$(P5-9A)$ The liquid$-$phase reaction

$A+$BlongrightarrowC

follows an elementary rate law and is carried out isothermally in a flow system. The concentrations of the A and $B$ feed streams are $2M$ before mixing. The volumetric flow rate of each stream is $5d\frac{m^3}{m}in,$ and the entering temperature is $300K.$ The streams are mixed immediately before entering. Two reactors are available. One is a gray, $200\mathrm{.}0-d{m}^{3}CSTR$ that can be heated to $77C$ or cooled to $0C,$ and the other is a white, $800\mathrm{.}0-$dm ${?}^3$ PFR operated at $300K$ that cannot be heated or cooled bot can be painted red or black. Note that $k=0\mathrm{.}07d\frac{m^3}{m}ol*min$ at $300K$ and $E=20$kca$\frac{l}{m}ol.$

$($a$)$ Which reactor and what conditions do you recommend? Explain the reason for your choice $($e$.$g$.$ color, cost, space available, weather conditions$).$ Back up your reasoning with the appropriate calculations.

$($b$)$ How long would it take to achieve $90\%$ conversion in a $200-$dm ${?}^3$ batch reactor with $C_{M0}=C_{B0}=1M$ after mixing at a temperature of $77C?$

$($c$)$ What would your answer to part $($b$)$ be if the reactor were cooled to $0C?($Ans$.2\mathrm{.}5$ days$)$