In packed towers, how do you calculate the slope of the operating line?

In packed towers, the slope of the operating line is derived from the relationship between the liquid and gas flow rates, as well as the concentrations of the species in the liquid and gas phases. The operating line represents the equilibrium between the phases throughout the tower.

The correct choice effectively relates the differences in concentrations of the components in the gas phase to those in the liquid phase, adjusted by the ratios of their flow rates. The equation Ls/Gs = (Ya1 - Ya2)/(Xa1 - Xa2) indicates that the slope of the operating line is determined by comparing the change in gas phase composition (Ya1 to Ya2) to the change in liquid phase composition (Xa1 to Xa2) over a specific segment of the tower. This reflects how the compositions of the two phases interact along the packed height, demonstrating a mass transfer relationship.

The numerator (Ya1 - Ya2) represents the difference in the gas phase compositions at two points, while the denominator (Xa1 - Xa2) shows the corresponding difference in the liquid phase compositions. This formulation is crucial because it facilitates graphical analysis of the mass transfer process in the tower, allowing for the determination of operational parameters effectively.

Understanding the slope of the operating line is essential for