A benzene$-$toluene mixture containing $30$mol$\%$ benzene is desired to be separated into a bottoms product containing $95$mol$\%$ toluene with the distillate containing $90$mol$\%$ benzene. The reflux ratio is $5.$ Determine the number of theoretical tray and the position of the feed tray

a$)$ If the feed is saturated vapor

b$)$ If the feed is at a temperature of $283K.$

PLEASE SOLVE IT BY SHOWING IT ON THE GRAPH.

$\backslash$table$[[x,0,0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}3,0\mathrm{.}4,0\mathrm{.}5,0\mathrm{.}6,0\mathrm{.}7,0\mathrm{.}8,0\mathrm{.}9,1],[y,0,0\mathrm{.}2,0\mathrm{.}37,0\mathrm{.}5,0\mathrm{.}6,0\mathrm{.}7,0\mathrm{.}78,0\mathrm{.}84,0\mathrm{.}9,0\mathrm{.}95,1]]$

$M_B=78\frac{g}{m}ol,T_{\text{B}\text{e}\text{n}\text{z}\text{e}\text{n}\text{e}}=353\mathrm{.}3K$

$M_T=92\frac{g}{m}ol,T_{\text{T}\text{o}\text{l}\text{u}\text{e}\text{n}\text{e}}=383\mathrm{.}8K$

$=30000k\frac{j}{k}$mol,$C_{PL}=1\mathrm{.}84k\frac{j}{k}gK$