Partial Properties & Derivation of the Gibbs-Duhem Equation

Partial molar properties play a crucial role in thermodynamics, especially in understanding mixtures. In this video, I start with the fundamental property relation and explain how partial properties are defined—as the rate of change of a mixture property when a small amount of a specific species is added. For example, how does the volume of a water-ethanol mixture change when one mole of pure ethanol is added? From there, I take you through the step-by-step mathematical derivation of the Gibbs-Duhem equation, showing how it emerges directly from the fundamental thermodynamic relationships. By the end of this video, you'll have a solid understanding of why the Gibbs-Duhem equation is important and how it constrains the behavior of partial molar properties in mixtures.