Solute Distribution

Chemical extractions proceed by a drive towards equilibrium. Consequently, knowledge of the equilibrium distribution of the solute between the phases is useful. Berthelot and Jungfleisch studied phase distribution in 1871 and twenty years later, in 1891, Nernst developed his distribution law in which KD = (concentration of solute in phase1)/(concentration of solute in phase 2), where KD is the distribution coef-icient. However, the simple ratio of solute concentrations is not thermodynamically rigorous, since it does not account for association or dissociation in either phase. The IUPAC (International Union of Pure and Applied Chemistry) definition of the distribution ratio, K', includes all species of the same component and is used when the solute does not chemically react in either phase. This definition discusses the ratio, in organic-aqueous systems, as 'the total analytical concentration of the substance in the organic phase to its total analytical concentration in the aqueous phase, usually measured at equilibrium'. This relationship follows from Gibbs' phase rule in which: P + V = C + 2, where P is the number of phases, V is the number of degrees of freedom (independent system variables), and C is the number of components. So for the example of a simple extraction with two immiscible phases and a single solute of interest, P = 2 and C = 3. At constant temperature and pressure, the number of degrees of freedom is one, meaning the solute concentration in each phase is fixed. (Note that while activities and concentrations are not strictly equivalent, they can generally be treated equally over practical concentration ranges.)

Distribution ratios cannot be determined from the relative solubility data for several reasons: (1) the extraction may not be at equilibrium, (2) mutual solubility of the phases, and (3) solubility differences, for example between hydrated and anhydrous forms of the solute. Therefore the ratio of solubilities is not the same as the distribution ratio for these same reasons. However, if solvation is properly considered, the relationship between solubility and extractability can be determined, especially for liquid-liquid systems. Assuming equilibrium and phase immiscibility, the fraction of solute extracted, E, can be determined for a given phase ratio, V or V1/V2, by the expres-

sions:

where C is the solute concentration, n is the number of extractions (assuming the extracted phases are pooled), and subscripts 1 and 2 represent the two phases. A practical application of the use of distribution ratios is shown in Figure 3, which illustrates the need for a series of extraction stages, rather than simply, an increase in the volume of extraction

Figure 3 Relationship between distribution ratio and amount (percent) of solute extracted for (A) phase ratio of one, (B) phase ratio of two, and (C) phase ratio often.

Table 2 Solute distribution between phases in multistage extraction

Stage

Distribution ofsolute

Initial equilibrated sample a

b

First transfer

0

a

b

0

Amount of solute

a

b

in each stage

Second transfer

0

ab

b2

ba

Amount of solute

b2

2ab

in each stage

Third transfer

0

ab2

b3

2b2a

Amount of solute

b3

3b2a

in each stage

Amount of solute

2ba2

3a2b in each stage upon subsequent transfers a2 0 a2

2ba2

(a # b)3 (a # b)n in each stage upon subsequent transfers solvent. In this example, assuming a constant distribution ratio of 1, a doubling of the extraction volume (from phase ratio = 1 to phase ratio = 2, where the phase ratio is the simple ratio of the extraction solvent volume to the sample volume) only increases the amount extracted in a single stage from about 50% to about 66%. A ten-fold increase in solvent volume only increases the amount extracted from about 50% to about 90%. As additional stages are added, the solute distributes itself in each phase. This is similar to the distribution studied by Craig and shown in Table 2. In this case, a solute distributes itself between the two phases in the ratio of a/b and the amount of solute in each stage can be determined. In practice, however, the stages are combined to maximize solute yield and recovery.

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