The elementary and gaseous reaction, $2AB+C,$ with specific reaction rate of $9\mathrm{.}5d\frac{m}{m}o\frac{l}{g}$ cat $\frac{?}{\text{m}\text{i}\text{n}}$ at $200C$ is carried out in a packed bed reactor $($PBR$)$ isothermally at $200C$ with pressure drop parameter, a$,$equals to $0\mathrm{.}01g^{-1}.$ Pure $A$ is fed at pressure of $10$atmospheresandat temperature of $200C,$ and a production rate of $120\frac{g}{m}in$ of $B$ is required.

The molecular weight of B is $60.$ Assume ideal gas law can be applied. The pressure drop in this PBR could be evaluated by the analytical solution of Ergun equation:

$\frac{P}{P_0}=(1-aW{)}^{0\mathrm{.}5}$

Please determine the catalyst weight if the conversion of A is to be $80\%?$