$(30)$ A fractional distillation column will be designed to separate $30000$kgmo$\frac{l}{h}$ of a mixture of $40$

mole $\%$ benzene and $60$ mole $\%$ toluene into an overhead product containing $97$ mole $\%$ benzene and a

bottom product containing $98$ moel $\%$ toluene. A reflux ratio of $3\mathrm{.}5$mol to $1$mol of product is to be used.

The molal latent heats of benzene and toluene are $7360$ and $7960ca\frac{l}{g}$mol, respectively. Benzene and

toluene form an ideal system with a relative volatility of about $2\mathrm{.}5$; use the equilibrium data given in

Table $2\mathrm{.}1.$ The feed has a boiling point of $95C$ at a pressure of $1$atm. Calculate the following

a$.(10)$ The flow rate of distillate $($D$),$ overhead product $($V$)$ and bottom product $($W$)$ per hour.

b$.(20)$ The number of ideal trays and the position of the feeding tray, minimum reflux ratio and the

minimum number of ideal trays for three different cases:

$($i$)(10)$ When the feed is saturated liquid $($liquid at its boiling point$)$;

$($ii$)(10)$ When the feed is a mixture of vapor $(50\%)$ and liquid $(50\%).$

Table $2\mathrm{.}1$ Liquid$-$Vapor Equilibrium data for benzene$($A$)-$toluene$($B$)$ system

Figure $2\mathrm{.}1$ Boiling Point diagram of Benzene$-$Toluene system