Four hundred and fity bmol$/$h $(204$ kmol$/$h$)$ of a mixture of $60$mol$\%$ benzene $($LK$)$ and $40$ mol$\%$ toluene $($HK$)$ is to be separated into a liquid distillate and a liquid bottoms product of $95$ mol$\%$ and $5$ mol$\%$ benzene, respectively. The feed enters the column with a molar percent vaporization equal to the distillate$-$to$-$feed ratio. Use the McCabe$-$Thiele method to compute, at $1$atm $(1013$ kPa$)($a$)$ Nmin. $($B$)$ Rmin and $($c$)$ number of equilbrium stages N$,$ for R$=$Rmin$*1\mathrm{.}3,$ and the optimal feed$-$stage location.

Equilithrim data:

$\backslash$table$[[x,04,02,03,04,0\mathrm{.}5,0\mathrm{.}6,07,0\mathrm{.}8,09,1],[y,02,035,051,063,071,078,0\mathrm{.}85,091,096,1]]$