Although the units of m appear to be dimensionless, they actually are (weight acetone-free water)/(weight acetone-free toluene).
If more than one solute is present, the preference, or selectivity, of the solvent for one (A) over the other (B) is the separation factor (a).
The separation factor (a^) must be greater than unity in order to separate A from B by solvent extraction, just as the relative volatility must be greater than unity to separate A from B by distillation.
The analogy with distillation can be carried a step further. The extract phase is like the vapor distillate, a second phase wherein the equilibrium distribution of ,4 with respect to B is higher than it is in the feed liquid (liquid bottoms).
Extraction requires that the solvent and feed liquor be at least partially immiscible (two liquid phases), just as distillation requires both a vapor and a liquid phase.
Extraction requires that the solvent and feed phases be of different densities.
Even though extraction may successfully remove the solute from the feed, a further separation is required in order to recover the solute from the solvent, and to make the solvent suitable for reuse in the extractor. This recovery may be by any other unit operation, such as distillation, evaporation, crystallization and filtration, or by further extraction.
Extraction is frequently chosen as the desired primary mode of separation or purification for one or more of the following reasons:
1. Where the heat of distillation is undesirable or the temperature would be damaging to the product (for example, in the recovery of penicillin from filtered broth).
2. Where the solute is present in low concentration and the bulk feed liquor would have to be taken overhead (most fermentation products).
3. Where extraction selectivity is favorable because of chemical differences, but where relative volatilities overlap.
4. Where extraction selectivity is favorable in ionic form, but not in the natural state (such as citric acid).
5. Where a lower form or less energy can be used. The latent heat of most organic solvents is less than 20% that of water, so recovery of solute from an organic extract may require far less energy than recovery from an aqueous feed.
The combinations of mixing both feed and solvent until the equilibrium distribution of the solute has occurred, and the subsequent complete separation of the two phases is defined as one theoretical stage (Fig. 1). The two functions may be carried out sequentially in the same vessel, simultaneously in two different zones of the same vessel, or in separate vessels (mixers and settlers).
Extraction may also be performed in a continuous differential fashion (Fig. 2), or in a sequential contact and separation where the solvent and feed phases flow countercurrently to each other between stages (Fig. 3).
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