The following elementary irreversible reaction is in liquid phase.

A $->$ B

The feed containing $75\%$ of A and $25\%$ of inert enters the reactor at $500$ K and P $=2$ atm with v$0=2\mathrm{.}5$ m$3/$min$.$ For the given data below:

$$H$\_$RX$=-2500$ J$/$mol

Activation energy, E $=50$ kJ$/$mol

k $=0\mathrm{.}05$ min$-1$ at $298$ K

CA$0=9\mathrm{.}3$ mol$/$dm$3$

CPA $=120$ J$/$mol$.$K

CPB $=150$ J$/$mol$.$K; CPI $=150$ J$/$mol$.$K

Calculate the volume of PFR and CSTR required to achieve $40\%$ conversion.

PLEASE SHOW FULL STEPS WITH INTEGRATION FOR PFR