An irreversible gas phase reaction is carried out in an isothermal flow reactor $($CSTR or PFR$)$ that operates at steady state. The reaction is

A $->$ B $+$ C

with $$ r$\_$A $=$ kC$\_$A ; k $=0\mathrm{.}5$ h$^1$

The feed stream is at $100$ kPa and $400$ K$,$ with molar flow rates $($Careful with units$)$

F$\_$A$0=0\mathrm{.}04$ mol$$min ; F$\_$B$0=0\mathrm{.}02$ mol$$min ; F$\_$C$0=0$

There is no pressure drop across the reactor, and all components are known to behave as ideal gases.

Component A is to have a fractional conversion of $80\%$ as it exits the reactor.

$($a$)$ What is the required volume of the reactor if it was a CSTR$?$

$($b$)$ If the reactor was a PFR$,$ would the required volume be smaller or larger than your answer to part $($a$)?$ Explain using no more than a few words. $($No explanation, no marks.$)$

$($c$)$ What is the required volume of the reactor if it was a PFR$?$