When added to one liter of an aqueous solution containing $150$ mmoles of NaCl, $50$ mmoles of compound $A_{3}x$ reversibly dissociates into to A and $x.$

$A_{3}x3A+x$

This dissociation reaction reaches equilibrium with an equilibrium constant, $K_c=25mM$ at $310K$ and $Kc=50mM$ at $320K.$

Find:

$($a$)$ Compute the standard free energy $G^{*}$ of this reaction $($use eqn $5\mathrm{.}2-6$ and the two known $K_c$ values $-$ divide one equation by the other$).$

$($b$)$ Assuming no volume change upon mixing, calculate the concentration of $A,x$ and $A_{3}x$ in the solution at equilibrium when $T=310K$ and $T=320K.$