Problem $1$:

a$.$ For a binary solution, the molar Gibbs free energy of mixing is expressed as

$x(1-x)+RT[xln(x)+(1-x)ln(1-x)],$ where $$ is a constant.

Calculate the following as a function of composition $(x)$

i$.$ molar entropy of mixing

ii$.$ molar enthalpy of mixing

iii. molar volume of mixing

b$.$ Which solution model $($Ideal$,$ Henrian or Regular$)$ does this follow? Justify.