P$6-5{?}_B$ For the reaction and data in Problem P$6-4{?}_B,$ we now consider the case when the reaction is reversible with $K_C=0\mathrm{.}025d\frac{m^6}{m}o{l}^2$ and the reaction is carried out at $300K$ in a membrane reactor where $C_2{H}_6$ is diffusing out. The membrane transport coefficient is $k_C=0\mathrm{.}08s^1.$

a$.$ What is the equilibrium conversion and what is the exit conversion in a conventional PFR$?$

$($Ans: $x_{eq}=0\mathrm{.}52,x=0\mathrm{.}47)$

b$.$ Plot and analyze the conversion and molar flow rates in the membrane reactor as a function of reactor volume up to the point where $80\%$ conversion of di$-$tert$-$butyl peroxide is achieved. Note any maxima in the flow rates.