# Phase Rule

Entry by Andrew Capulli

**Definition: Phase Rule** (Gibbs' Phase Rule)

The phase rule relates:

- F: The degrees of freedom of the system; see below.
- P: The number of phases that can coexist; any separable material in the system. A phase can be a pure compound (say water for example) or a mixture (solid or aqueous), but the phase must "behave" as a consistent substance. For example, ice and liquid water are two separate phases in a one component system (H20). Similarly, higher component systems may have phases made up of multiple components (ie a phase can be composed of more than one component).
- C: The number of components (that make up the phases)

**The Phase Rule States: the degrees of freedom of a system is equal to the number of components minus the number of phases plus two**... the 2 comes from the extensive variables Temperature and Pressure.

The 'degrees of freedom' of the system (at chemical equilibrium) refer to the number of conditions or variables that can be altered, independent of each other, without effecting the number of phases in the system. Essentially, the degrees of freedom of a system describe the dependency of parameters such as temperature and pressure on each other.

The Phase Rule describes the number of variables (and equations) that can be used to describe a system (at chemical equilibrium). The number of chemical components (C in the equation above) in addition to the "extensive variables" (temperature and pressure) comprise the 'variables' of a system. The degrees of freedom of a system dictate the number of phases (as described above in the bullet list) that can occur in the system.

*Note*

The critical point (on a phase diagram) can only exist at one temperature and pressure for a substance or system and thus the degrees of freedom at any critical point is zero.

*An Example of the Phase Rule: 1 Component System* :Take the generic 1 component phase diagram below (from class). So, at A, B, and C (and all points for that matter, we consider the system to have one component, ie C = 1. At A, there are two possible phases at a fixed temperature as shown by the red line drawn through point A; these phases are gas and liquid. Since there is one component and two phases, using the Phase Rule equation, the degrees of freedom of the system at A is one. At B there are three possible phases (gas, liquid, and solid) and consequently the degrees of freedom of the system is 0 (ie B is a critical point). Similarly we can find at C the degrees of freedom to be one because there are two possible phases (fluid or solid) as indicated by the red line drawn through C.

The Wikipedia article "Gibbs Phase Rule" has a number of examples using the phase rule on a phase diagram to determine the degrees of freedom of a system at a given point; it can be found at: http://en.wikipedia.org/wiki/Gibbs%27_phase_rule.

References:

[1] http://www.chemicool.com/definition/phase_rule.html

[2] http://serc.carleton.edu/research_education/equilibria/phaserule.html

[3] http://en.wikipedia.org/wiki/Gibbs%27_phase_rule

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