Gibbs' Phase Rule

The Phase Rule describes the possible number of degrees of freedom in a (closed) system at equilibrium, in terms of the number of separate phases and the number of chemical constituents in the system. It was deduced from thermodynamic principles by J. W. Gibbs in the 1870s.

The Degrees of Freedom [F] is the number of independent intensive variables (i.e. those that are independent of the quantity of material present) that need to be specified in value to fully determine the state of the system. Typical such variables might be temperature, pressure, or concentration.

A Phase is a component part of the system that is immiscible with the other parts (e.g. solid, liquid, or gas); a phase may of course contain several chemical constituents, which may or may not be shared with other phases. The number of phases is represented in the relation by P.

The Chemical Constituents are simply the distinct compounds (or elements) involved in the equations of the system. (If some of the system constituents remain in equilibrium with each other whatever the state of the system, they should be counted as a single constituent.) The number of these is represented as C.

The rule is:

F = C - P + 2.

For example:

A system with one component and one phase (a balloon full of carbon dioxide, perhaps) has two degrees of freedom: temperature and pressure, say, can be varied independently.

If you have two phases -- liquid and vapour for instance -- you lose a degree of freedom, and there is only one possible pressure for each temperature.

Add yet one more phase -- ice, water and water vapour in a sealed flask -- and you have a "triple point" with fixed temperature and pressure.