For the system $n-$pentane $(1)-n-$heptane $(2),$ the vapour pressures are given by

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$02000$ CHT$202052102$

the Antoine equation $ln{P}^s(kPa)=A-\frac{B}{T(K)+C}$

The constants are given as

$\backslash$table$[[$Component$,$A$,$B$,$C$],[$n$-$pentane,$13\mathrm{.}8183,2477\mathrm{.}07,40\mathrm{.}00],[$n$-$heptane,$13\mathrm{.}8587,2911\mathrm{.}32,56\mathrm{.}56]]$

Assuming that the solution formed is ideal, calculate:

$($i$)$ The composition of the liquid and vapour in equilibrium at $95$kPa and $336\mathrm{.}2K$

$($ii$)$ The composition of the vapour in equilibrium with a liquid containing $34\%($mol$)$ pentane if the equilibrium temperature is $344\mathrm{.}4K$ at pressure $P=95$kPa.

$($iii$)$ The total pressure and the vapour composition in equilibrium with a liquid of composition $x_1=0\mathrm{.}44$ at temperature $T=333\mathrm{.}2K.$