The first mathematical fit to an isotherm was published by Freundlich and Kuster (1906) and is a purely empirical formula for gaseous adsorbates:
where  is the mass of adsorbate adsorbed,  is the mass of the adsorbent,  is the pressure of adsorbate (this can be changed to concentration if investigating solution rather than gas), and  and  are empirical constants for each adsorbent–adsorbate pair at a given temperature. The function is not adequate at very high pressure because in reality  has an asymptotic maximum as pressure increases without bound. As the temperature increases, the constants  and  change to reflect the empirical observation that the quantity adsorbed rises more slowly and higher pressures are required to saturate the surface.