Estimate the hat$(f{)}_1,$hat$(f{)}_2,$hat$({)}_1,$ and hat$({)}_2$ of a mixture of ethylene $(1)$ and propylene $(2)$ at $T=120C$ and $P=30$ bar assuming $y_1=0\mathrm{.}3$ in the case of$...$

$($a$)$ a non$-$ideal mixture considering the interaction between species $1$ and $2,$ where $k_{12}=0\mathrm{.}03.$

$($b$)$ an ideal mixture $($no cross term needs to be considered, i$.$e$.,{}_{12}=0).$