Gas absorption design: For an absorber operating at steady state, the operating line on an equilibrium (y–x) diagram, relative to the equilibrium curve, typically lies where?

Introduction:
Graphical design of absorbers uses an equilibrium curve (y* vs. x) and an operating line (material balance). The relative position of these curves determines the driving force for mass transfer and the number of theoretical stages required.

Given Data / Assumptions:

• We consider absorption of a solute from gas to liquid (lean solvent).
• Coordinates: y for gas-phase solute fraction; x for liquid-phase solute fraction.
• Countercurrent contact with finite solvent flow rate.

Concept / Approach:
For absorption, the operating line must lie above the equilibrium curve to ensure a positive driving force (y − y*) across the column. If the operating line dipped below the equilibrium curve, portions of the column would have negative or zero driving force, making absorption infeasible. For stripping (desorption), the operating line is typically below the equilibrium curve.

Step-by-Step Solution:
Plot equilibrium relation y* = f(x).Write the operating line from overall/segment balances: y = m x + b.Ensure y ≥ y* throughout to maintain driving force for absorption.Therefore, the operating line lies above the equilibrium curve.

Verification / Alternative check:
Stage-by-stage (McCabe–Thiele) stepping fails if the operating line crosses below the equilibrium curve; practical design always keeps it above with margin for approach to equilibrium.

Why Other Options Are Wrong:

• Below or either side: Would imply loss of driving force.
• Velocity statement: Unrelated to y–x diagram placement.
• 45°-line comment: Not a general rule for absorption design.

Common Pitfalls:
Confusing absorption with stripping; remember the relative position reverses for desorption problems.

Final Answer:
line always lies above the equilibrium curve.