Exercise $7\mathrm{.}5$: Thiele modulus and Hougen$-$Watson kinetics

The following catalytic reaction is conducted in a $0\mathrm{.}25-cm$ radius spherical pellet.

$A+B_{2}C$

The mechanism for this reaction is shown below. $A,B_2$ and $C$ are in adsorption$-$

desorption equilibrium with the surface. The bimolecular surface reaction is irre$-$

versible and rate limiting$.$

$A+S={?}_{k_{-1}}^{k_1}{A}_{\text{a}\text{d}\text{s}}$

$B_2+2S{}^{k_{-2}}{?}^{k_2}2B_{\text{a}\text{d}\text{s}}$

$A_{\text{a}\text{d}\text{s}}+B_{\text{a}\text{d}\text{s}}{}^{k_3}{?}^{k_3}{C}_{\text{a}\text{d}\text{s}}+S$

$C+S{}_{k_{-4}}^{k_4}{C}_{\text{a}\text{d}\text{s}}$

Additional data needed for this problem are provided in the following table.

$($a$)$ Determine if the concentration of A changes appreciably within the pellet from

the value it has at the pellet surface.

$($b$)$ Estimate the concentration of $A$ at the center of the pellet.