A fractional distillation unit will be used to separate a mixture of $50$ mole $\%$ benzene and toluene at atmospheric pressure into products of $98\%$ purity using a reflux ratio $R=1\mathrm{.}2R_m.$ The feed is saturated liquid $($at the boiling point$).$ Use enthalpy balances to calculate

a$.(10)$ The vapor and distillate flows at the top of the column

b$.(10)$ The flow of bottom of the column

c$.(30)$ Find the number of theoretical trays with enthalpy$-$concentration method or Ponchon$-$Savarit method $($Specify which method is chosen in your solution$)$

Table $3\mathrm{.}1$ Properties of components

$\backslash$table$[[$Component$,\backslash$table$[[$Enthalpy of$],[$vaporization$,],[$cal$/$g mol$]],\backslash$table$[[$Specific heat at constant$],[$pressure$,$ cal$/$g mol$C$