F = C − P + 2
Gibbs phase rule F = C − P + 2 predicts the number of intensive variables (degrees of freedom) that can be independently varied without changing the number of phases in equilibrium. C = number of independent chemical components, P = number of phases, 2 accounts for temperature and pressure. For pure water (C=1): at the triple point (P=3), F=0 (fixed at T=0.01°C, P=611.73 Pa). At a phase boundary (P=2), F=1 (e.g., boiling point depends on pressure). In a single phase (P=1), F=2 (T and P independently variable). For binary mixtures (C=2), phase diagrams are richer: eutectic points, azeotropes, and miscibility gaps. The phase rule is essential in metallurgy, materials science, geology, and chemical engineering for understanding and controlling equilibrium.