Continuous fractionating column is required to separate a mixture containing $0\mathrm{.}695$ mole

fraction $n-$heptane $(C_7{H}_{16})$ and $0\mathrm{.}305$ mole fraction $n-$octane $(C_8{H}_{18})$ into products of $99$ mole

per cent purity. The column is to operate at $101\mathrm{.}3$kPa. The feed is all liquid at its boiling$-$point,

and this is supplied to the column at $1\mathrm{.}25k\frac{g}{s}.$ The boiling$-$point at the top of the column may

be taken as $372K,$ and the equilibrium data are:

Assume a total condenser, partial reboiler, saturated$-$liquid reflux, and optimal feed stage.

Please carry out the following by hand calculations:

a$)$ Determine $R_{\text{m}\text{i}\text{n}}.$

b$)$ Determine $N_{\text{m}\text{i}\text{n}}.$

c$)$ Determine the optimum feed tray location.

d$)$ Determine $Q_C$ and $Q_B.$

e$)$ Using $R=1\mathrm{.}3R_{\text{m}\text{i}\text{n}}$ determine the number of theoretical trays required to achieve the

required separation.

f$)$ If the Murphree vapor efficiency, EMV, is $50\%.$ determine the number of theoretical

trays required to achieve the required separation.