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

Mackay (1986), in an attempt to simplify this correlation, forced m to be –1 and
obtained a one-parameter equation, using the liquid vapor pressure,
©2001 CRC Press LLC
K QA = 6 ¥ 10 6 /P S L
where K QA is a dimensionless partition coefficient, i.e., a ratio of (mol/m 3 )/(mol/m 3 ),
and P S L has units of Pascals. Here, we use subscript Q to designate the aerosol phase.
This enables Z Q, the Z value of the chemical in the aerosol particle, to be estimated
as K QAZ A. It can be shown that K QA is 10 12 K P(r/1000) where r is the density of
the aerosol (kg/m 3 ), i.e., typically 1500 kg/m 3 . The 10 12 derives from the conversion
of µg to Mg. The fraction on the aerosol j can then be calculated as
j = K QA v Q/(1 + K QA v Q)
where v Q is the volume fraction of aerosol and is 10 –12 TSP/(r/1000) when TSP has
units of mg/m 3 . TSP is typically about 30 mg/m 3 , plus or minus a factor of 5; thus,
v Q is about 20 ¥ 10 –12 , plus or minus the same factor. Equipartitioning between air
and aerosol phases occurs when j is 0.5 or K P·TSP and K QAv Q equals 1.0. This
implies a chemical with a K P of 0.03 m 3 /mg or K QAof 0.05 ¥ 10 12 and a vapor pressure
of about 10 –4 Pa.
It is noteworthy that Z Q has a value of K QAZ A or about (6 ¥ 10 6 /P S L)(4 ¥ 10 –4 )
or 2400/P S L. This is comparable to Z P, the pure substance Z value of 1/v P S L, where
v is the chemical’s molar volume and is typically 100 cm 3 /mol or 10 –4 m 3 /mol, giving
a Z P of about 10,000/P S L. This implies that the solute is behaving near-ideally in the
aerosol, i.e., the solubility in the aerosol is about 24% of the solubility of a substance
in itself. This casts doubt on the surface sorption model, since it seems a remarkable
coincidence that the area is such that it gives this near-ideal behavior. It further
suggests that Z Q may correlate well with Z O for octanol.
This was explored by Finizio et al. (1997), Bidleman and Harner (2000), and
Pankow (1998), leading ultimately to a suggestion that
K P = 10 –12 K OA y (1000/820) = 10 –11.91 K OA y
where 820 kg/m 3 is the density of octanol, and y is the fraction organic matter in
the aerosol, which is typically 0.2.
This reduces to
K P = 10 –12.61 K OA or 0.25 ¥ 10 –12 K OA m 3 /mg
the use of K OA is advantageous, because it eliminates the need to deduce the fugacity
ratio, F, when calculating the subcooled liquid vapor pressure. It is also possible
that, for a series of chemicals, the activity coefficients in octanol and aerosol organic
matter are similar, or at least have a fairly constant ratio.
This approach is appealing, because it mimics the Karickhoff method of calculating
soil-water partitioning, except that partitioning is now to air instead of water;
thus, K OA replaces K OW.