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 \(\boxed{0.5}\).