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Imagine a culture of bacteria in a steady$-$state chemostat that secretes a

primary product. The specific growth rate of biomass is adequately described

by the Monod equation, and the rate of product is described

$q_p=Y_{\frac{p}{x}}$ in $kg\frac{P}{k}g\frac{x}{h}$

Because of this system's excellent characterization, the following constants are

understood:

$Y\frac{x}{S}=0\mathrm{.}3\frac{g}{g},Y\frac{P}{x}=0\mathrm{.}2\frac{g}{g},Y\frac{P}{S}=0\mathrm{.}8\frac{g}{g}$

$max=0\mathrm{.}6h-1,F=20\frac{L}{h},V=300L$

$KS=0\mathrm{.}1\frac{g}{L},S_o=10\frac{g}{L},$

There is an equal flow rate entering and leaving the chemostat, and the liquid

feed is sterile.

$1-$ Write steady$-$state mass balances for $S,x,$ and $P.$

$2-$ What is the steady$-$state concentration of $S?$

$3-$ What is the steady$-$state concentration of $x?$ If you were unable to obtain

an answer for $S$ in part $b,$ use $S=0\mathrm{.}2\frac{g}{L}.$

$4-$ If the volume of the reactor is kept constant, what value of the flow rate

would cause "washout" of the reactor?