P$4-5{?}_A$ 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 $800\mathrm{.}0-d{m}^3$ PFR operated at $300K$ that cannot be heated or cooled but can be painted red or black. Note $k=0\mathrm{.}07d\frac{m^3}{m}ol*min$ 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 $200-d{m}^3$ batch reactor with $C_{A0}=C_{B0}=1M$ after mixing at a temperature of $77C?$

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

$($d$)$ What concerns would you have to carry out the reaction at higher temperatures?

$($e$)$ Keeping Table $4-1$ in mind, what batch reactor volume would be necessary to process the same amount of species A per day as the flow reactors