Page 40 - Partition & Adsorption of Organic Contaminants in Environmental Systems

PARTITION BETWEEN AN ORGANIC SOLVENT AND WATER 31

K i,AB = C i,A C i,B = (g i,B g i,A )( V V A ) (3.4)
B
In natural aquatic systems, contaminants are usually present at subsaturated
levels in water, and thus one is largely interested in the partition coefficients
of contaminants at low concentrations between an organic phase and water.
The expressions for K* i,AB and K i,AB in Eqs. (3.2) and (3.4) have so far been
simplified with the assumption that the two solvent phases between which the
solute partitions (i.e., dissolves) are completely immiscible to each other. Thus,
the solubility behavior of the solute with the two separable phases is assumed
to be the same as that with the two pure solvents. Although this assumption
holds as a good approximation for a number of systems, such as mixtures of
water and a highly water-insoluble aliphatic hydrocarbon, it is not practical for
many systems in which the two solvent phases are mutually soluble to a sig-
nificant extent. A more general expression for the solute partition coefficient
should be written as
* * * * * *
K i,AB = C i,A C i,B = (g i,B g i, )( V B V ) (3.5)
A
A
where the associated terms are labeled with a superscript asterisk to take into
account the change of the property of one solvent by the saturated amount of
the other solvent as a result of their mutual saturation. Thus, C* is the con-
i,A
centration of the solute in solvent A–rich phase, which contains a saturated
amount of solvent B, g* is the activity coefficient of the solute at a given
i,A
concentration in solvent A–rich phase with a saturated amount of solvent B,
and V *
A is the molar volume of the solvent A–rich phase. In general, if the
solvent–solvent (or phase–phase) mutual saturation is not substantial, the
change in molar volume is usually less significant than the change in solute
activity coefficient. Further, the solvent mutual-saturation effect on solute
activity coefficient varies with the extent of solute solubility, while the effect
on the solvent molar volume is identical for all solutes. As expected, if the
solvent–solvent mutual saturation effect is insignificant, Eq. (3.5) simplifies to
Eq. (3.4). It must be kept in mind, however, that the derivations of Eqs. (3.1)
to (3.5) are theoretically rigorous only to the extent that the solute solubili-
ties in the two solvents are well represented by Raoult’s law: namely, that
there is no large molecular-size disparity between the solute and the solvent
of interest.

3.2 PARTITION BETWEEN AN ORGANIC SOLVENT AND WATER

Since we are commonly interested in the partition behavior of organic solutes
between water and partially water-miscible organic solvents, we consider first
Eq. (3.5) for solutes with a solvent–water mixture in terms of the associated
parameters. In the text that follows, the subscript s is used to refer to quanti-
ties associated with the organic-solvent phase and the subscript w to quanti-