A tubular reactor is running a second-order addition reaction (mathrm{A}+mathrm{B} ightarrow mathrm{C}) in the liquid phase.

A tubular reactor is running a second-order addition reaction \(\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}\) in the liquid phase. The rate law is first order in the concentrations of \(\mathrm{A}\) and \(\mathrm{B}\) with rate constant \(k^{\prime \prime}\) \(\left(\mathrm{mol}^{-1} \mathrm{~s}^{-1}\right)\). The reactor length is \(L\), the cross-sectional area is \(A_{c}\), and A and B are fed in stochiometric ratio at a volumetric flowrate of \(\dot{v}_{o}\) and concentration, \(c_{a o}=c_{b o}=c_{o}\). Determine an expression for evaluating the concentration of \(A\) at any point within the reactor.