Chapter 8, Problem 11P

The operation of a constant density plug flow reactor for the production of a substance via an enzymatic reaction is described by the equation below, where V is the volume of the reactor, F is the flow rate of reactant $C,C_{\text{in}}\text{ and }{C}_{\text{out }}$ are the concentrations of reactant entering and leaving the reactor, respectively, and $K\text{ and }{k}_{\text{max}}$ are constants. For a 100-L reactor, with an inlet concentration of $C_{\text{in}}=0.2\text{ M, }$ an inlet flow rate of $L/s,k_{\text{max}}={10}^{-2}{\text{s}}^{-1},\text{ and }K=0.1$ M, find the concentration of C at the outlet of the reactor.

$\frac{V}{F}=-{\int }_{C_{\text{in}}}^{C_{\text{out}}}\frac{K}{k_{\text{max}}C}+\frac{1}{k_{\text{max}}}dC$