Editing Adsorption (section)

=== Freundlich ===
{{Main|Freundlich equation}}
The first mathematical fit to an isotherm was published by Freundlich and Kuster (1906) and is a purely empirical formula for gaseous adsorbates:

:<math>\frac{x}{m} = kP^{1/n},</math>

where <math>x</math> is the mass of adsorbate adsorbed, <math>m</math> is the mass of the adsorbent, <math>P</math> is the pressure of adsorbate (this can be changed to concentration if investigating solution rather than gas), and <math>k</math> and <math>n</math> are empirical constants for each adsorbent–adsorbate pair at a given temperature. The function is not adequate at very high pressure because in reality <math>x/m</math> has an asymptotic maximum as pressure increases without bound. As the temperature increases, the constants <math>k</math> and <math>n</math> change to reflect the empirical observation that the quantity adsorbed rises more slowly and higher pressures are required to saturate the surface.