Question $1(4\mathrm{.}0$ mark$)($L$.$O$\mathrm{.}2)$

A homogeneous first order gas phase reaction takes place in a mixed flow reactor: $A2S,$

The feed contains $20\%$ inerts by volume to obtain $60\%$ conversion of $A.$

a$.$ If the mixed flow reactor is replaced by a plug flow reactor, all else remains unchanged, find the ratio of the plug flow reactor volume to the mixed flow reactor to obtain the same conversion $($Constant pressure condition$).$

b$.$ If the volume of mixed flow reactor is $2$ times than the original one, all else remains unchanged, find the new conversion of A $($Constant pressure condition$).$