Statistical thermodynamics - Thermodynamics of solutions

Understanding and determining complex equilibria is a major concern for thermodynamic chemists, as the practical problems they face often boil down to understanding these equilibria. Solving systems of equations representing the equilibrium of a system with different phases, each of which is made up of several constituents, requires us to express the enthalpy and entropy of formation or mixing of each of the phases, and not only to evaluate these quantities, but above all to formulate their variations with temperature and composition (see "Chemical thermodynamics" in this treatise).

This booklet deals with the statistical thermodynamics of condensed phases. Examples highlight the importance of phase structure.

We describe various interaction models that allow us to represent the thermodynamic quantities of mixing solid substitution or insertion solutions and liquid solutions. Indeed, it is possible to account for the properties of these solutions using simple atomic models (e.g. first-neighbor pairs, triplets, tetrahedra, surrounded atoms). For these various models, and to various orders of approximation, the calculation of the partition function of the solution becomes possible and enables the calculation of thermodynamic functions.

In particular, the free energy of mixing ΔF ' of a solution A-B from pure constituents A and B (which represents the variation in free energy of the system between the unmixed and mixed states) is given by : $\mathrm{\Delta }{F}^{\prime }=-\mathrm{\hspace{0.17em}}\mathit{kT}\left(\ln \mathrm{\hspace{0.17em}}{Q}_{\mathit{AB}}-\ln \mathrm{\hspace{0.17em}}{Q}_A-\ln \mathrm{\hspace{0.17em}}{Q}_B\right)$

Q _AB , Q _A and Q _B being respectively the partition functions of the solution and the pure components A and B.

This approach links the macroscopic properties of solutions to the atomic properties of their constituents. The originators of such models are Bragg and Williams [5] and Guggenheim [6] .

Please also refer to the table of notations in "Statistical thermodynamics. Overview". ....