This lecture covers the thermodynamic principles related to mixtures, focusing on the behavior of real gases and liquids. It begins with the interpretation of chemical potential and the application of Raoult's law to ideal solutions. The instructor explains the concepts of dew point and boiling point curves, illustrating how pressure affects the phase behavior of mixtures. The discussion includes examples of benzene and toluene mixtures, highlighting the differences in vapor pressures and the resulting phase transitions. The lecture further delves into fractional distillation, explaining how to separate components based on their boiling points and vapor compositions. The Gibbs-Duhem equation is introduced to describe the relationship between chemical potentials in binary systems. The instructor emphasizes the significance of activity coefficients in non-ideal solutions and how they influence the distillation process. The lecture concludes with a discussion on azeotropes and the limitations of separation techniques, providing a comprehensive understanding of thermodynamic principles in mixtures and distillation.