We can treat adsorption from a mixture of gases (at low pressures) by extending the Langmuir isotherm:
A(g)+S⇌A(ads)
B(g)+S⇌B(ads) These reactions are not independent because both species compete for the same
surface sites. The two equilibria must be solved simultaneously:
PA×[S][A(ads)]=KA PB×[S][B(ads)]=KB
As for the one-component case, we define surface coverages θA=[A(ads)]/[S]0
and θB=[B(ads)]/[S]0, and note that
[S]+[A(ads)]+[B(ads)]=[S]0, or [S]/[S]0=1−θA−θB
Then,
KA=PA×(1−θA−θB)θA KB=PB×(1−θA−θB)θB
and dividing, we get
θBθA=PBPAKBKA The ratio of A:B on the surface is therefore different than the ratio of A:B in the gas phase,
by precisely KA/KB, so the more strongly adsorbed component is enriched on the surface.
This is referred to as the thermodynamic selectivity, the
preference of the surface for one species of a mixture, and is the basis for many techniques to
separate gas mixtures.