Problem $1$

We have a binary liquid$-$vapor two$-$phase system, with components A and $B,$ where $A$ is the more volatile

matter. The molecular weight of component A is $90k\frac{g}{k}$mol and the molecular weight of component $B$

is $110k\frac{g}{k}$mol. Experimental results show that the relative volatility is $3\mathrm{.}0.$

$($a$)$ The feed flow rate is $120$kmo$\frac{l}{m}in$ and the concentration of the more volatile matter in the feed is

$60$ mole percent. The feed is half $(50\%)$ saturated liquid and saturated half $(50\%)$ vapour $($by mole$)$

at the temperature of the feed plate. The reflux ratio is $2\mathrm{.}0.$ If we would like to have $95$ mole percent

of component $A$ in the top distillate and the column has $5$ plates $($assuming $100$ percent plate

efficiency$)$ excluding the reboiler, what would be the composition of the bottom product? What are

the flow rates of the top and bottom products? Graphical solution required.

$($b$)$ Now, we would like to increase the feed flowrate by $20\%.$ Assume that we must use the existing

distillation column so that the heating capacity of the reboiler at the bottom cannot be increased, that

is$,$ the amount of vapour generated by the reboiler and flow up in the stripping section cannot be

increased. However, we may be able to squeeze in one or two more plates in the column if necessary.

In this case, if we still want to have the same level of separation as in Case $($a$),$ what would be the

new reflux ratio and how many theoretical plates are required? Graphical solution required.