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 $2\mathrm{.}5mo\frac{l}{m}in.$

a$.$ Using a conversion$-$based approach, calculate analytically the plug$-$flow volume and space time

for a CSTR achieving $90\%$ conversion.

b$.$ Using a conversion$-$based approach, obtain $x,F_A,F_B,$ and $F_C$ numerically $($python$)$ as a function

of PFR volume. Plot $($i$.)x$ and $($ii$.)F_A,F_B,$ and $F_C$ as a function of reactor volume. Estimate the

space time necessary to achieve $90\%$ conversion.

c$.$ Using a molar flowrate$-$based approach, obtain $x,F_A,F_B,$ and $F_C$ numerically $($python$)$ as a

function of PFR volume. Plot $($i$.)x$ and $($ii$.)F_A,F_B,$ and $F_C$ as a function of reactor volume.

Estimate the space time necessary to achieve $90\%$ conversion. $($The answer should be identical to

part b$.)$