Derive approximate expression by regular solution theory

[alan]

The question is about to derive an approximate expression by regular solution theory, It is difficult for me to find relevant source on this question. However, the question to me is so vague that I do not know how to answer.

What I have tried is to search what the interaction parameter is, it gives me the
Flory–Huggins solution theory.
For regular solution, it is in the domain on chemistry.
Please have a look on the attachment.

 

[mjc123]

The wikipedia article gives you the expression for the entropy of mixing. In terms of the interaction parameter, the molar enthalpy of mixing is RTχx₁x₂, where x₁ and x₂ are the mole fractions of the two components. Can you get an expression for the molar Gibbs energy of mixing? What would be the criterion, in terms of ΔG, for the limit of solubility?