Equilibrium distribution of gas molecules adsorbed on an active surface

We evaluate the exact equilibrium distribution of gas molecules adsorbed on an active surface with an infinite number of attachment sites. Our result is a Poisson distribution having mean X = mu PPs/P-e, with mu the mean gas density, P-s the sticking probability, P-e the evaporation probability in a time interval tau, and P Smoluchowski's exit probability in time interval tau for the surface in question. We then solve for the case of a finite number of attachment sites using the mean field approximation, recovering the Langmuir isotherm in this case.