In the case that the condensed matter contains other components, the equilibrium vapor pressure should have a different value. Here, let the equilibrium vapor pressure of a component A in a multi-component condensed matter at standard pressure be P_A^∅. Even in such a case, chemical potentials of a component A of a condensed phase and coexisting gas are equal. Therefore:

where μ_cond,A is the chemical potential of a component A with a fraction x_A in a multi-component condensed matter. Chemical potential of a component A in a multi-component condensed matter, μ_cond,A, is expressed using chemical component of a pure condensed matter, μ_cond,A^*

Now we define a quantity, activity, a_A, as follows:

Eq. (4) is expressed using Eq. (5) as follows:

Since activity should be a function of a mole fraction of a component in a multi-component condensed matter, we relate the activity and mole fraction using a quantity, activity coefficient, γ_A as follows:

Using Eqs. (6) and (7), chemical potential of component A in a multi-component condensed matter is expressed as a function of its molar fraction x_A: