Q$8$ Two gases A and B are adsorbed from the bulk phase onto a catalyst surface.

$($i$)$ If both species are diatomic and $($:$B_2\}$ and dissociate upon adsorption $($with each atom occupying a single site on the catalyst$),$ derive the relation between the partial pressure of gases in the bulk phase to the concentrations of atomic species A and B in the adsorbed phase.

$($ii$)$ If species $A$ is diatomic $(A_2)$ and adsorbs dissociatively as earlier, while species $B$ is monoatomic and adsorbs, how do these equations change?