Question $2$

In a study to evaluate the diffusion effect in a catalytic reaction, two different sizes of spherical

pellets resulted in measured reaction rates $($per unit reactor volume$)$ as shown below.

Pellet radius $(mm)$ Reaction Rate $(mo\frac{l}{s}d{m}_{Rx}^3)$

$R_1=50,(r_A{)}_1=0\mathrm{.}0008$

$R_2=2\mathrm{.}5,(r_A{)}_2=0\mathrm{.}004$

All other conditions were kept equal in the two experiments $($temperature$,$ concentration of A$,$

catalyst packing density, rate constant, catalyst surface area$).$ The results give a strong indication

of diffusion effect during the catalytic reaction. Assume that diffusion effects are important only

within the porous pellets, and that the reaction is first order with respect to A$.$

$($Note: you may need to use Excel solver to answer part $($a$)$ and $($b$))$

$($a$)$ Estimate the Thiele modulus ${}_S$ and effectiveness factor $$ for each pellet size.

$($Hint: You may start with finding the relation between the reaction rates ratio of the

pellets sizes and the Thiele moduli$)$

$($b$)$ Estimate the required pellet size to increase the catalyst effectiveness to $0\mathrm{.}99($to

minimize the diffusion effects$).$