The Law of Mass Action, Softcover reprint of the original 1st ed. 2001

'Why are atoms so small?' asks 'naive physicist' in Erwin Schrodinger's book 'What is Life? The Physical Aspect of the Living Cell'. 'The question is wrong' answers the author, 'the actual problem is why we are built of such an enormous number of these particles'. The idea that everything is built of atoms is quite an old one. It seems that l Democritus himself borrowed it from some obscure Phoenician source . The arguments for the existence of small indivisible units of matter were quite simple. 2 According to Lucretius observable matter would disappear by 'wear and tear' (the world exists for a sufficiently long, if not infinitely long time) unless there are some units which cannot be further split into parts. th However, in the middle of the 19 century any reference to the atomic structure of matter was considered among European physicists as a sign of extremely bad taste and provinciality. The hypothesis of the ancient Greeks (for Lucretius had translated Epicurean philosophy into Latin hexameters) was at that time seen as bringing nothing positive to exact science. The properties of gaseous, liquid and solid bodies, as well as the behaviour of heat and energy, were successfully described by the rapidly developing science of thermodynamics.

1 Maxwell — Boltzmann Statitics.- 1.1 Thermodynamics and probab ility. The Boltzmann — Planck theorem.- 1.1.1 The Boltzmann — Planck theorem 5.- 1.2 The Maxwell — Boltzmann distribution law.- 1.2.1 Contin uous Maxwell — Boltzmann distribution.- 1.3 Calculation of most probable and mean values.- 1.4 Indistinguishable molecules. The Gibbs’ paradox.- 1.5 Phase volume and the number of quantum states.- 1.6 Quantum statistics.- 1.6.1 Bose — Einstein statistics.- 1.6.2 Ferm i — Dirac statistics.- 1.6.3 Comparison of the three types of statis tics.- 1.6.4 Degenera te ideal gas.- 1.6.5 App lications of Bose — Einstein statistics: black-body radiation.- 1.6.6 Applications of Bose — Einstein statistics: heat capacity of solids.- 2 Ensembles, Partition Functions, and Thermodynamic Functions.- 2.1 Gibbs— approach, or how to avoid molecular interactions.- 2.2 The process of equilibration and increasing entropy.- 2.3 Microcanonical distribution.- 2.4. Canonical distribution.- 2.5 The probability of a macrostate.- 2.6 Thermodynamic functions derived from a canonical distribution.- 2.7 Some molecular partition functions.- 2.7.1 Degeneracy.- 2.7.2 Translational motion.- 2.7.3 Free rotation.- 2.7.4 Vibrational motion: linear harmonic oscillator.- 2.7.5 Total parti tion function of an ideal system.- 2.8 Fluctuations.- 2.9 Conclusions.- 3 The Law of Mass Action for Ideal Systems.- 3.1 The law of mass action, its origin and formal thermodynamic derivation.- 3.2 Statistical formulae for free energy.- 3.3 Statis tical formul ae for ideal sys tems.- 3.4 The law of mass action for ideal gases.- 3.4.1 Conversion to molar concent rations.- 3.4.2 Conversion to mole fractions.- 3.4.3 Standard sta tes and standard free energies of reaction.- 3.5 The law of mass act ion for an ideal crys tal. Spin crossover equilibria.- 3.6 Liquids.- 3.6.1 The law of mass action for an ‘ideal liquid’.- 3.7 ‘Breakdown’ of the law of mass action.- 3.8 Conclusions.- 4 Reactions in Imperfect Condensed Systems. Free Volume.- 4.1 Additive volume: a semi-empirical model of repulsive interactions.- 4.1.1 Binary equilibrium in a liquid with repul sive interactions.- 4.1.1 Non-isomolar equilibrium in a liquid with repulsive interactions.- 4.2. Lattice theories of the liquid state.- 4.3 The Lennard-Jones and Devonshir e model.- 4.4 Chemica l equi libria in Lennard-Jones and Devon shire liquids.- 4.5 The non-id eal law of mass action, activities, and standard states.- 4.6 Kinetic law of mass action.- 4.7 Conclusions.- 5 Molecular Interactions.- 5.1 Introduction.- 5.2 Empirical binary potentials.- 5.3 Taking into account nearest, next nearest, and longer range interactions in the conde nsed phase.- 5.4 Frequency of vibrations.- 5.5 The shape of the potential wcll in a cell.- 5.6 Free volume of a Lennard-Jones and Devons hire liquid.- 5.7 Experimental determ ination of parameters of the Lennard-Jones potential.- 5.7.1 Compressibility: thc Born’ Lande method.- 5.7.2 Acoustical meas urements: the B.B. Kudryavtsev method.- 5.7.3 Viscosity of gases: the Rayleigh’ Chapman method.- 5.8 Conclusions.- 6 Imperfect Gases..- 6.1 Introduction. The Virial Theorem.- 6.2 The Rayleigh equation.- 6.2.1 Virial coefficients: the Lennard-Jones method for the determination of the parameters of a binary potential.- 6.2.2 Free energy der ived from the Rayleigh equation of state.- 6.3 A gas with weak binary interactions: a statistical thermodynamics approach.- 6.4 Van der Waals equation of state.- 6.5 Chemical equilibria in imperfect gases.- 6.5.1 Isomolar equilibria in imperfect gases.- 6.5.2 A non-isomolar reaction in an imperfect gas.- 6.5.3 Separate conditions of ideal behaviour for attractive and repul sive molecular interactions.- 6.5.4 Associat ive equilibria in the gaseous phase.- 6.5.5 Mole cular interaction via a chemical reaction.- 6.6 Conclusions.- 7 Reactions in Imperferct 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.- 7.3 Exchange free energy.- 7.4 Phase separations in binary mixtures.- 7.5 The law of mass action for an imperfect mixture in the condensed state.- 7.6 The regular solut ion model of steep spin crossover.- 7.7 Heat capacity changes in spin crossover.- 7.8 Negative exchange energy. Ordering . The Bragg — Williams approximation.- 7.9. Description of order ing taking into account triple interactions.- 7.10 Chemica l equilibrium in ordered systems. Two-step spin crossover.- 7.11 Diluted systems.- 7.12 Conclusions.- 8 Chemical Correlations.- 8.1 Studies of variations of chemical reactivity.- 8.1.1 Molecular parameters governing variations of chemical reactivity.- 8.1.2. Solvent effects.- 8.1.3. Kinetic studies.- 8.1.4. Multidimensionality of var iations. Reference reactions.- 8.2 Linear free energy relationship. Modification of reactants.- 8.3 Linear free energy relationship. Variation of solvent.- 8.4 Isoequilibrium and isokinetic relationships.- 8.4.1 Statistical-mechanical model of the IER in ideal systems.- 8.4.2 The IER in gas-phase reactions.- 8.4.3 lsokinetic relationships.- 8.4.4 Non-ideality as a source of an IER.- 8.4.5 lER and exchange energy.- 8.5 Conclusions.- 9 Concluding Remarks.- 10 Appendices.- 10.1 Lagrange equations and Hamilt on (canonical) equations.- 10.2 Phase space.- 10.2.1 The phase space of a harmonic oscillator.- 10.2.2 The phase space of an ideal gas.- 10.3 Derivation of the canonical distribution.- 10.4 Free volume assoc iated with vibrations.- 10.5 Rotational con tribution to the equilibrium constant of the ionisation of water.- 10.6 Forms of the law of mass action employing the function approximation of the factorial.- 10.7 Derivation of the van der Waals equation of state.- 10.8 Exchange energy.- 10.9 Activity coefficients derived from the non-ideality resulting from triple interactions.- 10.10 The law of mass action for a binary equilibrium in a sys tem with non- additive volume and lattice energy.- 10.11 Physico-chemical constants and units of energy.