ISBN: 3540410783
TITLE: The Law of Mass Action
AUTHOR: Koudriavtsev/Jameson/Linert
TOC:

1 Maxwell - Boltzmann Statistics
1.1 Thermodynamics and probability. The Boltzmann - Planck theorem 1
1.1.1 The Boltzmann - Planck theorem 5
1.2 The Maxwell - Boltzmann distribution law 7
1.2.1 Continuous Maxwell - Boltzmann distribution 14
1.3 Calculation of most probable and mean values 17
1.4 Indistinguishable molecules. The Gibbs' paradox 21
1.5 Phase volume and the number of quantum states 24
1.6 Quantum statistics 26
1.6.1 Bose - Einstein statistics 27
1.6.2 Fermi - Dirac statistics 29
1.6.3 Comparison of the three types of statistics 29
1.6.4 Degenerate ideal gas 31
1.6.5 Applications of Bose - Einstein statistics: black-body radiation 34
1.6.6 Applications of Bose - Einstein statistics: heat capacity of solids 35
2 Ensembles, Partition Functions, and Thermodynamic Functions
2.1 Gibbs' approach, or how to avoid molecular interactions 43
2.2 The process of equilibration and increasing entropy 49
2.3 Microcanonical distribution 51
2.4 Canonical distribution 52
2.5 The probability of a macrostate 54
2.6 Thermodynamic functions derived from a canonical distribution 55
2.7 Some molecular partition functions.57
2.7.1 Degeneracy 58
2.7.2 Translational motion 59
2.7.3 Free rotation 61
2.7.4 Vibrational motion: linear harmonic oscillator 62
2.7.5 Total partition function of an ideal system 63
2.8 Fluctuations 64
2.9 Conclusions 69
3 The Law of Mass Action for Ideal Systems
3.1 The law of mass action, its origin and formal thermodynamic derivation 71
3.2 Statistical formulae for free energy 77
3.3 Statistical formulae for ideal systems 79
3.4 The law of mass action for ideal gases 81
3.4.1 Conversion to molar concentrations 83
3.4.2 Conversion to mole fractions 84
3.4.3 Standard states and standard free energies of reaction 85
3.5 The law of mass action for an ideal crystal. Spin crossover equilibria 89
3.6 Liquids 95
3.6.1 The law of mass action for an 'ideal liquid' 97
3.7 'Breakdown' of the law of mass action 99
3.8 Conclusions 105
4 Reactions in Imperfect Condensed Systems. Free Volume
4.1 Additive volume: a semi-empirical model of repulsive interactions 107
4.1.1 Binary equilibrium in a liquid with repulsive interactions 108
4.1.1 Non-isomolar equilibrium in a liquid with repulsive interactions 111
4.2. Lattice theories of the liquid state 117
4.3 The Lennard-Jones and Devonshire model 119
4.4 Chemical equilibria in Lennard-Jones and Devonshire liquids 122
4.5 The non-ideal law of mass action, activities, and standard states 129
4.6 Kinetic law of mass action 135
4.7 Conclusions 143
5 Molecular Interactions
5.1 Introduction 145
5.2 Empirical binary potentials 147
5.3 Taking into account nearest, next nearest, and longer range interactions in the condensed phase 151
5.4 Frequency of vibrations 155
5.5 The shape ofthe potential well in a cell 157
5.6 Free volume of a Lennard-Jones and Devonshire liquid 160
5.7 Experimental determination of parameters of the Lennard-Jones potential 164
5.7.1 Compressibility: the Born - LandC method .165
5.7.2 Acoustical measurements: the B.B. Kudryavtsev method 166
5.7.3 Viscosity of gases: the Rayleigh - Chapman method 170
Conclusions 171
6 Imperfect Gases.
6.1 Introduction. The Virial Theorem 173
6.2 The Rayleigh equation 176
6.2.1 Virial coefficients: the Lennard-Jones method for the determination of the parameters of a binary potential 177
6.2.2 Free energy derived from the Rayleigh equation of state 179
6.3 A gas with weak binary interactions: a statistical thermodynamics approach -180
6.4 Van der Waals equation of state 185
6.5 Chemical equilibria in imperfect gases 188
6.5.1 Isomolar equilibria in imperfect gases 189
6.5.2 A non-isomolar reaction in an imperfect gas 192
6.5.3 Separate conditions of ideal behaviour for attractive
and repulsive molecular interactions 195
6.5.4 Associative equilibria in the gaseous phase 196
6.5.5 Molecular interaction via a chemical reaction 198
6.6 Conclusions 200
7 Reactions in Imperfect Condensed Systems. Lattice Energy
7.1 Exchange energy 203
7.2 Non-ideality as a result of dependence of the partition function on the nature of the surroundings 205
7.3 Exchange free energy 208
7.4 Phase separations in binary mixtures 213
7.5 The law of mass action for an imperfect mixture in the condensed state 216
7.6 The regular solution model of steep spin crossover 219
7.7 Heat capacity changes in spin crossover 223
7.8 Negative exchange energy. Ordering. The Bragg - Williams approximation 226
7.9.Description of ordering taking into account triple interactions 232
7.10 Chemical equilibrium in ordered systems. Two-step spin crossover 234
7.11 Diluted systems 240
7.12 Conclusions 246
8 Chemical Correlations
8.1 Studies of variations of chemical reactivity 249
8.1.1 Molecular parameters governing variations of chemical reactivity 250
8.1.2. Solvent effects 252
8.1.3. Kinetic studies 254
8.1.4 Multidimensionality of variations. Reference reactions 257
8.2 Linear free energy relationship. Modification of reactants 261
8.3 Linear free energy relationship. Variation of solvent 267
8.4 Isoequilibrium and isokinetic relationships 270
8.4.1 Statistical-mechanical model of the IER in ideal systems 273
8.4.2 The IER in gas-phase reactions 276
8.4.3 Isokinetic relationships 278
8.4.4 Non-ideality as a source of an IER 282
8.4.5 IER and exchange energy 288
8.5 Conclusions 293
9 Concluding Remarks .295
10 Appendices
10.1 Lagrange equations and Hamilton (canonical) equations 303
10.2 Phase space 309
10.2.1 Thephasespaceofaharmonicoscillator 310
10.2.2 The phase space of an ideal gas 311
10.3 Derivation of the canonical distribution 313
10.4 Free volume associated with vibrations 314
10.5 Rotational contribution to the equilibrium constant of the ionisation of water 316
10.6 Forms of the law of mass action employing the lY function approximation of the factorial 317
10.7 Derivation of the van der Waals equation of state 318
10.8 Exchange energy 319
10.9 Activity coefficients derived from the non-ideality resulting from triple interactions .319
10.10 The law of mass action for a binary equilibrium in a system with non-additive volume and lattice energy 320
10.11 Physico-chemical constants and units of energy 322
11 Index 323
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