Saccharomyces cerevisiae yeast produces ethanol $(C_2{H}_{5}OH)$ from glucose $(C_6{H}_{12}{O}_6)$ under anaerobic conditions without external electron acceptors. The biomass yield from glucose is $0\mathrm{.}17\frac{g}{g}$ and the nitrogen source is $N{H}_3.$ The universal description is assumed for the cell composition. After the fermentation, the biomass is separated and the liquid mixture ethanol$/$water proceeds to a

distillation column from which pure ethanol is extracted at the bottom. In the distillation stage,

benzene is added to lower the volatility of the alcohol. Under these conditions, the overhead product

is a constant$-$boiling mixture of $10\%$ ethanol, $15\%H_{2}O,$ and $75\%$ benzene.

Set up the stoichiometric equation and the atomic balances for the fermentation. What is the

yield of ethanol from glucose? $(7)$

What is the composition $(\frac{w}{v}\%),$ of the liquid mixture leaving the fermenter and entering the

distillation tower? $(3)$

Draw the flow sheet of the distillation column. What is the volume of benzene in order to

produce $400L$ of pure ethanol? $(5)$

Additional data:

$H$ molar weight $=1\frac{g}{\text{m}\text{o}\text{l}}$

$C$ molar weight $=12($g$)/($mol$)$

$N$ molar weight $=14($g$)/($mol$)$

O molar weight $=16($g$)/($mol$)$

Benzene density $=0\mathrm{.}872\frac{g}{c}{m}^3$

Ethanol density $=0\mathrm{.}785\frac{g}{c}{m}^3$