Free energy of an ideal incompressible solution and chemical potentials

FREE ENERGY OF AN IDEAL INCOMPRESSIBLE SOLUTION AND CHEMICAL POTENTIALS 

Let us consider an ideal solution made of m components in a volume V. Each chemical species is denoted by an index st (with at = 1. m). The numbers of molecules belonging to each species in the solution will be represented by the symbols and the concentrations by 

Let us try to calculate the Gibbs free energy of the solution it reads 

is the energy and S the entropy. For an ideal solution, we may write 

When the molecular volumes of the various chemical species are equal, the problem is simple. In fact, in this case, we can admit that the molecules occupy the N sites of a lattice. Then the number of different configurations is 

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