Q$8($Catalysis and Catalytic Reactors$)$:

When the decomposition of cumene was carried out over a LaY zeolite catalyst, deactivation of the catalyst was found to occur by coking. The reaction is first$-$order anc was carried out in a differential reactor containing $1g$ of catalyst at $.$ Eng. Chem. Process Des. Dev., $22,609(1983)].$ The exit molar flow rate of propylene was monitored as a function of time.

$($a$)$ From the data below, determine the decay functionality, with the amount of coke on the catalyst together with the apparent cumene kinetics.

$($b$)$ Determine the functionality of the decay function with respect to time and partial pressure of cumene. $($Ans: $-d\frac{a}{d}t=k_d{a}_c^{2p_c^{1,3}})$

$($c$)$ Calculate the reactor height necessary to achieve $60\%$ conversion in a CSTR$.$ The catalyst particle velocity is $1\frac{m}{s}.$ Cumene is to enter the reactor at a rate of $7mo\frac{l}{s}.$ The total molar feed rate to the reactor is $10mo\frac{l}{s}.$ The bulk density of the catalyst is $0\mathrm{.}5k\frac{g}{m^3}$ and the reactor cross$-$sectional area is in $d{m}^3.$

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