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=&mgr;PP(s)/P(e), with &mgr; 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.