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 specific reaction rate 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 $2\mathrm{.}5mo\frac{l}{m}in.$ Calculate volume and space

time to achieve $90\%$ conversion in:

$($a$)$ a CSTR

$($b$)$ a PFR

$($c$)$ Assume that the reaction is reversible with $K_C=0\mathrm{.}025mo\frac{l^2}{d}{m}^6$ and calculate the

equilibrium conversion and then redo $($a$)$ and $($b$)$ to achieve a conversion that is $90\%$ of the

equilibrium conversion.