Problem $1(50/100)$: The elementary irreversible gas phase reaction $AB+C$ is carried out

adiabatically in a packed bed reactor at $10$atm $($pressure drop is negligible$).$ Pure A is fed to the

reactor with a volumetric flow rate of $20d\frac{m^3}{s}$ and feed temperature of $450K.$

What is the catalyst bed weight $($in $kg)$ necessary to achieve $80\%$ conversion in the

reactor?

Use numerical integration.

Additional information:

$H_A(273K)=-70k\frac{J}{m}ol,H_B(273K)=-50k\frac{J}{m}ol,H_C(273K)=-40k\frac{J}{m}ol$

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

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