Modified Fogler P$10-3.$ 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 of excess TBA can achieve reasonable

miscibility.

The reaction mechanism is believed to be

$I+SI*S$

$W+SW*S$

$W*S+I*STBA*S+S$

TBA$*STBA+S$

a$.$ Write rate laws for each elementary step: adsorption of I, adsorption of W$,$ dual$-$

site surface reaction between surface$-$bound I and W$,$ and desorption of TBA