A total mixture of $100$mol that contains $60\%$ mol of $n-$ pentane and $40\%$mol of $n-$ heptane is undergoing a single $-$ stage distillation at $1$atm. The process aims to yield $40$mol vapor and $60$mol liquid that are in equilibrium with each other. Determine the composition of the vapor and liquid. Use the data below $($mole fractions of $n-$ pentane$)$: $(10$ PTS$)$

$\backslash$table$[[x,1\mathrm{.}000,0\mathrm{.}867,0\mathrm{.}594,0\mathrm{.}398,0\mathrm{.}254,0\mathrm{.}145,0\mathrm{.}059,0],[y,1\mathrm{.}000,0\mathrm{.}984,0\mathrm{.}925,0\mathrm{.}836,0\mathrm{.}701,0\mathrm{.}521,0\mathrm{.}271,0]]$