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

©2001 CRC Press LLC
5.4 PARTITION COEFFICIENTS
5.4.1 Fugacity and Solubility Relationships
If we have two immiscible phases or media (e.g., air and water or octanol and
water), we can conduct experiments by shaking volumes of both phases with a small
amount of solute such as benzene to achieve equilibrium, then measure the concentrations
and plot the results as was shown in Figure 5.1. It is preferable to use
identical concentration units in each phase of amount per unit volume but, when
one phase is solid, it may be more convenient to express concentration in units such
as amounts per unit mass (e.g., mg/g) to avoid estimating phase densities. The plot
of the concentration data is often linear at low concentrations; therefore, we can write
C 2/C 1 = K 21
and the slope of the line is K 21. Some nonlinear systems are considered later. Now,
since C 2 is Z 2f 2 and C 1 is Z 1f 1, and at equilibrium f 1 equals f 2, it follows that K 21 is
Z 2/Z 1. A Z value can be regarded as “half” a partition coefficient. If we know Z for
one phase (e.g., Z 1 as well as K 21), we can deduce the value of Z 2 as K 21Z 1. This
proves to be a convenient method of estimating Z values.
The line may extend until some solubility limit or “saturation” is reached. In
water, this is the aqueous solubility, but, for some substances such as lower alcohols,
there is no “solubility,” because the solute is miscible with water. In air, the “solubility”
is related to the vapor pressure of the pure solute, which is the maximum
partial pressure that the solute can achieve in the air phase.
Partition coefficients are widely available and used for systems of air-water,
aerosol-air, octanol-water, lipid-water, fat-water, hexane-water, “organic carbon”water,
and various minerals with water.
Applying the theory that was developed earlier and noting that, at equilibrium,
the solute fugacities will be equal in both phases, we can define partition coefficients
for air-liquid and liquid-liquid systems.
For air-water as an example at a total atmospheric pressure P T,
Thus,
f = x ig if R = y iP T = P i
y i/x i = g if R/P T
But if we use concentrations C i (mol/m 3 ) instead of mole fraction, y i is C iAv A or
C iART/P T where v A is the molar volume of air. Similarly, x i is C iWv W where v W is
the molar volume of the solution and is approximately that of water. Since f R is also
P S , the partition coefficient K AW is then given by
K AW = C iA/C iW = g i v W f R/RT = g i v W P S /RT = S iA/S iW