Given: this reactor is a first order reaction and is carried out in a plug flow reactor in which the volumetric flow rate, $v,$ is constant, $v_0=v$

$de{l}_{AO}$

Derive an equation relating the reactor volume to the entering and exiting concentrations of $A,$ the rate constant $k,$ and the volumetric flow rate, $v_0.$ Then, derive an equation to solve for the concentration of $A$ as a function of reactor volume.

Determine the reactor volume, $V_1,$ necessary to reduce the exiting concentration to $10\%$ of the entering concentration, i$.$e$.,C_{A0}=0\mathrm{.}1C_{A0},$ when the volumetric flow rate is $10\frac{L}{m}in$ and the specific reaction rate, $k=0\mathrm{.}23mi{n}^{-1}.$