Twophase Distribution Equilibria

Definitions The process of extraction, by definition, requires that the analyte be transferred from the matrix to a different phase. When the extracting medium first contacts the matrix, the analytes will become distributed between the two phases in a well-defined ratio. Since the matrix is usually a liquid or solid, and the extracting medium can be a solid, liquid or fluid, this usually refers to liquid-liquid and liquid-solid distribution equilibria.

These distribution equilibria can be described by several important equations. First, the distribution ratio, D, for extracting from phase 1 into phase 2 is defined as:

Reproduced with permission of ACCTA, Inc.

where C is the stoichiometric concentration of the analyte in each of the phases. (Actually, D is related

to the ratio of activities rather than concentration, but in dilute solution the difference is negligible.)

This ratio is a constant that depends on the analyte, the two phases, the composition of the phases (pH, ionic strength, etc.) and the temperature.

The fraction extracted, 6, in any one equilibration is defined as:

6 DP 6 = T#Dft where ft is the phase ratio, the ratio of the volumes of the two phases ( = V2/VT). The fraction remaining in the initial phase (VT) is, of course 1—6.

The amount extracted depends on the physico-chemical interactions between the two phases and the analyte, and the volume of each phase. A change in these variables will cause a change in the extraction result.

Effect of analyte structure on D Actual values of D in Table 2 show how simple changes in molecular structure have a profound influence on the success of an extraction.

The addition of nonpolar functional groups (methyl- and chloro-) to benzene make the molecule more nonpolar, so that the new molecule favours the hexane phase (larger value for D). Conversely, adding polar groups (amine, hydroxy, carboxylic acid) makes the molecule more like the water phase (smaller D). It is important to keep these general principles in mind when developing an extraction method and understanding the results.

Multiple extractions When multiple extractions are performed on the same sample, the amount extracted into phase 2 and the amount remaining in phase Tare calculated using the equations shown in Table 3.

In general, several extractions with the same total volume of extracting solvent will always produce better recovery than a single extraction with the same

Table 2 Distribution ratios for extraction from water into hexane


Added functional

Functional group

D (25°C)















Moderately polar










Benzoic acid


Very polar


Reproduced with permission from Sekine and Hasegawa (1977)

Reproduced with permission from Sekine and Hasegawa (1977)

Table 3 Equations used for multiple extractions

Extraction number

Fraction extracted

Fraction remaining

into phase 2

in phase 1



1— 6


6(1 — 6)

(1 — 6)2


6(1 — 6)2

(1 — 6)3


6(1 — 6)"~1

(1 — 6)n

volume of solvent, although it is seldom worth carrying out more than three extractions.

Effect of variations in D and ft The effects of variations in D and ft on extraction results are shown in Table 4. The total recovery after multiple extractions is calculated for various combinations of D and ft. These calculations show the importance of all three variables: phase ratio, distribution ratio and number of extractions.

In summary, two-phase distribution equilibria are an important part of every analytical extraction, and the laboratory scientist must ensure that all critical variables are controlled in order to generate reliable results.

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