Q$.5$ A gas$-$solid catalytic reaction of the type

$A+BC$

assuming the operating condition of the catalyst is such that the external and internal diffusion resistances are negligible; propose rate equations for the following cases:

$($a$)$ The mechanism is the reaction between adsorbed A and adsorbed B molecules on the catalyst. The controlling step is the surface reaction

$($b$)$ The mechanism is a reaction between adsorbed A and $B$ in the gas phase. The controlling step is the surface reaction