Researchers have studied a catalyzed reaction in a $($incompressible$)$ liquid phase $($C$)$

$A+BP$

where $C$ is a catalyst. It was reported that the second$-$order rate constant for this reaction is equal to

$k=1\mathrm{.}15*{10}^{-3}{m}^{3}mo{l}^{-1}kse{c}^{-1}$ at $20C.$ And the kinetic equation expressing the overall reaction rate is as

follows

$r_V=k{c}_A{c}_B$

Determine the volume of plug flow reactor that would be necessary to achieve $40\%$ conversion of the

compound $B$ assuming isothermal operating conditions and a liquid feed rate of $0\mathrm{.}500m^{3}kse{c}^{-1}.$ The

feed composition is as follows

$c_A^0=184$ mole. $m^{-3}$

$c_B^0=96\mathrm{.}5$ mole. $m^{-3}$If a calculation iExcel is necessary, please attach