The microscopic model of a perfect solution

We have already given (see relation [A.2.28] and Table A.2.1 in Appendix 2) the macroscopic representation of a perfect solution and the resulting properties. Now, we are going to construct a microscopic model, to see which hypotheses yield the same expression for the Gibbs energy of mixing given by expression [A.2.6] (see Table A.2.1). 

We letum to the previous model (section 3.1), and we shall now determine Y by adding a seventh hypothesis to our model the exchange energy is null, i.e.  

by substituting this value into relation [3.13], we see that the total enthalpy is equal to the sum of the enthalpies of the two pure liquids, and therefore the enthalpy of mixing is zero. This means that our two solutions are mixed with no alteration of the energy - i.e. with no thermal effect. 

The Helmholtz energy of mixing is the same as the Gibbs energy of mixing (as the mixing volume is null), and in hght of relation [3.19] (w = 0), we calculate  

We can see that this relation is indeed identical to expression [A. 6] (see Table A.2.1 in Appendix 2). Thus, we have here a model of the perfect solution, and note tiiat this solution is not, as might be imagined, a solution in which there are no inter-molecular interactions, as is the case with a perfect gas. Rather, it is a solution in which the energy of interaction ab between two molecules of A and of B is the arithmetic mean of the energies of the A-A and B-B pairs because, in view of relations [3.4] and [3.23], we obtain  

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