A distillation column composed of theoretical plates is used to separate a benzene$-$toluene mixture. The

feed is $500mo\frac{l}{h}$ introduced as saturated liquid and contains $40$mol$\%$ benzene. During a run, liquid and

vapor samples of streams leaving a stage in the rectifying section are taken, and the analyses are y$=0\mathrm{.}63$ mole fraction benzene, x$=0\mathrm{.}51$ mole fraction benzene

The total condenser produces a stream of $96$mol$\%$ benzene, and the thermosyphon reboiler produces a liquid

$($bottom$)$ stream with $5$mol$\%$ benzene. The equilibrium curve for the benzene follows the equation