The irreversible, liquid phase reaction $AB$ takes place in an isothermal, porous$-$wall reactor. The

inert liquid $C$ diffuses through the reactor walls at a constant rate of $4c\frac{m^3}{s}$ per $cm$ of reactor

length. The feed is pure A$,$ with a concentration of $0\mathrm{.}0045mo\frac{l}{c}{m}^3$ and the inlet volumetric flow

rate is $25c\frac{m^3}{s}.$ The reaction is the first order and the rate constant is $0\mathrm{.}30s^{-1}.$ Assume plug flow

behavior. The reactor diameter is $2cm.$ What reactor length is required for $40\%$ conversion?