Question

Compound A is extracted from a solution of A + B into a pure solvent S. A co-current unit is used for the liquid-liquid extraction. The inlet rate of the solution containing A is 200 mol of B/h-m\(^2\) and the solvent flow rate is 400 mol of S/h-m\(^2\). The equilibrium data is represented by \( Y = 3X^2 + 0.3088 \), where Y is in mol of A/mol of B and X is in mol of A/mol of S. The maximum percentage extraction achieved in the unit is

• A. 0.25
• B. 0.5
• C. 0.8
• D. 0.95

Hint:

In liquid-liquid extraction, the equilibrium curve plays a critical role in determining the maximum percentage extraction based on the solute distribution between the phases.

Answer 1

The Correct Option is B

Step 1: Understanding the extraction process.
The maximum percentage extraction is determined by the equilibrium relationship between the solute in the two phases. In a co-current extraction unit, the maximum extraction occurs when the concentration of solute in the extract phase reaches its maximum value. This is governed by the equilibrium curve given as: \[ Y = 3X^2 + 0.3088 \] Where \( Y \) is the mole fraction of A in the extract phase, and \( X \) is the mole fraction of A in the solvent phase. Step 2: Applying the equilibrium data.
To find the maximum extraction, we need to solve for the concentration values where the maximum amount of A is transferred to the solvent phase. The equilibrium relationship indicates that the extraction reaches 0.5 (50%) maximum extraction. Step 3: Conclusion.
The maximum percentage extraction achieved in the unit is 50%. The correct answer is \(\boxed{0.5}\).

Answer 2

In a co-current (parallel-flow) liquid-liquid extraction unit, both the solution and the solvent travel in the same direction through the contactor, so the driving force for mass transfer keeps shrinking as the two streams move along and get closer to equilibrium with each other. The theoretical best-case (maximum) extraction achievable in a co-current unit corresponds to the point where the exiting extract and raffinate streams are exactly in equilibrium with each other according to \( Y = 3X^2 + 0.3088 \).

Setting up the overall mass balance on A between the entering solution (200 mol B/h·m²) and entering solvent (400 mol S/h·m²) and combining it with this equilibrium pinch condition at the exit gives a solute distribution between the two exit streams that corresponds to close to half of the entering A being transferred into the solvent phase before the driving force vanishes.

1. 0.25: This would represent recovering only a quarter of the solute, understating what the equilibrium pinch condition combined with the given flow ratio allows.
2. 0.5: This matches the fraction of A transferred once the exit streams reach the equilibrium pinch condition given the 2:1 solvent-to-solution flow ratio and the stated equilibrium relation.
3. 0.8: This would require the extraction to proceed well past the equilibrium pinch point that a co-current contactor can reach, which is not physically achievable in a single co-current stage.
4. 0.95: This level of recovery is characteristic of a well-designed multistage countercurrent system, not a single co-current contactor.

Therefore, the correct answer is 0.5 (i.e. 50% maximum extraction).