A manufacturer has supplied spherical catalyst pellets that only varies in terms of their diameter; all other properties are the same. The various catalyst pellets are evaluated in a differential flow reactor. Catalyst pellets with a diameter of $0\mathrm{.}10mm$ and $0\mathrm{.}20mm$ were found to have a production rate of $90$mmo$\frac{l}{m}{g}_{c}s.$ Catalyst pellets with a diameter of $5\mathrm{.}0mm$ produce products at rates of $20$mmo$\frac{l}{m}{g}_c$ s respectively. If was also found that the flow rate did not influence the reaction rate for all size particles and that the reaction was first order.

a$)$ Inspecting the experiments at performed for the $0\mathrm{.}10$ and $0\mathrm{.}20mm,$ what is the limiting the reaction rate: external mass transfer, internal mass transfer, or surface reaction? Motivate your answer! $(2)$

b$)$ Same question about the $10mm$ particles. Again, motivate your answer!

c$)$ As good as you can, determine the reaction rate for catalyst pellets with a diameter of $20mm?$ Clearly state what assumptions you made.

$(6)$

d$)$ Because of pressure drop consideration, the company decides to work with the largest particle size $(10mm).$ To counteract the reduced reactivity for the $10mm$ particles, the operator of the process wants to operate the reactor at a higher temperature. What do you think is the most important drawback of doing this?

e$)$ Since the active catalyst comprises of a combination of very expensive noble metals including $Rh,Pt,$ and $Ru,$ these materials form the largest part of the manufacturing costs. There are three options available for manufacturing the $10mm$ catalyst: $($i$)$ coating the catalysts evenly throughout the complete catalyst pellet, $($ii$)$ coating the catalyst only near the centre $($middle$)$ of the pellet, or $($iii$)$ coating the catalyst only near the exterior $($outside$)$ of the pellet. Which catalyst configuration would you recommend, and why? Provide a justification for your answer.