This lecture focuses on the design and analysis of distillation columns for the separation of binary mixtures. The instructor begins by discussing the limitations of single-stage flash columns and the importance of understanding the key components of distillation columns. The lecture outlines the intended learning outcomes, which include writing and solving mass and energy balances, calculating the number of stages using the McCabe-Thiele method, and determining the optimal feed location. The instructor explains the equilibrium relationship between liquid and vapor phases and how to influence the operation through flow rates. A significant portion of the lecture is dedicated to graphical methods for solving distillation problems, including the introduction of quizzes to engage students. The instructor emphasizes the importance of heat management within the column, detailing the roles of reboilers and condensers in maintaining temperature and achieving desired purity levels. The lecture concludes with a discussion on the design of trays and stages within the column, highlighting the need for effective liquid-vapor contact to ensure equilibrium and efficient separation.