Isomerization of n$-$pentene $($N$)$ to i$-$pentene over alumina catalyst is described as below

N $$ I

N $+$ S $$ N$$S Adsorption of cumene

N$$S $$ I$$S Surface reaction

I$$S $$ I $+$ S Desorption of benzene from the surface

Treat that each of the reaction as elementary rate law, derive an expression considering surface reaction is the rate$-$limiting step.