The irreversible elementary gas phase reaction

$2$A $->$ B

is performed in a constant volume batch reactor. Pure A was charged to the batch reactor at an initial

concentration of $0\mathrm{.}2$ mol$/$dm$3.$ In the batch reactor, $50\%$ conversion is achieved in $1$ hour.

a$)$ If the same reaction is carried out in a Continuous stirred tank reactor $($CSTR$),$ calculate the volume

required to achieve $50\%$ conversion for feed conditions of FA$0=500$ mol$/$hour and CA$0=0\mathrm{.}2$ mol$/$dm$3$

$.$

b$)$ If the same reaction is carried out in a Plug Flow Reactor $($PFR$),$ calculate the volume required to

achieve $50\%$ conversion for feed conditions of FA$0=500$ mol$/$hour and CA$0=0\mathrm{.}2$ mol$/$dm$3$

$.$ if we have to find k$,$ how we will find