The A$->$ B reaction is carried out on a $40$ cm diameter packed bed reactor.

Catalysts are spherical in shape. The reaction takes place first according to the concentration of A on the catalyst surface.

is of degree:

$$rA$=$ k$$CAs

The feed is pure A and $30$ atm $500$ K is applied. The volumetric flow rate at the entrance to the reactor is $10$ dm$3/$sec $($i$.$e$\mathrm{.}10,000$ cm$3/$sec$).$ Calculate the weight of catalyst required to achieve $50\%$ conversion of A$.$

a$.$ Isothermal operation.

b$.$ Adiabatic process.

Additional info:

Filled bed diameter $($D$)=40$ cm

Kinematic viscosity v: $=0\mathrm{.}02$ cm$2/$sec

Particle diameter: dp $=0\mathrm{.}1$cm

Catalyst surface area $/$ catalyst bed mass: a $=60$ cm$2/$ g cat.

Diffusivity of A: De $=10^-2$ cm$2/$s $(500$ Kde$)$

Heat of reaction: $\backslash$Delta H$0$Rx$=-20,000$J$/$gmoIA

Heat capacities: CpA $=$ CpB $=25$ j$/$g mol.K

k$\text{'}($at $500$ K$)=0\mathrm{.}3$ cm$3/$s$.$g cat with E $=20000$ J$/$mol