text: In condensed phases (solutions), adsorption to a solid surface is a competitive process between the solvent (A) and the solute (B) to occupy the binding site. The thermodynamic equilibrium is described as
  : Solvent (bound) + Solute (free) ↔ Solvent (free) + Solute (bound).
  If we designate the solvent by the subscript "1" and the solute by "2", and the bound state by the superscript "s" (surface/bound) and the free state by the "b" (bulk solution / free), then the equilibrium constant can be written as a ratio between the activities of products over reactants:
  For dilute solutions the activity of the solvent in bulk solution  and the activity coefficients () are also assumed to ideal on the surface. Thus,  , and  where  are mole fractions.
  Re-writing the equilibrium constant and solving for  yields
  Note that the concentration of the solute adsorbate can be used instead of the activity coefficient. However, the equilibrium constant will no longer be dimensionless and will have units of reciprocal concentration instead. The difference between the kinetic and thermodynamic derivations of the Langmuir model is that the thermodynamic uses activities as a starting point while the kinetic derivation uses rates of reaction. The thermodynamic derivation allows for the activity coefficients of adsorbates in their bound and free states to be included. The thermodynamic derivation is usually referred to as the "Langmuir-like equation".