Question $3(3\mathrm{.}0$ mark$)($L$.$O$\mathrm{.}2)$

The aqueous elementary reversible reaction $A,\frac{k_1}{k_2},B$ is conducted in batch reactor at $27C.$ If without $R$ in the feed, it was observed that after $100$min, the conversion of reactant A was $40\%.$ When the conversion reached $90\%,$ no change was observed anymore.

Determine the volume of the plug flow reactor if the outflow of the product $R$ was $0\mathrm{.}20$mol$\frac{R}{m}in,$ feed stream was aqueous solution without $R$ and concentration of reactant $A$ at $0\mathrm{.}4$ molA L$,$ flowrate at $1\mathrm{.}0\frac{L}{m}in$ and $27C$