This lecture covers the fundamentals of vapor-liquid phase diagrams and their significance in separation processes. It begins with a recap of thermodynamics, defining key concepts such as phase, steady-state, and phase equilibrium. The instructor explains that phase equilibrium occurs when the temperature, pressure, and chemical potential of a component in one phase equals those in another phase. The discussion includes thermal, mechanical, and chemical equilibria, illustrating how heat and pressure differences drive spontaneous changes until equilibrium is reached. The lecture also introduces the concept of degrees of freedom in a system, explaining how to determine the number of independent variables based on the Gibbs phase rule. The instructor emphasizes the importance of understanding these principles for creating accurate phase diagrams, which are essential in various separation processes like distillation and extraction. Overall, the lecture provides a comprehensive overview of the principles governing phase behavior and equilibrium in thermodynamic systems.