P$6-3{?}_C$ OEQ $($Old Exam Question$).$ The second$-$order liquidphase reaction

$C_6{H}_{5}COC{H}_{2}Br+C_6{H}_{5}N{C}_6{H}_{5}COHC{H}_{2}N{C}_5{H}_{5}Br$

is carried out in a batch reactor at $35C.$ The specific reaction$-$rate constant is $0\mathrm{.}0445d\frac{m^3}{m}o\frac{l}{m}in.$ Reactor $1$ is charged with $1000d{m}^3,$ where the concentration of each reactant after mixing is $2M.$

What is the conversion after $10,50,$ and $100$ minutes?

Now, consider the case when, after filling reactor $1,$ the drain at the bottom of reactor $1$ is left open and it drains into reactor $2,$ mounted below it$,$ at a volumetric rate of $10d\frac{m^3}{m}in.$

What will be the conversion and concentration of each species in reactor $1$ after $10,50,$ and $80$ minutes in the reactor that is being drained? $($Ans: At $t=10$min then $x=0\mathrm{.}47)$

What is the conversion and concentration of each species in reactor $2$ that is filling up with the liquid from reactor $1$ after $10$ and after $50$ minutes? $($Ans: At $t=50$min then $x=0\mathrm{.}82)$

At the end of $50$ minutes, the contents of the two reactors are added together. What is the overall conversion after mixing?

Apply one or more of the six ideas in Preface Table P$-4,$ page xxvii, to this problem.