The following isomerization reaction takes place in a packed bed reactor $($PBR$).$

The elementary reaction is carried out at isothermal conditions at $740K$ in a reactor with

catalyst weight of $50kg$ and an initial pressure of $400$kPa. However, there is pressure drop in

the reactor. Initial molar rate of $A$ is $1$kmo$\frac{l}{h}.$

a$.$ Set$-$up the two coupled differential equations and any additional equations needed to be

solved.

b$.$ If $($the pressure drop parameter$)$ is $0\mathrm{.}005k{g}^{-1}.$ Determine the pressure ratio $p=\frac{P}{P}o.$

What is the pressure drop $(P=Po-P)?$

c$.$ Determine the conversion achieved in the reactor if $k=0\mathrm{.}1\frac{m^3}{k}g.$h$.$