Problem $2(50/100)$: The elementary irreversible organic gas$-$phase reaction $AB+C$ is

carried out in a packed bed reactor with heat exchange. Pressure drop is negligible. Pure A enters

the reactor at a volumetric flow rate of $20d\frac{m^3}{s},10$atm, and $450K($feed temperature$).$ Heat is

removed by a heat exchanger jacketing the reactor. The flow rate of coolant through the jacket is

sufficiently high so that the heat transfer fluid temperature is constant at $323K.$

Derive differential equations describing the change of conversion and temperature with respect

to the catalyst weight. Calculate all parameters and write the resulting differential equations as

a sole function of conversion and temperature $($by substituting numerical values for parameters

and writing the reaction rate expression explicitly$).$

Additional information:

$C_{PA}=40\frac{J}{\text{m}\text{o}\text{l}\text{K}},C_{PB}=25\frac{J}{\text{m}\text{o}\text{l}\text{K}},C_{PC}=15\frac{J}{\text{m}\text{o}\text{l}\text{K}}$

$H_A=-70k\frac{J}{m}ol,H_B=-50k\frac{J}{m}ol,H_C=-40k\frac{J}{m}ol($ referenced $to370K)$

$k=0\mathrm{.}133$exp$[\frac{E}{R}(\frac{1}{450}-\frac{1}{T})]\frac{d{m}^3}{k{g}_{\text{c}\text{a}\text{t}}(s)}$;$E=31\mathrm{.}4k\frac{J}{m}ol$;

$\frac{Ua}{{}_b}=0\mathrm{.}08\frac{J}{skgK}$The elementary irreversible organic gas$-$phase reaction A $$ B $+$ C is

carried out in a packed bed reactor with heat exchange. Pressure drop is negligible. Pure A enters

the reactor at a volumetric flow rate of $20$ dm$3$

$/$s$,10$ atm, and $450$ K $($feed temperature$).$ Heat is

removed by a heat exchanger jacketing the reactor. The flow rate of coolant through the jacket is

sufficiently high so that the heat transfer fluid temperature is constant at $323$ K$.$