$(10$ pts$)$ A binary system of $n-$Hexane and $n-$Octane is introduced in a flash operation.

$($a$)$ determine the the q$-$line equation, if $40$mol$\%$ of feed is $n-$Hexane. Assume $60$mol$\%$ of feed is aimed to be vaporized in flash at atmospheric pressure.

$($b$)$ It is known that q$-$line intersects equilibrium curve when the liquid fraction of $n-$hexane is $0\mathrm{.}192.$ Then what is the corresponding fraction of $n-$hexane in gas phase at equilibrium?