Metals A and $B$ form non$-$ideal regular solid solution and the enthalpy of mixing is given by $H_{\text{m}\text{i}\text{x}}=$

$x(1-x)kJmol{e}^{-1},$ where $x$ represents mole fraction of the component B and $=9\mathrm{.}993kJmol{e}^{-1}.$

$($a$)$ Calculate the change in Gibbs free energy $(G)$ associated with the decomposition of a homogeneous

alloy of uniform composition $\stackrel{}{x}$ into B$-$rich and A$-$rich parts of compositions $\stackrel{}{x}+x$ and $\stackrel{}{x}-x$

respectively at temperatures of $($i$)250C$ and $($ii$)350C.$ It is given that $\stackrel{}{x}=0\mathrm{.}4,x=0\mathrm{.}1$ and gas

constant $R=8\mathrm{.}314Jmo{l}^{-1}{K}^{-1}.$

$($b$)$ Draw schematic free energy$-$composition curves at $($i$)250C$ and $($ii$)350C$ to show the $G$ values

calculated above