Design goal in extraction: A process that requires less solvent and yields a more concentrated extract phase is best achieved with what magnitude of distribution coefficient (D) for the solute?

Introduction:In countercurrent liquid–liquid extraction, solvent usage and extract concentration are controlled by equilibrium partitioning. Understanding how the distribution coefficient D influences material balances is central to solvent selection and stage optimization.

Given Data / Assumptions:

• D = C_extract/C_raffinate at equilibrium for the solute of interest.
• Fixed phase flow rates aside from solvent choice.
• Countercurrent operation considered for efficiency.

Concept / Approach:Large D values favor transfer of solute into the solvent with few stages and minimal solvent flow, producing a concentrated extract. Small D values require more solvent and/or more stages to achieve the same recovery, diluting the extract phase and increasing equipment size.

Step-by-Step Solution:Write overall extraction factor E = D * (S/F) where S and F are phase flow rates.For fixed S/F, larger D gives larger E and higher stage efficiency.To meet a target recovery at small D, S must be increased, which dilutes the extract.Therefore, a large D minimizes solvent usage and maximizes extract concentration.

Verification / Alternative check:Graphical McCabe–Thiele constructions show that, for given S/F, higher D steepens tie lines and reduces the number of stages, while increasing extract composition—consistent with the design goal stated.

Why Other Options Are Wrong:Small or very small D: imply poor partitioning; more solvent and stages are needed, hurting concentration.

“Constant” D without magnitude: magnitude matters; only a large D achieves the stated objective.

Common Pitfalls:

• Ignoring temperature and pH dependence of D.
• Confusing distribution coefficient with selectivity; both matter but address different objectives.

Final Answer:A large distribution coefficient