t-Butyl alcohol (TBA) is an important octane enhancer that is used to replace lead additives in gasoline (Ind. Eng. Chem. Res., 27, 2224 (1988)). TBA was produced by the liquid-phase hydration (W) of isobutene (I) over an Amberlyst-15 catalyst. The system is normally a multiphase mixture of hydrocarbon, water, and solid catalysts. However, the use of cosolvents or excess TBA can achieve reasonable miscibility. The reaction mechanism is believed to be
I+S←→I⋅S(P10-3.1)
W+S←→W⋅S(P10-3.2)
W+S+I⋅S←→TBA⋅S+S(P10-3.3)
TBA⋅S←→TBA+S(P10-3.4)
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 I⋅S+W→TBA⋅S(P10-3.5) and the surface reaction is limiting.
d. Isobutene (I) and water (W) are adsorbed on different sites.
I+S1←→I⋅S1(P10-3.6)
W+S2←→W⋅S2(P10-3.7)
TBA is not on the surface, and the surface reaction is rate-limiting.
(Ans:rTBA′=−r1′=k[C1CW−CTBA/Kc](1+KWCW)(1+K1C1))