Page 44 - Partition & Adsorption of Organic Contaminants in Environmental Systems

TEMPERATURE DEPENDENCE OF PARTITION COEFFICIENT 35

DH sw =DH s -DH w (3.23)

where DH sw is the enthalpy (heat) of partition when a mole of the solute is
transferred from water to an organic phase of interest at equilibrium.
It is evident from derivations above that the heat associated with the equi-
librium of a solute (whether it is a liquid or a solid substance) between an
organic phase and water is the difference of the solute’s molar heats of
solution in the organic phase and water. For solid solutes, the heat of fusion
(DH fus ), which affects the solid solubility in a single phase (e.g., water), has no
net effect on the solute partition coefficient (K sw ) or on the heat of solute
partition (DH sw ).
For most low-polarity organic compounds with a limited solubility in water,
both DH w and DH s are positive with DH w >DH s , and therefore the K sw value
would exhibit an exothermic heat that is smaller in magnitude than the reverse
heat of solution of the solute in water (-DH w ). In other words, while the K sw
will normally decrease and the S w increase with a temperature rise, the extent
of variation would be much smaller for K sw than for S w . The opposing heat
effects (i.e., the temperature dependencies) between K sw and S w are often
greatly magnified for solid solutes because DH fus is part of DH w , but not of
DH sw , as described by Eqs. (3.20) and (3.23). For most solutes in organic–water
mixtures, the DH sw values are normally less than 12kJ/mol in exothermicity.
The estimated variation in K sw for a solute with a temperature rise from 20°C
to 25°C is therefore less than 10%.
If the organic phase of interest is macromolecular in nature, in which Eq.
(3.13) or (3.14) defines more properly the solute partition coefficient, one may
derive relations identical to those of Eqs. (3.17) to (3.23) by assuming that the
molar volume terms are largely invariant with temperature and by substitut-
ing c/2.303 for logg* s . Thus, the relations of Eqs. (3.17) to (3.23) hold for solutes
of a limited solubility in water at dilution, much independent of the relative
molecular sizes of the solute and the organic phase.
For solid substances of interest, if one knows the molar heat of fusion
(DH fus ) and the melting point (T m ), the activity of the solid can then be deter-
mined, through Eq. (3.18), as

o
s
)
2
Ú dln( P P ) = Ú T T m (D H fus RT dT (3.24)
s
with the boundary condition that P /P° = 1 at T = T m. If one assumes that DH fus
is practically constant between T and T m, one gets the important equation
P s -D H fus T m - T
s
lna = ln o = (3.25)
P R TT m
where the term DH fus/T m =DS fus is the molar entropy of fusion of the solid sub-
stance (at T = T m, the solid and its melt are at equilibrium, thus DG fus = 0). The