For the following gas systems, estimate hat$({)}_1,$hat$({)}_2,$hat$(f{)}_1$ and hat$(f{)}_2($Using two methods: $1)$ through application of Equation $11\mathrm{.}63$ for binary mixtures and $2)$ assuming that the mixture is an ideal solution$)$:

$($a$)$ ethylene $(1)/$propylene$(2)$ at $T=120C,P=30$ bar, and $y_1=0\mathrm{.}45.$

$($b$)$ ethylbenzene$(1)/$benzene $(2)$ at $T=140C,P=2$ bar, and $y_1=0\mathrm{.}45.$