$9\mathrm{.}3$ The variation, with composition, of $G^{xS}$ for liquid $Fe-Mn$ alloys at $1863K$ is as follows:

$\backslash$table$[[x_{Mn},0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}3,0\mathrm{.}4,0\mathrm{.}5,0\mathrm{.}6,0\mathrm{.}7,0\mathrm{.}8,0\mathrm{.}9],[G_{xS}J,395,703,925,1054,1100,1054,925,703,395]]$

a$.$ Does the system exhibit regular solution behavior?

b$.$ Calculate ${?}_{-}^{-xs}$ and ${?}_{Ge}^{-xs}$ at $x_{Mn}=0\mathrm{.}6.$

c$.$ Calculate $A{G}^M$ at $x_{Mn}=0\mathrm{.}4.$

d$.$ Calculate the partial pressures of $Mn$ and $Fe$ exerted by the alloy of $x_{Mn}=0\mathrm{.}2.$