$7\mathrm{.}24.$ Calculation of distillation graphically and analytically.

A saturated$-$liquid feed of $69\mathrm{.}4$ mol$\%$ benzene $($B$)$ in toluene $($T$)$

is to be distilled at $1$ atm to produce a distillate of $90$ mol$\%$ benzene,

with a yield of $25$ moles of distillate per $100$ moles of feed. The feed

is sent to a steam$-$heated reboiler, where bottoms is withdrawn continuously.

The vapor from the reboiler goes to a partial condenser

and then to a phase separator that returns the liquid reflux to the

reboiler. The vapor from the separator, which is in equilibrium with

the liquid reflux, is sent to a total condenser to produce distillate. At

equilibrium, the mole rat$7\mathrm{.}24.$ Calculation of distillation graphically and analytically.

A saturated$-$liquid feed of $69\mathrm{.}4$mol$\%$ benzene $($B$)$ in toluene $(T)$ is to be distilled at $1$atm to produce a

distillate of $90$mol$\%$ benzene, with a yield of $25$mols of distillate per $100$moles of feed. The feed is sent

to a steam$-$heated reboiler, where bottom is withdraw continuously. The vapor from the reboiler goes to a

partial condenser and then to a phase separator that returns the liquid to reflux to the reboiler. The vapor

from the partial condenser is sent to a total condenser to produce distillate. At equilibrium the mole ratio

of $B$ to $T$ in the vapor from the reboiler is $2\mathrm{.}5$ times the mole ratio of $B$ to $T$ in the bottoms.

Calculate analytically and graphically the total moles of vapor generated in the reboiler per $100$mol of

feed.

Hint:

Graphical Method:On the McCabe$-$Thiele diagram below, the equilibrium curve isobtained from Eq$.(7-3),$

$y=\frac{x}{1+x(-1)}=\frac{2\mathrm{.}5x}{1+1\mathrm{.}5x},$

the equilibrium $x,y$ data are calculated and plotted below.