The following equations have been proposed to represent the

activity coefficients for a system at tixed $T$ and $P$ :

$ln{}_1=x_2^2(0\mathrm{.}5+2x_1)$

$ln{}_2=x_1^2(1\mathrm{.}5-2x_1)$

$($a$)$ Do these equations satisty the Gibbs Duhem equation?

$($b$)$ Determine an expression for $\frac{GE}{RT}$ for the system.