Question $4[20$ Marks$]$

A Renewable Energy Research Lab has developed a prototype chemical reactor to convert waste cooking oils into diesel, a biofuel to power a $3-$wheeled Tuktuk vehicle. The waste cooking oils is to be converted to biodiesel through a gas$-$phase pyrolysis as shown in the reaction scheme below:

This scheme can be modeled as first$-$order irreversible reaction with a measured $k=5{10}^{-3}$ min$-1$ at $150C$ and a measured $E_a=85k\frac{J}{m}$ole. In one of the test runs, waste cooking oil at a flowrate of $2\mathrm{.}5mo\frac{l}{m}in$ was fed to into the reactor operating at $T=227C.$ At this temperature all the species are in the vapor phase. The steady$-$state pressure in the reactor was $10$atm.

Using these experimental reactor operating conditions, Calculate the volume of the reactor required to achieve $90\%$ conversion, if

$($a$)$ The reactor is a CSTR

$[10$ Marks$]$

$($b$)$ The reactor is a PFR

$[10$ Marks$]$