Gas absorption design: the “absorption factor” is defined using slopes as A = (slope of operating line) / (slope of equilibrium line). Which ratio expresses this?

Introduction / Context:
In gas absorption, the absorption factor simplifies stage calculations and helps screen solvent-to-gas ratios. Using a linear equilibrium relation y* = m x and an operating line y = y1 + (L/G)(x − x1), the absorption factor A relates mass-transfer driving forces to operating conditions.

Given Data / Assumptions:

• S1 = slope of equilibrium line = m.
• S2 = slope of operating line = L/G (on appropriate coordinates).
• Linear equilibrium and dilute systems assumptions apply for the definition.

Concept / Approach:
By definition, A = (L/G) / m = S2 / S1. Values of A > 1 generally indicate favorable absorption (sufficient solvent flow), whereas A close to or below 1 indicates more trays or higher solvent rates are needed for the same removal.

Step-by-Step Solution:

Verification / Alternative check:
Classic stagewise design methods (Kremser equations) use A directly; plugging in S2/S1 matches the textbook definition.

Why Other Options Are Wrong:

• S1/S2 or products/inverses do not match the definition.
• Sums of slopes are not used for A.

Common Pitfalls:
Using inconsistent coordinates or units so that S2 is not L/G; applying A outside the linear-dilute regime.

Final Answer:
S2/S1