$($a$)$ Expian whty intereat diffusion is a rate$-$imisng step in o heterogoneous catalyst recocton system and how a

$[7$ Marks$]$

$($b$)$ A commercial process for the d genation of uses $3-$mm sphenical calalyst partcles with stracht cyindrical pores. The catalyst pore damnter k $70nm.$ The reaction tnmperalure is $625C.$ The raie consdarl is $15s$; and the diffusivity of etrylbenzene in steam is $41{10}^5{m}^2=3$ under reaclion condrions Assume then the pore diameter a large enough that the buk diffusvity appies. Select appropriate oquations from Table $7($from the FORMULA SHEET$)$ and devermana a likely lower and upper bound for the isothermal effectiveness factor.

$[16$ Marks$]$

$($c$)$ For the elementary reaction,

Select appropriale equation from the Formula Sheet $($attached$)$ and calculate the PFR$,$ volume wher the volumetric fow rate to $205\%$ inert. The reacinr temperahurn is $125C,$ the rnaction rate co stant is $1\mathrm{.}3mi{n}^{-1}$ and $90\%$ comersion.

$[10$ Marks$]$

TOTAL $(33$ Marks$)$