Abstract: In the teaching of phase equilibrium in physical chemistry, the presentation of Gibbs’ phase rule often emphasizes intuitive phase diagram analysis while neglecting integration with fundamental thermodynamic principles and prerequisite empirical laws like Raoult’s law. This oversight limits students’ comprehensive understanding of the dynamic and systematic aspects of multicomponent phase equilibria. Using the condition of freedom f (or f *) = 1 in the phase rule as a pedagogical starting point, this study employs a process-oriented teaching approach to systematically integrate characteristic analyses of two-phase regions in single-component and binary system phase diagrams with theoretical formulations including the Clapeyron equation and Raoult’s law. By developing constraint equations and incorporating phase diagram interpretation, we elucidate the physical significance of “independent variables”, thereby deepening the understanding of intrinsic thermodynamic relationships in two-phase equilibrium systems. This teaching strategy, guided by intuitive empirical rules and combining numerical and graphical methods to analyze phase diagram configurations and thermodynamic constraints, not only enhances the internal coherence and logical progression of the knowledge system but also improves students’ ability to comprehend the scientific essence of the phase rule and apply this knowledge through transfer learning.

Key words: Thermodynamics, Phase ruleDegree of freedom, Phase equilibrium, Numerical-graphical integration