The liquid$-$phase reaction:

$A+BC$

follows an elementary rate law and is carried out isothermally in a flow system. Right before entering a

reactor, the concentrations of A and $B$ are $\frac{1}{M}$ each in a feed of $10\frac{L}{m}in.$ The entering temperature is

$300K.$ There are two reactors available. One is a $200$ L CSTR that can be heated to $77C$ or cooled to $0$

$C.$ The other is an $800L$ PFR that can be operated solely at $300K.$ The rate constant is $k=0\mathrm{.}07\frac{L}{\text{m}\text{o}\text{l}*min}$

at $300K$ and the activation energy is $E=20$kca$\frac{l}{m}ol.$

a$)$ Determine the highest possible conversion with the CSTR$.($Answer: $0\mathrm{.}926)$

b$)$ Determine the conversion with the PFR$.($Answer: $0\mathrm{.}848)$

c$)$ Which reactor can deliver the highest conversion $x?$

d$)$ How long would it take to achieve $90\%$ conversion in a $200L$ batch reactor with $C_{A0}=C_{B0}=1M$

operating at $77C?($Answer: $1\mathrm{.}07$min $).$

What if the batch reactor was operated at $0C?($Answer: $2\mathrm{.}47$ days$)$