$($continuing Homework Set $3$ #$3.)$ 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 reaction rate constant

at $50C$ is ${10}^{-4}mi{n}^{-1}$ 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 $2\mathrm{.}5mo\frac{l}{m}in.$

d$.$ A leak is found and it is determined that your reactor is leaking ethane uniformly through the

sides of the PFR$,$ resulting in performance as a membrane reactor with $k_c=0\mathrm{.}2mi{n}^{-1}.$ What

plug$-$flow volume for this membrane reactor will result in $90\%$ conversion?