culture of bacteria that secrete a product in a chemostat that is operated at steady state. The

specific growth rate of biomass is described by the Monod equation, and the volumetric rate

of product formation is described by Leudeking$-$Piret kinetics: $\frac{dP}{dt}=(+)x$

This system is well characterized, such that the following constants are known:

$Y\frac{x}{s}=0\mathrm{.}7g\frac{x}{g}S,=0\mathrm{.}3g\frac{P}{g}x,S_0=20g\frac{S}{L}$

${}_{\text{m}\text{a}\text{x}}=1\mathrm{.}2h^{-1},=0\mathrm{.}6g\frac{P}{g}x-h,F=30L{h}^{-1}$

$Ks=0\mathrm{.}4\frac{g}{L},Y\frac{p}{s}=1\mathrm{.}6g\frac{P}{g}S,V=1000L$

The liquid feed to the chemostat is sterile and the flow rates entering and exiting the chemostat are

equal.

$1$ What is the steady state concentration for $S$ and $x,$ respectively?

$2$ If the volume of the reactor is kept constant, what value of the flow rate would cause 'washout'

of the reactor?

$3$ What should the flow rate be adjusted to in this chemostat to achieve the optimal productivity

of product formation?

$4$ What is the specific rate of product formation during cell maintenance alone?

$5$ Define the $$ coefficient in Leudeking$-$Piret kinetics. What is the total specific rate of product

formation?