TBA was produced by the liquid$-$phase hydration $($W$)$ of isobutene $($I$)$ over an Amberlyst$-15$

catalyst. The reaction mechanism is believed to be:

$I+$SharrI$*S$

$W+$SharrW$*S$

$W*S+I*SharrTBA*S+S$

TBA$*SharrTBA+S$

Derive a rate law assuming:

a$)$ The surface reaction is rate$-$limiting$.$

b$)$ The adsorption of isobutene is limiting$.$

c$)$ The reaction follows Eley$-$Rideal kinetics, and the surface reaction is limiting$.$

$I*S+W$TBA$*S$