$5-$ A first order heterogeneous reaction: $AC$ is performed catalytically in a packed

bed reactor working at steady state using porous spherical catalyst particle with

iameter of $0\mathrm{.}15cm.$ The diameter of the reactor is $60cm,$ the catalyst density is $2\mathrm{.}3$

$g\frac{m}{c}{m}^3.$ The bed voidage is $0\mathrm{.}3$ and the porosity of the catalyst particle is $0\mathrm{.}4.$ The

volumetric flow rate to the reactor is $50000c\frac{m^7}{sec}$ and the reaction rate constant is

$10(c\frac{m^4}{g}$mcat.$sec),$ and diffusion coefficient inside the pellet is $0\mathrm{.}5c\frac{m^7}{sec}.$ The

inlet concentration of A into the reactor is ${8\mathrm{.}5}^{**}{10}^{-}$mole $\frac{?}{c{m}^{**}}.$ Assume isothermal

operation and negligible dispersion. Calculate:

a$)$ Thicle modulus.

b$)$ The effectiveness factor.

c$)$ The amount of the catalyst required for $85\%$ conversion.