The chemical potential of species  in solution depends on the activity a using the following equation:
where  is the chemical potential of the -th component,  is the chemical potential of the -th component at a reference state,  is the gas constant,  is the temperature, and  is the activity of the -th component.
Differentiation of the chemical potential equation results in:
where  is the activity coefficient of component , and  is the concentration of species  in the bulk phase.
If the solutions in the  and  phases are dilute (rich in one particular component ) then activity coefficient of the component  approaches unity and the Gibbs isotherm becomes:
The above equation assumes the interface to be bidimensional, which is not always true. Further models, such as Guggenheim's, correct this flaw.