This lecture covers the fundamentals of vapor-liquid phase diagrams and their application in separation processes. It begins with an introduction to graphical methods, specifically the T-x-y diagram, where a subcooled liquid mixture is heated to form saturated liquid and vapor phases in equilibrium. The instructor explains how to estimate the quantities of these phases using the lever rule, emphasizing the relationship between the distance of the equilibrium point from the liquid and vapor lines. The lecture also discusses the similarities and differences between T-x-y and H-x-y diagrams, highlighting the significance of the tie line and its implications for enthalpy. The instructor presents a practical example involving a biofuel fermentation plant, illustrating how to increase the concentration of biofuel using phase diagrams. The session concludes with a discussion on the importance of understanding these diagrams for designing effective separation processes, particularly in industrial applications.