Why can repeated extractions with fresh solvent remove more material than one extraction with a large volume of solvent?

In liquid-liquid extraction, repeated extractions with fresh solvent are more efficient than a single extraction using the same total volume of solvent because of the nature of chemical equilibrium.

When a substance is distributed between two immiscible liquids, it reaches an equilibrium state defined by its distribution coefficient. In a single-stage extraction, the amount of material removed is limited by this equilibrium ratio. By removing the solvent containing the extracted material and replacing it with an equal volume of fresh solvent, you disrupt the established equilibrium. This forces the system to re-equilibrate, allowing a fresh portion of the remaining material to partition into the new solvent.

Consequently, performing multiple consecutive equilibrations with smaller, fresh portions of solvent extracts a higher cumulative percentage of the target material than a single extraction with a large volume of solvent, which quickly reaches a point of diminishing returns where no further significant transfer occurs.1