Page 41 - Partition & Adsorption of Organic Contaminants in Environmental Systems

32 INTERPHASE PARTITION EQUATIONS

ties associated with the water phase. By Eq. 3.5 and omitting the subscript i,
one finds that

V V (3.6)
w
logK sw = logg* - logg* s + log * w - log * s
If the solute has a low solubility in water, one obtains from Eqs. (2.2), (2.5),
and (3.3) the molar solubility of the solute in water (S w) as
l ()
S w = 1 g w V w for liquid solutes (3.7)

and
s ()
s
S w = a g w V w for solid solutes (3.8)
o
s
s
s
where a is the activity of the pure solid substance at T (i.e., a = P /P ) as
defined by Eq. (2.4). From Eqs. (3.7) and (3.8), the supercooled liquid solu-
(s)
(l)
bility of a solid, S w , is related to the solid solubility S w as follows:
l ( )
s ()
o
s
s
S w = S w s () a = S w ( P P ) (3.9)
Substituting Eq. (3.7) into (3.6), one obtains for liquid (or supercooled-liquid)
solutes,
* * * *
logK sw =- logS w - logV s - logg s - log(g w g w + V w ) (3.10)
) log(V w
In Eq. (3.10), the S w value for a solid solute is that of the supercooled liquid,
as determined according to Eq. (3.9). The melting-point effect that affects the
solid solubility in a single phase (e.g., water) does not affect the partition
coefficient (K sw) because the effect cancels out in solute partition between any
two separable phases. The g w/g* w term corrects for the effect of the dissolved
organic solvent in water on the solute water solubility. The value of g w/g* w is
usually greater than 1 and is called the solubility enhancement factor.In
solvent–water systems, where the solvent has a limited solubility in water, the
change in the molar volume of water due to solvent saturation is not substan-
tial (i.e., V * w/V w 1). Under this condition, Eq. (3.10) is further reduced to
* * *
logK sw =- logS w - logV s - logg s - log(g w g w ) (3.11)

3.3 PARTITION BETWEEN A MACROMOLECULAR
PHASE AND WATER

The solute partition coefficient at dilution between an amorphous polymeric
or macromolecular organic substance and water (K pw ) cannot be represented
by Eq. (3.6) or (3.11). This is because the solubility of common organic solutes
in a macromolecular phase, as expressed by Eqs. (2.13) and (2.15), is under-