Page 45 - Partition & Adsorption of Organic Contaminants in Environmental Systems

36 INTERPHASE PARTITION EQUATIONS

s
relation between the P of a solid substance and the P° of the corresponding
supercooled liquid at temperature T is illustrated graphically in Figure 1.2.
s
Once the a of a solid is determined by Eq. (3.25), it then enables one to cal-
culate the supercooled liquid solubility at T from the measured solid solubil-
ity by Eq. (3.9).

3.5 CONCENTRATION DEPENDENCE OF
PARTITION COEFFICIENT

In derivations of the partition coefficients for solutes between an organic
phase and water, we have assumed that the solutes are present at dilution in
both solvent phases. For solutes that are sparingly soluble in water, this
assumption is closely met in the water phase and similarly met in the organic
phase if the concentration is kept low. If the solute of interest is a solid with
a relatively high melting point (say, t m >> 100°C), the maximum solute con-
centration in any solvent will always be low in absolute magnitude and hence
the dilute-solution approximation will always hold, largely independent of the
solute concentration. For liquid solutes or other solid solutes with low melting
points that are relatively soluble in the organic phase of a solvent–water
mixture (or a macromolecular phase–water mixture), the partition coefficients
may be concentration dependent if the concentration is more than 10 to 20%
in the organic phase. Although it is not common to measure the partition co-
efficient at such high concentrations, it is of interest to consider the possible
concentration dependence of the partition coefficient, since the result may be
of value to the characterization of the association of an organic solute with a
natural organic substrate.
To evaluate the dependence of the partition coefficient (K sw ) on concen-
tration, one makes use of an isotherm that relates the solute concentration in
the organic–solvent phase (C s ) to that in water (C w ) over a wide range of C w
at a given temperature. If the dilute-solution approximation holds for the
entire concentration range, as for solutes (liquids or solids) that exhibit small
solubilities in both solvents, the relation between C s and C w by Eq. (3.11), or
that between C p and C w by Eq. (3.13), should be virtually linear from C w = 0
to C w = S w , as depicted in Figure 3.1.
On the other hand, if the solute is very soluble in the organic phase but
does not behave nearly ideally, the isotherm will not have a linear shape but
will instead exhibit a moderate concave-upward curvature at the high C w
region, as depicted in Figure 3.2. In this case the expression for partition coef-
ficient is more sophisticated than that given by Eq. (3.11) or (3.13). The main
cause for the nonlinear partition coefficient is the change in solute activity
coefficient in the organic phase (g* s or the equivalent c H ) with solute concen-
tration. This may be expected on the grounds that when the solute concen-
tration reaches an appreciable level in an organic phase, the composition of
the organic phase is modified significantly, such that it becomes appreciably