A distillation column is separating a mixture of benzene, toluene, ethylbenzene and cumene. The feed to the column is $5\mathrm{.}0$ mol$\%$ benzene, $15\mathrm{.}0$ mol$\%$ toluene, $35\mathrm{.}0$ mol$\%$ ethylbenzene and $45\mathrm{.}0$mol$\%$ cumene. Feed rate is $100\mathrm{.}0$kmo$\frac{l}{h}$ and is a saturated liquid. We wish to produce a distillate that is $0\mathrm{.}58$ mole fraction ethylbenzene, $0\mathrm{.}07$ mole fraction cumene, and the remainder is toluene and benzene. The bottoms should contain no benzene or toluene. If we select toluene as the reference component, the relative volatilities are approximately constant in the and cormene $=0\mathrm{.}210.$

a$.$ Find distillate and bottoms flow rates.

b$.$ Find the number of equilibrium stages at total reflux. $R_{}$Nmin

c$.$ Which case $(A$ or $B$ or $C)$ will you use to calculate $R_{\text{m}\text{i}\text{n}}$ using Underwood second equation, and why?

d$.$ Calculate the number of equilibrium stages required for the above separation, if $R_{\text{m}\text{i}\text{n}}=2\mathrm{.}3$ and $R=1\mathrm{.}5(R_{\text{m}\text{i}\text{n}}).$