The exothermic reaction of stilbene $($A$)$ to form the economically important trospophene $($B$)$ and methane $($C$)$: $AB+C,$ was carried out adiabatically and the following data recorded:

$\backslash$table$[[x,0,0\mathrm{.}2,0\mathrm{.}4,0\mathrm{.}45,0\mathrm{.}5,0\mathrm{.}6,0\mathrm{.}8,0\mathrm{.}9],[-r_A(mo\frac{l}{d}{m}^3*min),1,1\mathrm{.}67,5\mathrm{.}0,5\mathrm{.}0,5\mathrm{.}0,5\mathrm{.}0,1\mathrm{.}25,0\mathrm{.}91]]$

The entering molar flow rate of A was $300mo\frac{l}{m}in$

a$)$ What are the PFR and CSTR volumes necessary to achieve $40\%$ conversion?

b$)$ Over what range of conversions would the CSTR and PFR reactor volumes be identical?

c$)$ What is the maximum conversion that can be achieved in a $105d{m}^3$ CSTR$?$

d$)$ What conversion can be achieved if a $72d{m}^3$ PFR is followed in series by a $24d{m}^3$ CSTR$?$

e$)$ What conversion can be achieved if a $24d{m}^{3}CSTR$ is followed in series by a $72d{m}^3$ PFR$?$

f$)$ Plot the conversion and rate of reaction as a function of PFR reactor volume up to a volume of $100d{m}^3.$