Page 87 - Partition & Adsorption of Organic Contaminants in Environmental Systems

78 CONTAMINANT PARTITION AND BIOCONCENTRATION

In those systems where a good linear correlation between logK sw,2 and logK sw,1
is observed, the correlation is frequently called a linear free-energy relation-
ship (LFER), since the logarithmic term of a partition coefficient (which is an
equilibrium constant, K) is related to the molar free-energy change of the
G
solute at some chosen standard state (i.e., D ° =-RTlnK). In this particular
case, it refers to the free-energy change when 1 mole of the solute at unit con-
centration in one solvent (e.g., water) is transferred to a water-saturated
organic solvent where the solute is kept at a unit concentration (note that the
two solute solutions at the standard state specified are not in equilibrium so
G
that D ° π 0). LFERs developed for a specific set of solutes with some model
solvents are useful for assessing the partition behavior of similar organic com-
pounds with the same or compositionally similar solvents, biological compo-
nents, and natural organic phases. The LFER correlation in the form of Eq.
(5.19) was developed by Collander (1951) for systems where the two organic
solvents with K sw,1 and K sw,2 are similar in composition or contain similar func-
tional groups, such as i-butanol versus i-pentanol, or n-octanol versus oleyl
alcohol. Earlier we have seen that n-octanol and triolein provide another case
for such a linear correlation.
From the illustrated partition characteristics of solutes with different
organic solvents (including lipids), it is recognized that the magnitude of K sw
depends critically on the solute solubility in water and on the composition and
polarity of the solvent. Consequently, the numerical values of a and b in Eq.
(5.19) are expected to vary with respect to solute and solvent properties. From
Eqs. (3.6) and (5.19), the coefficient a is simply

d ( g* o)
w g*
log
dlog K sw,2 2
a = = (5.20)
o)
dlog K sw,1 d ( g* w g*
log
1
and the constant b is simply the value of logK sw,2 for a hypothetical (or extra-
polated) solute in the series with logK sw,1 = 0 (i.e., at K sw,1 = 1). The second
expression in Eq. (5.20) suffices when the solute–solvent solution obeys
Raoult’s law to a good approximation. Thus, a expresses the rate of change in
logK sw,2 with respect to the rate of change in logK sw,1 for a selected set of
solutes that spans a specific range of logK sw,1 and logK sw,2. Since the b con-
stant is in most cases an extrapolated value, often outside the range of actual
logK sw,1 , it defies a rigorous interpretation, especially when the selected set of
solutes come from a diversity of classes. The coefficient a itself is by no means
indicative of the relative solvency of the two organic solvents involved, which
is manifested instead by the magnitudes of K sw,1 and K sw,2 for any solute of
interest.
The simplest case in which a and b in Eq. (5.19) can be well rationalized is
when the two organic solvents in K sw,1 and K sw,2 have closely similar structures
and polarities, such that they exhibit similar compatibilities with any of the
solutes, and exhibit comparable solvent–water mutual saturation effects on