The elementary gas$-$phase reaction

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

is carried out isothermally in a flow reactor with no pressure drop. The spe$-$

cific reaction rate at $50C$ is ${10}^{-4}mi{n}^{-1}($from pericosity data$)$ and the acti$-$

vation 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 $2\mathrm{.}5mo\frac{l}{m}in.$ Calculate the reactor

volume and space time to achieve $90\%$ conversion in:

$($a$)$ a PFR $($Ans$.$: $967d{m}^3)$

$($b$)$ a CSTR $($Ans$.$: $4700d{m}^3)$