$(30$ pts$)$ For the mixture of $n{C}_6(H)$ and $n{C}_8(C),$ using the $y-x$ and $T-y-x$ diagrams at $14\mathrm{.}7$ psia in the Figures below, determine $(1)$ the ratio of mole fraction in Vapor and Liquid phases at $175F$ and $z_H=0\mathrm{.}85$; $(2)$ plot the $q-$line in the $y-$x Figure and determine the compositions of the vapor and liquid phases. Mole fraction $n-$hexane in liquid, $x$