P$6-4$ B The elementary gas$-$phase reaction

$(C{H}_3{)}_3\frac{C}{O}OC(C{H}_3{)}_3{C}_2{H}_6+2C{H}_{3}COC{H}_3$

$AB+2C$

is carried out isothermally at $400K$ in a flow reactor with no pressure drop. The specific reaction rate at $50C$ is ${10}^{-}{?}^{4}mi{n}^{-1}($from pericosity data$)$ and the activation energy is $85k\frac{J}{m}ol.$ Pure di$-$tert$-$butyl peroxide enters the reactor at

$10$atm and $127C$ and a molar flow rate of $2\mathrm{.}5mo\frac{l}{m}in,$ that is$,F_A=2\mathrm{.}5mo\frac{l}{m}in.$

Use the algorithm for molar flow rates to formulate and solve the problem. Plot $F_A,F_B,F_C,$ and then $x$ as a function of plug$-$flow reactor volume and space time to achieve $90\%$ conversion.

Calculate the plug$-$flow volume and space time for a CSTR for $90\%$ conversion.