Problem $4(20\%)$: Consider the following reaction for the

production of benzene via the homogeneous thermal dealkylation of

toluene in the temperature range $700C$ to $950C$ :

$C_7{H}_8+H_2{C}_6{H}_6+C{H}_4$

toluene benzene

$-r_{\text{t}\text{o}\text{l}}=3\mathrm{.}0{10}^{10}{e}^{-\frac{25,614}{{}_{[K]}}}{c}_{\text{t}\text{o}\text{l}}{c}_{H_2}^{0\mathrm{.}5}[\frac{\text{m}\text{o}\text{l}}{m^3}of$ reactor $\frac{?}{s}]$

where the concentrations of reactants are in mol$/$liter reactor and

the temperature is in $K.$ The heat of reaction is $-52\mathrm{.}0k\frac{J}{m}ol($at

$900C)$ and at $700C),$ and the average specific heats

of the reactor feed and effluent are at $950C)$ and

$3\mathrm{.}042k\frac{J}{k}\frac{g}{K}(700C).$

If feed enters the reactor at $700C$ and $25$ bar, solve the material

and energy balances for a plug flow reactor to determine the volume

of reactor needed to give $90\%$ conversion of toluene. The feed to

the reactor comprises $80$kmo$\frac{l}{h}$ of toluene and $320$kmo$\frac{l}{h}$ of

hydrogen. Plot the conversion and temperature profiles in the

reactor.