The Freundlich isotherm is the most important multi-site adsorption isotherm for rough surfaces.
where α and C are fitting parameters. This equation implies that if one makes a log–log plot of adsorption data, the data will fit a straight line. The Freundlich isotherm has two parameters, while Langmuirs equations has only one: as a result, it often fits the data on rough surfaces better than the Langmuirs equations. However, the Freundlich equation is unique; consequently, if the data fit the equation, it is only likely, but not proved, that the surface is heterogeneous. The heterogeneity of the surface can be confirmed with calorimetry. Homogeneous surfaces (or heterogeneous surfaces that exhibit homogeneous adsorption (single-site)) have a constant  of adsorption as a function of the occupied-sites fraction. On the other hand, heterogeneous adsorption (multi-site) have a variable  of adsorption depending on the sites occupation. When the adsorbate pressure (or concentration) are low, high-energy sites are occupied, and as the pressure (or concentration) increases, the lesser-energy sites become occupied, resulting in a lower  of adsorption.
A related equation is the Toth equation. Rearranging the Langmuir equation, one can obtain
Toth modified this equation by adding two parameters α</sub> to formulate the Toth equation: