3Box 16.3. Clapeyron Equation . . . . . . . . . . . . 1091
16.23.4Box 16.4. Estimation of V1 in the Hard Sphere Model 1092
16.23.5Box 16.5. Critical Constants Tc, Pc, and Vc . . . . . 1093
16.23.6Box 16.6. Joule-Thomson Coefficient and Inversion
Temperature . . . . . . . . . . . . . . . . . . . . . . 1093
16.23.7Box 16.7. Electrical Work to Transfer Ions into Concentrated
Solution . . . . . . . . . . . . . . . . . . . 1095
16.23.8Box 16.8. Activity Coefficient of Solute From Activity
Coefficient of Solvent. . . . . . . . . . . . . . . . 1095
16.23.9Foundation 16.1. Some Formal Thermodynamic Relationships
. . . . . . . . . . . . . . . . . . . . . . . 1096
16.23.10Foundation 16.2. Distribution of Ions at a Charged
Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . 1103
16.23.11Supplement 16.1 ? Molecular Perspective on Solid-
Gas Equilibria . . . . . . . . . . . . . . . . . . . . . 1106
16.23.12Supplement 16.2. Virial Equation of State . . . . . . 1110
16.23.13Supplement 16.3 Distinguishing Between Phases . . 1112
16.24Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1113
17 REACTION EQUILIBRIA IN AQUEOUS SOLUTIONS
AND BIOSYSTEMS 1127
17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1127
17.2 Proton Transfer Reactions: Dissociation of Weak Acids . . . 1128
17.2.1 Henderson-Hasselbalch Equation . . . . . . . . . . . 1128
17.2.2 Degree of Dissociation in Aqueous Solution . . . . . 1130
17.2.3 Degree of Dissociation in a Buffer Solution . . . . . 1131
17.2.4 Titration Curve of aWeak Acid . . . . . . . . . . . 1132
17.3 Stepwise Proton Transfer . . . . . . . . . . . . . . . . . . . 1133
17.3.1 Diprotic Acid . . . . . . . . . . . . . . . . . . . . . . 1133
17.3.2 Amino Acids . . . . . . . . . . . . . . . . . . . . . . 1135
17.4 Electron Transfer Reactions . . . . . . . . . . . . . . . . . . 1137
17.4.1 Electron Transfer from Metal to Proton: Dissolution
ofMetals in Acid . . . . . . . . . . . . . . . . . . . . 1137
17.4.2 Electron Transfer from Metal 1 to Metal 2 Ion: Coupled
Redox Reactions . . . . . . . . . . . . . . . . . 1139
17.4.3 Electron Transfer to Proton at pH 7: ?G¦0 . . . . . 1140
17.4.4 Photoinduced Electron Transfer . . . . . . . . . . . . 1141
17.5 Electron Transfer Coupled with Proton Transfer . . . . . . 1143
xx
17.6 Group Transfer Reactions in Biochemistry . . . . . . . . . . 1146
17.6.1 Group Transfer Potential . . . . . . . . . . . . . . . 1148
17.6.2 Coupled Reactions in Biology . . . . . . . . . . . . . 1149
17.7 Bioenergetics . . . . . . . . . . . . . . . . . . . . . . . . . . 1150
17.7.1 Synthesis of Glucose . . . . . . . . . . . . . . . . . . 1150
17.7.2 Combustion of Glucose . . . . . . . . . . . . . . . . 1152
17.7.3 Energy Balance of Formation and Degradation (Combustion)
of Glucose . . . . . . . . . . . . . . . . . . . 1152
17.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 1153
17.9 Problems and Exercises . . . . . . . . . . . . . . . . . . . . 1153
17.9.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 1153
17.9.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . 1156
17.10Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 1158
17.11Boxes and Foundations . . . . . . . . . . . . . . . . . . . . . 1159
17.11.1Foundation 17.1 Titration of Acetic Acid by NaOH . 1159
17.11.2Foundation 17.2 Two Coupled Chemical Equilibria. 1161
17.12Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 1164
18 Chemical Reactions in Electrochemical Cells 1171
18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1171
18.2 ?G and Potential E of an Electrochemical Cell . . . . . . . 1172
18.3 Simple Cells and Nernst Equation . . . . . . . . . . . . . . 1175
18.3.1 Metal/Metal Ions . . . . . . . . . . . . . . . . . . . . 1175
18.3.2 Gas Electrodes . . . . . . . . . . . . . . . . . . . . . 1177
18.3.3 Nernst Equation and Standard Potential . . . . . . . 1178
18.4 Standard Potential E¦ and Reference Electrodes . . . . . . 1180
18.4.1 Practical Determination of E¦ . . . . . . . . . . . . 1181
18.4.2 Absolute Electrode Potential . . . . . . . . . . . . . 1182
18.5 Use of Electrochemical Cells for Thermodynamic Measurements
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1187
18.5.1 pH Electrodes . . . . . . . . . . . . . . . . . . . . . . 1187
18.5.2 Measurement of Mean Activity Coefficient ?ñ
. . . . 1188
18.5.3 Measurement of Equilibrium Constant . . . . . . . . 1191
18.5.4 Liquid-Liquid Junctions . . . . . . . . . . . . . . . . 1191
18.6 Applications of Electrochemical Cells . . . . . . . . . . . . . 1194
18.6.1 Galvanic Cells. Batteries and Accumulators . . . . . 1194
18.6.2 Fuel Cells . . . . . . . . . . . . . . . . . . . . . . . . 1197
18.6.3 Electrolysis and Electrosynthesis . . . . . . . . . . . 1198
18.6.4 Overvoltage . . . . . . . . . . . . . . . . . . . . . . . 1199
18.7 Conductivity of Electrolyte Solutions . . . . . . . . . . . . . 1201
18.7.1 Mobility of Ions . . . . . . . . . . . . . . . . . . . . . 1201
18.7.2 Generalization . . . . . . . . . . . . . . . . . . . . . 1202
18.7.3 Mobility of H+ . . . . . . . . . . . . . . . . . . . . . 1204
18.7.4 Ion Transport throughMembranes . . . . . . . . . . 1205
18.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 1206
xxi
18.9 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 1206
18.10Exercises and Problems . . . . . . . . . . . . . . . . . . . . 1206
18.10.1Exercises . . . . . . . . . . . . . . . . . . . . . . . . 1206
18.10.2Problems . . . . . . . . . . . . . . . . . . . . . . . . 1209
18.11Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 1214
18.12Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 1214
19 Chemical Kinetics 1225
19.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1225
19.2 Collision Theory for Gas Reactions . . . . . . . . . . . . . . 1226
19.2.1 Counting the Number of Collisions . . . . . . . . . . 1226
19.2.2 Activation . . . . . . . . . . . . . . . . . . . . . . . . 1228
19.2.3 Steric Factor . . . . . . . . . . . . . . . . . . . . . . 1229
19.3 Rate Equation for Elementary Bimolecular Reactions . . . . 1229
19.3.1 Rate Constant and Frequency Factor for a Gas Phase
Reaction . . . . . . . . . . . . . . . . . . . . . . . . . 1230
19.3.2 Rate Constant and Frequency Factor for a Reaction
in Solution . . . . . . . . . . . . . . . . . . . . . . . 1232
19.4 Rate Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1236
19.4.1 What is a Rate Law? . . . . . . . . . . . . . . . . . 1237
19.4.2 Zero Order Rate Law . . . . . . . . . . . . . . . . . 1237
19.4.3 First Order Rate Law . . . . . . . . . . . . . . . . . 1238
19.4.4 Second Order Rate Law . . . . . . . . . . . . . . . . 1239
19.5 Activation Energy and Frequency Factor . . . . . . . . . . . 1242
19.5.1 Arrhenius Plot . . . . . . . . . . . . . . . . . . . . . 1242
19.5.2 The Chemist?s Rule of Thumb . . . . . . . . . . . . 1243
19.6 Combinations of Elementary Reactions . . . . . . . . . . . . 1243
19.6.1 Reactions Leading to Equilibrium . . . . . . . . . . 1243
19.6.2 Parallel Reactions . . . . . . . . . . . . . . . . . . . 1246
19.6.3 Consecutive Reactions . . . . . . . . . . . . . . . . . 1248
19.7 Complex Reactions . . . . . . . . . . . . . . . . . . . . . . . 1249
19.7.1 Approximation Methods . . . . . . . . . . . . . . . . 1249
19.7.2 Lindemann-HinshelwoodMechanism . . . . . . . . . 1252
19.7.3 Chain Reactions . . . . . . . . . . . . . . . . . . . . 1254
19.7.4 Enzyme Reactions (Michaelis-Menten Mechanism) . 1256
19.7.5 Autocatalytic Reactions . . . . . . . . . . . . . . . . 1259
19.7.6 Bistability . . . . . . . . . . . . . . . . . . . . . . . . 1263
19.7.7 Oscillating Reactions . . . . . . . . . . . . . . . . . . 1264
19.7.8 ChemicalWaves . . . . . . . . . . . . . . . . . . . . 1266
19.8 ExperimentalMethods . . . . . . . . . . . . . . . . . . . . . 1268
19.8.1 Monitor Reaction Progress and Sampling . . . . . . 1268
19.8.2 FlowMethods . . . . . . . . . . . . . . . . . . . . . 1269
19.8.3 QuenchingMethods . . . . . . . . . . . . . . . . . . 1269
19.8.4 Flash Photolysis . . . . . . . . . . . . . . . . . . . . 1270
19.8.5 RelaxationMethod . . . . . . . . . . . . . . . . . . . 1271
xxii
19.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 1274
19.10Problems and Exercises . . . . . . . . . . . . . . . . . . . . 1274
19.10.1Exercises . . . . . . . . . . . . . . . . . . . . . . . . 1274
19.10.2Problems . . . . . . . . . . . . . . . . . . . . . . . . 1280
19.11Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 1283
19.12Boxes and Foundations . . . . . . . . . . . . . . . . . . . . . 1283
19.12.1Box 19.1. Activation Factor . . . . . . . . . . . . . . 1283
19.12.2Box 19.2. Rate Law for Chain Reaction . . . . . . . 1284
19.12.3Box 19.3. Critical Bromide Concentration . . . . . . 1285
19.12.4Box 19.4. Rate Constants of Belousov-Zhabotinsky
Reaction . . . . . . . . . . . . . . . . . . . . . . . . . 1286
19.13Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 1287
20 Transition States and Chemical Reactions 1307
20.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1307
20.2 Transition State in a Statistical View . . . . . . . . . . . . . 1307
20.2.1 Transition State Theory for Bimolecular Reactions . 1308
20.2.2 Transition State Theory for Unimolecular Reactions 1315
20.2.3 Applications of Transition State Theory . . . . . . . 1317
20.3 Transition State in a Dynamical View . . . . . . . . . . . . 1323
20.3.1 Transition State Spectroscopy . . . . . . . . . . . . 1325
20.3.2 Reaction Cross-Sections and the Thermal Rate Constant
. . . . . . . . . . . . . . . . . . . . . . . . . . . 1326
20.4 Transition State Theory and Reactions in Solution . . . . . 1331
20.4.1 Unimolecular Reactions and Frictional Coupling . . 1331
20.4.2 Dissociation Reactions . . . . . . . . . . . . . . . . . 1333
20.4.3 Proton Transfer Reactions . . . . . . . . . . . . . . . 1335
20.5 Electron Transfer Reactions . . . . . . . . . . . . . . . . . . 1338
20.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 1338
20.7 Foundations and Boxes . . . . . . . . . . . . . . . . . . . . . 1339
20.7.1 Box 20.1. Rigorous Derivation of Rate Equation (20.16)1339
20.7.2 Box 20.2. Comparison of Transition State Theory To
Collision Theory . . . . . . . . . . . . . . . . . . . . 1340
20.7.3 Supplement 20.1 Thermal Rate Constants . . . . . . 1342
20.7.4 Supplement 20.2 Derivation of the Kramers formula.
. . . . . . . . . . . . . . . . . . . . . . . . . . 1344
20.8 Problems and Exercises . . . . . . . . . . . . . . . . . . . . 1350
20.8.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 1350
20.8.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . 1358
20.9 Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 1366
21 MACROMOLECULES 1377
21.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1377
21.2 RandomCoil . . . . . . . . . . . . . . . . . . . . . . . . . . 1377
21.2.1 A Chain of Statistical Chain Elements . . . . . . . . 1379
xxiii
21.3 Measuring the Length of Statistical Chain Elements . . . . 1381
21.3.1 Light Scattering . . . . . . . . . . . . . . . . . . . . 1381
21.3.2 Hydrodynamics: Coil Approximated as a Sphere . . 1383
21.3.3 Hydrodynamics: Macroscopic Modelling . . . . . . . 1387
21.4 Uncoiling a Coil and its Recoiling . . . . . . . . . . . . . . . 1392
21.4.1 Unraveling Coil by Force Applied at Chain Ends . . 1392
21.4.2 Fully Unraveling a Coil in a Flowing Medium . . . . 1394
21.4.3 Partially Unraveling a Coil in a Flowing Medium . . 1396
21.4.4 Restoring Coil . . . . . . . . . . . . . . . . . . . . . 1398
21.5 Proteins as Biopolymers . . . . . . . . . . . . . . . . . . . . 1399
21.6 Motion Through Entangled Polymer Chains . . . . . . . . . 1402
21.6.1 Moving Random Coil by Winding Through Meshwork:
Gel Electrophoresis of DNA Fragments . . . . 1402
21.7 Rubber Elasticity . . . . . . . . . . . . . . . . . . . . . . . . 1404
21.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 1405
21.9 Problems and Exercises . . . . . . . . . . . . . . . . . . . . 1406
21.9.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 1406
21.9.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . 1410
21.10Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 1415
21.11Boxes and Foundations . . . . . . . . . . . . . . . . . . . . . 1415
21.11.1Box 21.1. Statistical Chain Elements . . . . . . . . . 1415
21.11.2Box 21.2. Bending of DNA Strand . . . . . . . . . . 1416
21.11.3Box 21.3. Force Contracting Chain Held at Chain Ends1417
21.11.4Box 21.4 Extension of an Unraveled Coil . . . . . . . 1418
21.11.5Box 21.5: Time to Restore Random Coil from Unraveled
Chain . . . . . . . . . . . . . . . . . . . . . . 1419
21.11.6Box 21.6. Diffusion of a Random Coil in a Gel in the
Absence of an Electric Field and Force-Induced Motion1420
21.11.7Foundation 21.1: Light Scattering of Macromolecules 1422
21.11.8 Supplement 21.1. Stretching a Chain . . . . . . . . . 1424
21.11.9 Supplement 21.2. Viscosity of Dilute Solutions of Polymers
andMacroscopicModels . . . . . . . . . . . . . 1425
21.12Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 1430
22 ORGANIZED MOLECULAR ASSEMBLIES 1447
22.1 Liquid Surfaces and Liquid/Liquid Interfaces . . . . . . . . 1447
22.1.1 Surface Tension and Interfacial Tension . . . . . . . 1447
22.1.2 Surface ActiveMolecules (Surfactants) . . . . . . . . 1451
22.2 Films on Solid Surfaces . . . . . . . . . . . . . . . . . . . . 1454
22.2.1 Langmuir-Blodgett Films (LB Films) . . . . . . . . . 1454
22.2.2 Self-AssembledMonolayers (SAM) . . . . . . . . . . 1455
22.2.3 Contact Angle . . . . . . . . . . . . . . . . . . . . . 1456
22.3 Micelles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1457
22.3.1 Spherical Micelles. Critical Micelle Concentration . . 1458
22.3.2 Geometry of Packing . . . . . . . . . . . . . . . . . . 1463
xxiv
22.4 Membranes . . . . . . . . . . . . . . . . . . . . . . . . . . . 1464
22.4.1 Liposomes . . . . . . . . . . . . . . . . . . . . . . . . 1465
22.4.2 Soap lamella . . . . . . . . . . . . . . . . . . . . . . 1465
22.4.3 Black lipid membranes . . . . . . . . . . . . . . . . . 1465
22.5 Biomembranes . . . . . . . . . . . . . . . . . . . . . . . . . 1468
22.5.1 Lateral Diffusion . . . . . . . . . . . . . . . . . . . . 1468
22.5.2 Ion Transport Through aMembrane . . . . . . . . . 1469
22.5.3 Transport of Small Protein Through a Membrane . . 1471
22.6 Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . 1472
22.6.1 Optics Applications of Liquid Crystals . . . . . . . . 1473
22.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 1475
22.8 Problems and Exercises . . . . . . . . . . . . . . . . . . . . 1476
22.8.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 1476
22.8.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . 1482
22.9 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 1486
22.10Boxes and Foundations . . . . . . . . . . . . . . . . . . . . . 1486
22.10.1Box 22.1. Surface Film; Gibbs Adsorption Equation 1486
22.10.2 Supplement 22.1 Head-to-Head Repulsion Energy . . 1487
22.11Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 1488
23 SUPRAMOLECULAR MACHINES 1507
23.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1507
23.2 Idea of a Supramolecular Machine . . . . . . . . . . . . . . 1508
23.2.1 A Simple Energy Transduction Device . . . . . . . . 1508
23.2.2 Programmed InterlockingMolecules . . . . . . . . . 1508
23.3 Manipulating PhotonMotion . . . . . . . . . . . . . . . . . 1510
23.3.1 Energy Transfer Between DyeMolecules. FRET: Ruler
in Nanometer Range. SNOM . . . . . . . . . . . . . 1510
23.3.2 Functional Unit by Coupling Chromophores . . . . . 1514
23.3.3 Dye Aggregate as Energy Harvesting Device . . . . . 1515
23.3.4 Solar Energy Harvesting in Biosystems . . . . . . . . 1519
23.3.5 Manipulating Luminescence Lifetime by Programming
Echo Radiation Field. . . . . . . . . . . . . . . . . . 1521
23.4 Manipulating ElectronMotion . . . . . . . . . . . . . . . . 1523
23.4.1 Photoinduced Electron Transfer in Designed Monolayer
Assemblies . . . . . . . . . . . . . . . . . . . . 1523
23.4.2 Tunneling Current Through Monolayers . . . . . . . 1526
23.4.3 Conduction Through Single Molecules . . . . . . . . 1529
23.4.4 ConjugatedMolecular Tethers . . . . . . . . . . . . 1532
23.4.5 Electron Transfer in Protein . . . . . . . . . . . . . . 1533
23.4.6 Solar Energy Conversion: The Electron Pump of Plants
and Bacteria . . . . . . . . . . . . . . . . . . . . . . 1535
23.4.7 Electron Transfer in SoftMedium . . . . . . . . . . 1538
23.4.8 Artificial Photoinduced Electron Pumping . . . . . . 1539
23.4.9 Inverted Region of Electron Transfer Reactions . . . 1540
xxv
23.5 Manipulating NuclearMotion . . . . . . . . . . . . . . . . . 1542
23.5.1 Light-Induced Change of Monolayer Properties . . . 1542
23.5.2 Mechanical Switching Devices . . . . . . . . . . . . . 1545
23.5.3 Photoinduced Sequence of Amplification Steps: The
Visual System . . . . . . . . . . . . . . . . . . . . . 1545
23.5.4 Solar Energy Conversion in Halobacteria . . . . . . . 1546
23.5.5 Biomotors . . . . . . . . . . . . . . . . . . . . . . . . 1549
23.5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . 1559
23.6 Problems and Exercises . . . . . . . . . . . . . . . . . . . . 1559
23.6.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 1559
23.6.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . 1566
23.7 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 1570
23.8 Boxes and Foundations . . . . . . . . . . . . . . . . . . . . . 1570
23.8.1 Box 23.1 Manipulation of Monolayer Assemblies . . 1570
23.8.2 Box 23.2. Polarization of Retinal in the Coulomb
Field of Amino Acids D85 and D212 . . . . . . . . . 1571
23.8.3 Foundation 23.1. Energy Transfer . . . . . . . . . . . 1572
23.8.4 Foundation 23.2. Electron Transfer Between ã-Electron
Systems . . . . . . . . . . . . . . . . . . . . . . . . . 1575
23.8.5 Foundation 23.3. Marcus Equation . . . . . . . . . . 1582
23.8.6 Foundation 23.4. Chloride Ion Pump and Sensory Receptor
of Halobacteria . . . . . . . . . . . . . . . . . 1585
23.8.7 Supplement 23.1. Energy Transfer from Exciton to
Acceptor . . . . . . . . . . . . . . . . . . . . . . . . 1587
23.8.8 Supplement 23.2: Radiation Echo Field . . . . . . . 1589
23.8.9 Supplement 23.3 Calculation of Ebarrier . . . . . . . 1592
23.9 Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 1593
24 ORIGIN OF LIFE. MATTER CARRYING INFORMATION.
1629
24.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1629
24.2 Investigation of Complex Systems . . . . . . . . . . . . . . . 1630
24.2.1 Need for SimplifyingModels . . . . . . . . . . . . . 1630
24.2.2 Increasing Simplification with Increasing Stages of
Complexity . . . . . . . . . . . . . . . . . . . . . . . 1630
24.3 Can Life Emerge by Physicochemical Processes? . . . . . . 1630
24.3.1 Bioevolution as a Process of Learning How to Survive
as a Species . . . . . . . . . . . . . . . . . . . . . . 1630
24.3.2 Model Case for the Learning Mechanism . . . . . . . 1631
24.4 Modeling the Emergence of the Genetic Apparatus . . . . . 1633
24.4.1 BasicQuestions . . . . . . . . . . . . . . . . . . . . . 1633
24.4.2 Evolution of the Universe and Evolution of Life: the
Big Bang and the Tiny Bang . . . . . . . . . . . . . 1635
24.4.3 Fundamental Requirements . . . . . . . . . . . . . . 1635
24.4.4 Definition of Life in the Present Context . . . . . . . 1637
1
24.4.5 Modelling a Continuous Sequence of Physicochemical
Processes Leading to a Genetic Apparatus . . . . . . 1637
24.5 General Aspects of Life?s Emergence and Evolution . . . . . 1641
24.5.1 Information and Knowledge . . . . . . . . . . . . . . 1641
24.5.2 Processing Information and Genesis of Information
and Knowledge . . . . . . . . . . . . . . . . . . . . . 1642
24.5.3 Limits of Physicochemical Ways of Thinking . . . . 1645
24.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 1647
24.7 Problems and Exercises . . . . . . . . . . . . . . . . . . . . 1648
24.7.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 1648
24.8 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . 1650
24.9 Boxes and Foundations . . . . . . . . . . . . . . . . . . . . . 1650
24.9.1 Box 24.1.Genetic Apparatus . . . . . . . . . . . . . 1650
24.9.2 Foundation 24.1. Maxwell?s Demon . . . . . . . . . . 1650
24.9.3 Supplement 24.1: Search for Logical Conditions Driving
the Emergence of a Genetic Translation Device . . . 1653
24.9.4 Supplement 24.2. The Emergence of a Simple Genetic
Apparatus Viewed as a Supramolecular Engineering
Problem. A Thought Experiment. . . . . . . . . . . 1656
24.9.5 Supplement 24.3. Attempts to Model the Origin of Life1660
24.9.6 Supplement 23.4. Later Evolutionary Steps: Emergence
of an EyeWith Lens . . . . . . . . . . . . . . 1666
24.10Figure Captions . . . . . . . . . . . . . . . . . . . . . . . . . 1667