Q1: The expression, ln(F/W) = is

ANS:A - differential distillation equation

The differential distillation equation is a mathematical expression used to describe the process of distillation, which involves separating a mixture of liquids based on their differences in volatility (boiling points). The equation provides a quantitative understanding of how the compositions of the liquid and vapor phases change as the distillation process progresses. The fundamental principle underlying the equation is based on the concept of vapor-liquid equilibrium, where at any given temperature and pressure, the composition of the vapor phase and the composition of the liquid phase are related. The general form of the differential distillation equation is: 𝑑𝑦𝑑𝑥=𝐾⋅(𝑥−𝑦)(1−𝑥)⋅(𝑦−𝑥)dxdy​=(1−x)⋅(y−x)K⋅(x−y)​ Where:

• 𝑦y is the mole fraction of the more volatile component in the vapor phase.
• 𝑥x is the mole fraction of the more volatile component in the liquid phase.
• 𝐾K is the equilibrium constant or the vapor-liquid equilibrium ratio.

This equation describes the change in composition of the more volatile component as it moves from the liquid phase to the vapor phase. The equation essentially states that the rate of change of the mole fraction of the more volatile component in the vapor phase (𝑑𝑦𝑑𝑥dxdy​) is proportional to the driving force for distillation, which is given by (𝑥−𝑦)(x−y), and is inversely proportional to the difference in the compositions of the liquid and vapor phases ((1−𝑥)⋅(𝑦−𝑥)(1−x)⋅(y−x)). In practical distillation processes, this equation helps in predicting how the composition of the distillate (vapor) changes with respect to the composition of the liquid feed as it travels through the distillation column. It is a fundamental tool for designing and optimizing distillation processes in various industries such as petrochemicals, pharmaceuticals, and beverage production.