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
w + s > < w * s
w * s + i * s > < tba * s + s
tba * s > < tba + s

1. derive a rate law assuming:
a) the surface reaction is rate - limiting
b) the adsorption of isobutene is limiting.