Originally formulated by the American scientist Josiah Willard Gibbs in the 1870’s, the phase rule determines the number of independent variables that must be specified to establish the intensive state of any system at equilibrium. The derivation of the general phase rule is shown in chapter 6, but here we state it without proof:

(1.10)

Here, F = degrees of freedom of the thermodynamic system in question; N = Number of components; π = number of co-existing phases, and r = number of independent reactions that may occur between the system components. For a non-reactive system, the phase rule simplifies to: