From the emf measurements at $527C,$ the following values of the activity coefficient of $Cd$ in $Zn-Cd$ solutions have been obtained:

$\backslash$table$[[x_{Cd},0\mathrm{.}2,0\mathrm{.}3,0\mathrm{.}4,0\mathrm{.}5],[{}_{Cd},2\mathrm{.}153,1\mathrm{.}817,1\mathrm{.}544,1\mathrm{.}353]]$

Calculate the values of

$($a$)$ The partial molar heat of mixing $($cal$/$mole$)$ of $Zn$ and $Cd(10p)$

$($b$)$ The integral molar heat of mixing $($cal$/$mole$)(5p)$

$($c$)$ The integral molar entropy of mixing $(ca\frac{l}{K}*mole)(5p)$

$($d$)$ The partial molar Gibbs free energy of mixing $($cal$/$mole$)$ of $Zn$ and $Cd(10p)$

$($e$)$ The integral molar Gibbs free energy of mixing $($cal$/$mole$)(5$ p$)$

For an equi$-$atomic solution of $Zn-Cd,$ assuming regular solution behaviour at $527C.$

$R=0\mathrm{.}0821\frac{lt*atm}{\text{m}\text{o}\text{l}\text{e}*K}=1\mathrm{.}987\frac{\text{c}\text{a}\text{l}}{\text{m}\text{o}\text{l}\text{e}*K}=8\mathrm{.}3144\frac{J}{\text{m}\text{o}\text{l}\text{e}*K}$