In aqueous solution, and in contact with the right catalyst, reactant $A$ is converted to product $R$ by the elementary reaction $A2R.$ Find the mass of catalyst needed in a packed bed reactor for $90\%$ conversion of ${10}^4$mol$\frac{A}{h}r$ of feed having $C_{A0}={10}^{3}mo\frac{l}{m^3}.$ For this reaction

$18\mathrm{.}34.k^{\text{'}\text{'}\text{'}\text{'}}=8{10}^{-4}\frac{m^3}{m^3}$ bed $*s$

Additional data:

Diameter of porous catalyst pellets $=6mm$

Effective diffusion coefficient of $A$ in the pellet $=4{10}^{-8}\frac{m^3}{m}$ cat $*s$

Voidage of packed bed $=0\mathrm{.}5$

Bulk density of packed bed $=2000k\frac{g}{m^3}$ of bed