This lecture covers the principles of liquid-liquid extraction, focusing on the purification of acetic acid from an aqueous solution using 1-butanol as a solvent. The instructor presents a problem involving an aqueous solution containing 1.8 mole% acetic acid, aiming to reduce this concentration to 0.2% through countercurrent extraction. The flow rates of both the acetic acid solution and the solvent are provided, and the instructor guides the audience through the calculations required to determine the number of stages needed for the extraction process. The lecture also discusses the graphical method for calculating concentrations and stages, emphasizing the importance of equilibrium and operating lines in the extraction process. Additionally, the instructor introduces the concept of cross-flow extraction, explaining how it differs from countercurrent extraction and the implications for solvent flow rates and compositions. The session concludes with a quiz to reinforce understanding of the concepts presented, including the identification of key points in the extraction process.