$1$ liter$/$s of a $20\%$ ozone$-80\%$ air mixture at $1\mathrm{.}5$ atm and $93C$ passes

through a plug flow reactor. Under these conditions ozone decomposes by

homogeneous reaction

$2O_{3}3O_2,-r_{\text{o}\text{z}\text{o}\text{n}\text{e}}=k{C}_{\text{o}\text{z}\text{o}\text{n}\text{e}}^2,k=0\mathrm{.}05\frac{\text{l}\text{i}\text{t}\text{e}\text{r}}{\text{m}\text{o}\text{l}*s}$

What size reactor is needed for $50\%$ decomposition of ozone?

Table $5\mathrm{.}2$ Performance Equations for $n$ th$-$order Kinetics and ${}_{A}0$