Q$6$ Consider gases A and B both of which are adsorbable on to the surface of a catalyst. The following three possible forms of adsorption occur.

Adsorption of gas $A$ on a vacant site:

Adsorption of gas B on a vacant site:

$A+sA.s$

Adsorption of gas B on adsorbed A forming a complex:

$B+sB.s$

A$.$s $+B$ A$.$s$.B$

$($i$)$ Derive expressions for concentration A and B in terms of their concentrations in the bulk gas phase.

$($ii$)$ At a given partial pressure $p_A$ for gas $A,$ how does the presence $($or absence$)$ of gas B affect its adsorption?

$($iii$)$ At a given partial pressure $p_B$ for gas B$,$ how does the presence $($or absence$)$ of gas A affect its adsorption?