The 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 $X = {\mu P P_s \over P_e}$, 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 in this case the Langmuir isotherm.