What is the operating line equation for packed towers?

The operating line equation for packed towers is crucial in the analysis of mass transfer operations. In gas absorption and distillation units like packed towers, the relationship between the liquid and gas phases is depicted by the operating line, which represents the balance of mass transfer between these phases.

The correct choice reflects that the actual liquid-to-gas ratio (Ls/Gs) is proportional to the difference in concentrations of the solute (or species) in the gas and liquid phases across two points in the packed tower, represented by (Y1 - Y2) for the gas phase and (X1 - X2) for the liquid phase. This equation arises from the overall material balance along the packed column.

Consider that Y1 and Y2 are the concentrations of the component in the gas phase at two different locations, and X1 and X2 are the concentrations in the liquid phase at the same locations respectively. By focusing on the change in these concentrations, the operating line can effectively illustrate the performance of the mass transfer process, yielding insights into the efficiency of the tower.

This balance captures the essence of how changes in concentration drive the mass transfer between the two phases, ensuring that the correct operating line equation aligns with the principles of mass transfer and phase equilibrium for packed