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?

Difficulty: Easy

Correct Answer: A large distribution coefficient

Explanation:


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

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