The following gas phase first$-$order reaction is taking place in a PBR$.$

$AB$

The reaction rate and the rate constant are given by:

$-r_A^{\text{'}}=k{p}_A\frac{\text{m}\text{o}\text{l}}{kg\text{c}\text{a}\text{t}-h}$

$k=0\mathrm{.}75\frac{\text{m}\text{o}\text{l}}{\text{a}\text{t}\text{m}-kg\text{c}\text{a}\text{t}-h}$

A is fed to the reactor with $50\%$ inerts at $327C$ and $1$ atmosphere. Feed rate of A is $37\mathrm{.}5$

moles $\frac{?}{h}.$ The pressure drop parameter $=0\mathrm{.}0045k{g}^{-1}.$ Obtain an expression that relates the

conversion in the reactor to the weight of the catalyst used. State your assumptions.

What conversion can you obtain with $100kg$ of the catalyst?