$13\mathrm{.}13.$ Batch rectification at constant composition.

An acetone$-$ethanol mixture of $0\mathrm{.}5$ mole fraction acetone is to be

separated by batch distillation at $101$kPa.

Vapor$-$liquid equilibrium data at $101$kPa are as follows:

$($a$)$ Assuming an $\frac{L}{D}$ of $1\mathrm{.}5$ times the minimum, how many stages

should this column have if the desired composition of the distillate

is $0\mathrm{.}90$ mole fraction acetone when the residue contains $0\mathrm{.}1$ mole

fraction acetone?

$($b$)$ Assume the column has eight stages and the reflux rate is varied

continuously so that the top product is maintained constant at

$0\mathrm{.}9$ mole fraction acetone. Make a plot of the reflux ratio versus

the still$-$pot composition and the amount of liquid left in the

still$-$pot.

$($c$)$ Assume the same distillation is carried out at constant reflux

ratio $($and varying product composition$).$ It is desired to have a resi$-$

due containing $0\mathrm{.}1$ and an $($average$)$ product containing $0\mathrm{.}9$ mole

fraction acetone. Calculate the total vapor generated. Which method

of operation is more energy$-$intensive? Suggest operating policies

other than constant reflux ratio and constant distillate compositions

that lead to equipment or operating cost savings.