Gas absorption design — The absorption factor (A) is defined in terms of slopes as (S1 = slope of the operating line, S2 = slope of the equilibrium curve). Which expression is correct?

Introduction:
Design of packed and plate absorbers relies on graphical methods (McCabe–Thiele) and dimensionless groups. The absorption factor A links operating conditions to equilibrium behavior and influences the number of transfer units or theoretical stages required for a given separation.

Given Data / Assumptions:

• Operating line slope S1 = L/G for molar flows of lean solvent and gas (on appropriate basis).
• Equilibrium relation y* = m x with slope S2 = m for dilute systems.
• Linear equilibrium approximation in the region of interest.

Concept / Approach:

The absorption factor is defined as A = L/(m G), which compares solvent flow to the product of gas flow and equilibrium slope. In slope notation, A = S1/S2. Large A indicates a strong solvent or high solvent rate (steeper operating line relative to equilibrium), generally reducing the number of stages at the expense of higher solvent circulation.

Step-by-Step Solution:

Verification / Alternative check:

Stage-to-height relationships and Kremser equations use A explicitly; comparing slopes on the McCabe–Thiele diagram matches the S1/S2 form.

Why Other Options Are Wrong:

A inverts the factor; C and D are not dimensionally meaningful in this context; E is unrelated to established definitions.

Common Pitfalls:

Confusing slope of equilibrium with its inverse; always check the diagram axes and definitions to avoid inversion mistakes.

Final Answer:

S1/S2