For simplicity, let$$s assume ethanol is easily separated from the products such that a saturated

liquid mixture of $65$ mol$\%$ ethyl acetate, with balance acetic acid, needs to be distilled to produce

a distillate of $95$ mol$\%$ ethyl acetate and a bottoms of $10$ mol$\%$ ethyl acetate. Assume a total

condenser and partial reboiler.

The vapor$-$liquid equilibrium data are given as mole fractions of ethyl acetate and plotted as

shown:

Liquid, x Vapor, y

$0\mathrm{.}0000\mathrm{.}000$

$0\mathrm{.}1630\mathrm{.}473$

$0\mathrm{.}3170\mathrm{.}689$

$0\mathrm{.}5800\mathrm{.}893$

$0\mathrm{.}7310\mathrm{.}949$

$0\mathrm{.}9030\mathrm{.}979$

$0\mathrm{.}9300\mathrm{.}987$

$1\mathrm{.}0001\mathrm{.}000$

In answering the following questions, please provide all number of stages to one decimal place.

Note you can use the lever rule to estimate fractional stages. You may find it helpful to copy the

graph above for each sub$-$part of the problem and draw the lines onto the graph. Also, note that a

partial reboiler is an equilibrium stage but not considered a tray in the column.

a$.$ What is the minimum number of equilibrium stages needed for this system?

b$.$ What is the minimum reflux ratio $($Rmin$)$ needed for this separation to occur? Note that at

minimum reflux, the number of stages goes to infinity. What is the boilup ratio at this

reflux?

c$.$ Let R $=1\mathrm{.}5$ Rmin $.$ How many equilibrium stages are required for this separation? What is

the optimal feed stage