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?
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AS2/S1
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BS1/S2
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CS1 − S2
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DS1 × S2
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E(S1 + S2)/2
Answer
Correct Answer: S1/S2
Explanation
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:
Start from A = L/(m G).Identify S1 = L/G and S2 = m.Substitute: A = (L/G)/m = S1/S2.Thus the correct expression is S1/S2.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