The $4m^3$ volume plug flow reactor has been used for reversible reaction below:

AharrR,$(-r_A)=0\mathrm{.}04C_A-0\mathrm{.}01C_R$;$,(-r_A$:$mo\frac{l}{l}.$min$)$

Flow rate of feed is $200\frac{l}{m}in($liquid$),$ initial concentration of reactant $C_{A_0}=0\mathrm{.}1mo\frac{l}{l}$;$C_{R_0}=0mo\frac{l}{l}.$

a$)$ Find the conversion in this reactor?

b$)$ If we replace the plug flow reactor by mixed flow reactor, find the volume of this mixed flow reactor to have the same conversion in question a$.$