P$8-3B_B$ The following reactions

$A{}^{k_1}D,-r_{1A}=k_1[C_A-\frac{C_D}{K_{1A}}]$

$A{}^{k_2}U,-r_{2A}=k_2[C_A-\frac{C_U}{K_{2A}}]$

take place in a batch reactor.

Additional information:

$k_1=1\mathrm{.}0mi{n}^{-1},K_{1A}=10$

$k_2=100mi{n}^{-1},K_{2A}=1\mathrm{.}5$

$C_{A0}=1mo\frac{l}{d}{m}^3$

$($Adapted from a problem by John Falconer, University of Colorado.$)$

$($a$)$ Plot and analyze conversion and the concentrations of A$,$ D$,$ and $U$ as a function of time. When would

you stop the reaction to maximize the concentration of $D?$ Describe what you find.

$($b$)$ When does the maximum concentration of $U$ occur? $($Ans$.$: $t=0\mathrm{.}31$min $)$

$($c$)$ What are the equilibrium concentrations of $A,D,$ and $U?$

$($d$)$ What would be the exit concentrations from a CSTR with a space time of $1\mathrm{.}0$min $?$ Of $10\mathrm{.}0$min $?$

Of $100$min $?$