How is vapor-liquid equilibrium used to calculate the separation of different substances during distillation?

Vapor-liquid equilibrium (VLE) is a fundamental concept used to predict and calculate the separation of different substances during distillation because it describes the distribution of components between the vapor and liquid phases at a given temperature and pressure when the system is in equilibrium. In distillation, the goal is to separate components with different boiling points. VLE data provides information on how the composition of the vapor phase relates to the composition of the liquid phase for a mixture of substances. For an ideal mixture, Raoult's Law states that the partial pressure of a component in the vapor phase is equal to the mole fraction of that component in the liquid phase multiplied by its vapor pressure in the pure state. However, most real-world mixtures, especially those containing alcohols and water, deviate from ideal behavior, requiring more complex thermodynamic models to accurately predict VLE. These models, such as the Antoine equation or activity coefficient models like NRTL or UNIQUAC, account for the non-ideal interactions between molecules. To calculate the separation during distillation, VLE data is used in conjunction with mass and energy balance equations to model the distillation process. For example, in a simple distillation, the VLE data is used to determine the composition of the vapor that is produced when the liquid is heated. The vapor will be enriched in the component with the lower boiling point. In a fractional distillation column, VLE is used to model the equilibrium stages within the column. At each stage, vapor and liquid are assumed to be in equilibrium, and the composition of the vapor and liquid phases are calculated based on the VLE data. These calculations are then used to determine the number of theoretical plates required to achieve a desired separation. Therefore, understanding and applying VLE principles is essential for designing and optimizing distillation processes to achieve the desired purity and composition of the final product.