In a facility, a mixture whose composition $($mole fractions$),$ boiling point and equilibrium constants are

given below will be separated by distillation. The column pressure is $P=13\mathrm{.}6$atm. The feed $(F=100mo\frac{l}{h})$ is in saturated

liquid form. The entire condenser is used in the system. Propane of $98\%$ purity is obtained with $98\%$ recovery. It

can be assumed that the molar fluxes and aj values through the column are constant and there is no pentane in the peak

product. The top temperature of the column is $40C$ and the bottom temperature is $110C.$

Calculate the following:

a$)$ Peak and bottom product flow rates $($mol$/$hour$)$ and composition $(\%$ mol$),$

b$)$ Minimum number of shelves required for total return flow,

c$)$ Minimum reflux rate,

d$)$ Theoretical number of shelves for reflux ratio $5.$