Part of JOC-09 — Practical & Purification of Organic Compounds

Differential Extraction and Distribution Law

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Principle: Nernst distribution law — a solute distributes between two immiscible solvents such that the ratio of concentrations is constant at a given temperature:

K = C(organic phase) / C(aqueous phase) — the partition coefficient

If K > 1 for ether/water, the compound prefers the organic phase → extraction is favorable.

Mathematical proof that multiple small extractions are better than one large extraction:

If total volume V of organic solvent is used, and the aqueous phase has volume W, with initial mass m of solute:

After one extraction with V mL: mass remaining = m x WW+KV\frac{W}{W + KV}

After n extractions with V/n mL each: mass remaining = m x [WW+KV/n\frac{W}{W + KV/n}]^n

Since [WW+KV/n\frac{W}{W + KV/n}]^n < WW+KV\frac{W}{W + KV} for n > 1, multiple extractions always leave less compound behind.

Practical rule: 3 extractions with 1/3 volume each recover significantly more than 1 extraction with full volume.

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