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An adsorption isotherm relates equilibrium uptake to surrounding pressure or concentration at fixed temperature. For a gas, specify the partial pressure of the adsorbing chemical species. An uptake trace during incomplete equilibration need not be an adsorption isotherm.

At chemical equilibrium, adsorption and desorption balance:Canceling $M$ and rearranging givesThus $K_{\mathrm{ads}}=b$ when the kinetic and thermodynamic descriptions refer to the same ideal surface and energy convention. In particular,The ratio fixes the adsorption isotherm, while the individual rate constants also determine relaxation toward equilibrium. Here $k_a$ has units of inverse pressure per time and $k_d$ of inverse time, so $K_{\mathrm{ads}}$ is dimensional. This equivalent-site arrival/departure argument is the simple case of the Langmuir adsorption model.^[ref]

Thomas M. McDonald investigated cooperative carbon dioxide uptake in diamine-appended metal–organic frameworks. Insertion into metal–amine bonds forms ammonium-carbamate chains, connecting a molecular reaction with the sharp step observed in an adsorption isotherm.^[ref]