$(50$ pts$)$ The feed $(325$kmo$\frac{l}{h}r)$ consists of methanol and water containing $43$ mole $\%$ methanol and $57$ mole $\%$ water. The overhead product is to contain $95$ mole $\%$ methanol and the bottom product contains $4$ mole $\%$ methanol. The feed is cold and for each mole of feed, $0\mathrm{.}28$ moles of vapor is condensed on the feed plate. The column runs with $R={1\mathrm{.}75}^{***}$Rmin, Assume constant relative volatility ${}_{A-B}=2\mathrm{.}8.$

alculate;

a$.$ The amount of distillate and bottom product flow rate

b$.R_{\text{m}\text{i}\text{n}}$

c$.q$ and $R$

d$.$ Percent recovery of methanol and the number of theoretical stages