Question $(2)$: please explain all the steps and draw on paper.

$(5$marks$)$

A liquid mixture of benzene and toluene is being distilled in a fractionating column at $101\mathrm{.}3$kPa. The feed of $100$kmo$\frac{l}{h}$ enters the column at a dew point $($saturated vapour$)$ and it contains $45\%$ benzene and $55\%$ toluene. A distillate containing $95\%$ benzene and $5\%$ toluene and a bottom containing $10\%$ benzene and $90\%$ toluene is required $($specifications$).$ If the amount of liquid fed back to the column at the top is $4$ times the distillate product.

Calculate:

The rate of distillate and the rate of bottom. $(1$mark$)$

Number of theoretical stages at the operating reflux. $(2$marks$)$

The minimum number of theoretical stages required at total reflux. $(0\mathrm{.}5$marks$)$

If the actual number of stages are $10,$ what is:

$($a$)$ The overall efficiency at operating condition. $(0\mathrm{.}5$mark$)$

$($b$)$ The overall efficiency at total reflux. $(0\mathrm{.}5$mark$)$

$($c$)$ What is the overall efficiency increased at operating condition compared to the condition of total reflux? $(0\mathrm{.}5$mark$)$

VLE Equilibrium Data

$\backslash$table$[[$Benzene$-$liquid mole fraction,Benzene$-$vapour mole fraction$],[1,1],[0\mathrm{.}78,0\mathrm{.}9],[0\mathrm{.}58,0\mathrm{.}777],[0\mathrm{.}45,0\mathrm{.}657],[0\mathrm{.}258,0\mathrm{.}456],[0\mathrm{.}13,0\mathrm{.}261],[0,0$