McKay, Donald. "Front matter" Multimedia Environmental Models ...

In terms of solubilities, S iA and S iW, K AW is simply S iA/S iW, the ratio of the two
solubilities.
The pioneering work on air-water partitioning was done by Henry, who measured
P i as a function of x i and discovered that the solubility in water was proportional to
the partial pressure P i. The proportionality constant H´ is g if R and has units of pressure
(Pa). Interestingly, for super-critical gases such as oxygen, f R cannot be measured,
but g if R can be measured. If concentration is expressed as mol/m 3 , i.e., C i instead of
mole fraction x i, another and more convenient Henry’s law constant H can be defined
as P i/C i and is g iv Wf R. K AW is then obviously H/RT, and it is also Z A/Z W. Note that
H is also P S L/S iW and is 1/Z W, as was shown earlier. K AW is sometimes (wrongly)
referred to as a Henry’s law constant. Atmospheric scientists, who are concerned
with partitioning from air to water (e.g., into rain) use K WA, the reciprocal of K AW,
and often refer to it as a Henry’s law constant. Extreme care thus must be taken
when using reported values of Henry’s law constants because of these different
definitions.
For a liquid solute in a liquid-liquid system such as octanol-water,
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f = x iW g iW f R = x iO g iO f R
where subscripts W and O refer to water and octanol phases.
It follows that
and
x iO/x iW = g iW/g iO
C iO/C iW = K OW = g iW v W/g iO v O = S iO/S iW
If the solute is solid the same final equation applies because F, like f R, cancels.
Because v W and v O are relatively constant, the variation in K OW between solutes
is a reflection of variation in the ratio of activity coefficients g iW/g iO. Hydrophobic
substances such as DDT have very large values of g iW and low solubilities in water.
The solubility in octanol is usually fairly constant for organic solutes, thus K OW is
approximately inversely proportional to S iW. Numerous correlations have been proposed
between log K OW and log S iW, which are based on this fundamental relationship.
Finally, for completeness, the octanol-air partition coefficient can be shown to be
K OA = S iO/S iA = RT /g i v O P S L
where g i applies to the octanol phase. It can be shown that Z O is 1/g i v O P S L and that
K OA is Z O/Z A.
Measurements of solubilities and partition coefficients are subject to error, as is
evident by examining the range of values reported in handbooks. An attractive
approach is to measure the three partition coefficients, K AW, K OW, and K OA, and