Q$1.$ A first$-$order, heterogeneous and irreversible reaction, A $(g)B(g),$ is taking placed

within a packed bed reactor with a spherical, porous catalyst pellets of $3cm$ diameter. The

reactor is designed to achieve $98\%$ conversion with the residence time of $16$ minutes. The

catalyst bed has a voidage of $0\mathrm{.}4.$

a$)$ Calculate the effective diffusivity $(D_e)$ for the reactant within the catalyst particle

$(c\frac{m^2}{s})$ when the Thiele modulus of this system is $2\mathrm{.}5.$ Assume the reactor operates

isothermally and that external mass$-$transfer resistance is negligible.

b$)$ To what diameter should the pellet be reduced if the internal effectiveness factor is to

be $0\mathrm{.}85?$ A step in this problem requires numerical solving. This can be done using any

method or software and does not need to be attached.

c$)$ What conversion do you predict if the pellets were increased $40\%$ in diameter to reduce

pressure drop in the reactor?

d$)$ For diffusional limitation to be considered insignificant, the internal effectiveness must

be higher than $0\mathrm{.}95.$ A new catalyst particle is designed with $S_g$ is decreased $30\%,{}_p$ is

reduced by $20\%,$ and effective diffusivity $(D_e)$ increases $100\%$ compared to those in part

a$).$ Determine the maximum diameter of the new catalyst particle to have an internal

effectiveness of $0\mathrm{.}95?$ A step in this problem requires numerical solving. This can be

done using any method or software and does not need to be attached.