Page 39 - Partition & Adsorption of Organic Contaminants in Environmental Systems

Partition and Adsorption of Organic Contaminants in Environmental Systems. Cary T. Chiou
Copyright ¶ 2002 John Wiley & Sons, Inc.
ISBN: 0-471-23325-0

3 Interphase Partition Equations

3.1 PARTITION BETWEEN TWO SEPARATE PHASES

In Chapter 2 we have conveniently expressed the chemical potential of a
component in solution at temperature T and constant pressure in terms of its
concentration and its pure-liquid or supercooled-liquid reference chemical
potential at T. To establish the equilibrium partition coefficient of an organic
solute (contaminant) between any two separable solvent phases, one equates
the chemical potential of the solute in one phase with that in the other. Let
us designate the two separate phases of interest as A and B. By Eq. (1.41), the
equality in chemical potential of the solute in phases A and B requires
that the solute activities in the two phases be identical at equilibrium (i.e.,
a i,A = a i,B ), or

( x i g ) = ( x i g ) (3.1)
i A i B
where x i and g i are as defined earlier. Thus, the partition coefficient of solute
i on the basis of its mole fractions in phases A and B is then

*
K i,AB = x i,A x i,B = g i,B g i,A (3.2)
To the extent that g i,A and g i,B may vary with x i,A and x i,B , respectively, K* i,AB may
then vary with x i,A and x i,B . If the solute is present at low concentrations in
both phases A and B, as is commonly the case, K* i,AB will be practically invari-
ant because g i,B and g i,A should be essentially constant.
The partition coefficient of a solute is expressed more frequently as the
ratio of the solute molar concentrations rather than the respective mole frac-
tions in the two phases involved, because the former can be measured more
readily and finds more practical utility. If the solute of interest is dilute, the
solute mole fraction and the solute molar concentration are linearly related
to each other such that

x i,A = C i,A V A and x i,B = C i,B V B (3.3)

where C i,A is the molar concentration of solute i in phase A (mol/L), C i,B the
molar concentration of solute i in phase B, V A the molar volume of the phase
A solvent (L/mol), and V B the molar volume of the phase B solvent. Substi-
tuting Eq. (3.3) into (3.2) gives
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