$9-8$ Reinicker and Gates $$ investigated the liquid phase reaction between phenol and acetone to bisphenol A and water at $364$ K $.$ The catalyst was a sulfonated styrene$-$divinylbenzene copolymer. The reaction is:

$2C_6{H}_{5}OH+(C{H}_3{)}_{2}CO(OH)C_6{H}_4-C(C{H}_3{)}_2-C_6{H}_{4}OH+H_{2}O$

AIChE J$.,20,933(1974).$

$386$

CHEMICAL ENGINEERING KINETICS

Derive a rate equation based upon the following elementary steps acetone, $-S{O}_{3}H=$ active group in the polymer, $P=$ phenol, $I=$ tertiary alcohol intermediate$)$:

$($a$)$ reversible adsorption of acetone

$($b$)$ reversible reaction of adsorbed acetone and phenol $($not adsorbed$)$ to give the adsorbed tertiary alcohol intermediate

$($c$)$ irreversible surface reaction between adsorbed phenol and adsorbed tertiary alcohol to give adsorbed water and bisphenol $A($not adsorbed$).$

Assume that step $($c$)$ is rate controlling. This mechanism is an approximation to the more careful development of Reinicker and Gates.