$(20\%)$ A binary A$-$B liquid solution is at constant temperature $T$ and pressure $P,$ and the

Gibbs energies of pure liquid A and $B$ are $G_A^0$ and $G_B^0,$ respectively.

$($a$)$ If the solution is an ideal solution, what are the enthalpy change of mixing, entropy

change of mixing and Gibbs energy change of mixing?

$($b$)$ If the solution is not an ideal solution, and its excess Gibbs energy is given by the

following equation: $\frac{G^E}{R}T=x_A{x}_B(0\mathrm{.}4x_A+0\mathrm{.}2x_B).$ Draw a schematic Gibbs

energy$-$composition diagram, and indicate on the diagram the values of the partial

Gibbs energy, $\frac{?}{\text{b}\text{a}\text{r}}(G_A)$ and $\frac{?}{\text{b}\text{a}\text{r}}(G_B),$ at $x_B=0\mathrm{.}7.$