The conditions for there to be equilibrium between two more phases are that the Pressure, P, Temperature, T, and Chemical Potential, μi, of each substance should have the same value in every phase. These conditions impose a restriction on the possible number of phases that can be in mutual equilibrium.
The Phase Rule is usually expressed in the form:
where P is the number of phases present, C is the number of components, and F is the number of degrees of freedom. The degrees of freedom refer to the values of pressure, temperature and mole fraction in a particular phase, which can be varied at will. It is important that no other variable be treated as a degree of freedom. One common mistake is to treat an overall mole fraction as a degree of freedom.
A single component system has C = 1 and hence P + F = 3. If there is but a single phase present, F = 2 and the variable pressure and temperature can both be varied indepenently. If two phases are present, say liquid and gas, only pressure (or temperature) can be varied independently; i.e., we are moving along the vapor pressure curve. If three phases are present, nothing can be varied—we are at the triple point. In a two component system, C = 2 and P + F = 4. If two phases are present, F = 2 and we can vary independently any two of pressure, temperature, mole fraction of, say, component 1 in phase 1, or mole fraction of component 1 in phase 2. A knowledge only of the overall composition and either P or T is not sufficient to specify the state.