A mixture containing $40$ mol$\%$ of benzene and $60$ mol$\%$ of chlorobenzene is separated

by flash distillation until $70\%$ of the initial charge is taken off as overhead. Further the vapor stream from the flash distillation is subjected to a condenser before it fed to a

fractionation distillation column. A distillated product from the fractionation column

containing $95$ mol$\%$ of benzene and a bottom containing $90$ mol$\%$ of chlorobenzene.

The reflux ratio for this process is $1\mathrm{.}3$ and the q value used is $0\mathrm{.}6.$ Equilibrium data for

benzene$-$chlorobenzene system is given below.

xA $00\mathrm{.}10\mathrm{.}20\mathrm{.}40\mathrm{.}60\mathrm{.}80\mathrm{.}91\mathrm{.}0$

yA $00\mathrm{.}370\mathrm{.}570\mathrm{.}780\mathrm{.}890\mathrm{.}950\mathrm{.}981\mathrm{.}0$

a$)$ Sketch the schematic diagram of the system.

$($b$)$ Determine the number of theoretical trays.

$($c$)$ If the reflux ratio were increased, explain the effect to the number of

theoretical stages.