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:

(3)

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}^{*}

(4)

Now we define a quantity, activity, *a*_{A}, as follows:

(5)

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

(6)

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:

(7)

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}:

(8)