Question $3-$ Steady$-$state Chemostat Operation: Mass Balance $(20$ Points$)$

In a steady$-$state chemostat operation a microorganism receives Phenyl Acetic Acid $($PAA$)$ as the substrate $($S$)$ and produces Penicillin $($Pen$)$ as the product $($P$).$ The inflow to the chemostat is $0\mathrm{.}10\frac{m^3}{h}$ and contains $10$mol PAA $\frac{?}{m^3}.$ The outflow has a flow rate of $0\mathrm{.}12\frac{m^3}{h}$ and contains $6\mathrm{.}3$mol PAA $\frac{?}{m^3}$ and $2\mathrm{.}0$molPE$\frac{N}{m^3}.$ For pH$-$control a titrant flow enters to the chemostat at $0\mathrm{.}02\frac{m^3}{h}.$

$($a$)$ Illustrate the flowsheet $($as black$-$box model$)$ for the chemostat as described in the problem statement. Write down the quantitative information regarding the streams. $(8$ Points$)$

$($b$)$ Calculate the yield of PEN production per PAA consumed as mol ratio $($Yp$/$s$).(12$ Points$)$