QUESTION $1.$

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The nitration of aromatic compounds is a highly exothermic reaction that generally uses catalysts that tend to be corrosive $($e$.$g$.,($e$.$g$.,HN\frac{O_3}{H_2}S{O}_4).$ A less corrosive reaction employs $N_2{O}_5$ as the nitrating agent as illustrated below:

$N_2{O}_5+2C_6{H}_{6}2C_6{H}_{5}N{O}_2+H_{2}O$

The reaction is conducted in CTSR with cooling system. The reaction rate is first order in $N_2{O}_5$ and second order in $C_6{H}_6.$ The reactants enter the reactor at a temperature of $30C$ and the volumetric flow rate is $100\frac{L}{m}in.$ The initial concentration of $N_2{O}_5$ is $0\mathrm{.}1mo\frac{l}{L}.$

What is the reactor volume $($Liters$)$ to achieve $35\%$ conversion of $N_2{O}_5?$

Additional information:

$HR=-370\mathrm{.}1k\frac{J}{m}ol$

$C_{PA}=84\mathrm{.}5\frac{J}{m}ol-K$

$F_{AO}=10mo\frac{l}{m}in$

$U{A}_H=9000\frac{J}{m}in{d}_{\text{m}\text{o}\text{l}-K}$

$C_{PC}=170\frac{J}{m}ol-K$

$C_{PB}=137\frac{J}{m}ol-K,C_{PC}=170\frac{J}{m}ol-K,C_{PD}=75\frac{J}{m}ol$

$F_{BO}=30mo\frac{l}{m}in,K=0\mathrm{.}09\frac{L^2}{mol{l}^2-\text{m}\text{i}\text{n}}at303K,E=40k\frac{J}{m}o$

$T_C=323K,$