The following reversible gas$-$phase reaction is carried out at on a flat catalyst plate

A$($g$)-->$ B$($g$)$

The rate of surface reaction is

r$\_($A$)=$k$\_(1)($C$\_($As$)-$KC$\_($BS$))[($molA$)/($m$^(2)$s$)]$

where C$\_($As$)$ and C$\_($Bs$)$ are the gas$-$phase concentrations of A and B at the surface of the catalyst. For the reaction, A diffuses to the catalyst surface through a stagnant gas film of thickness $\backslash$delta $.$ Outside the film gas mixture contains pure A at pressure P$\_($t$)$ and temperature T$.$ The diffusivity of A in B is D$\_($AB$).$

a$)$ Derive an expression for the mol fraction of A at the catalyst surface