Page 43 - Partition & Adsorption of Organic Contaminants in Environmental Systems

34 INTERPHASE PARTITION EQUATIONS

very sensitive to T and because the solubility enhancement factor (g w /g* w ) will
not vary strongly with T if the solvent has a small solubility in water.
We consider first the effect of T on logS w . For a liquid or a supercooled-
liquid solute at T, one finds according to Eq. (3.7) that

dlog S w dlogg w D H w ex
=- = (3.17)
dT dT 2.303 RT 2

in which DH ex
w is called by Hildebrand et al. (1970) the molar excess heat of
mixing for the solute with a solvent (water). (Note that in an ideal solution,
where g= 1, DH ex is therefore zero.)
Although the S w term for a solid solute in partition equilibrium is that of
the corresponding supercooled liquid, it is of interest to illustrate the differ-
ent temperature dependence of the solid solubility with temperature. By Eq.
s
s
(3.8) with a = P /P°, one obtains
o
s
dlog S w s () dlogg w dlog( P P ) D H w ex D H fus
=- + = + (3.18)
dT dT dT . 2 303 RT 2 . 2 303 RT 2
in which DH fus =DH sub -DH evap according to Eq. (1.52). Thus, the molar heat
of solution (DH w ) for a solute in water may be expressed as:

(3.19)
ex
Ï DH w for liquid solutes
DH w = Ì
ex
Ó DH w + DH fus for solid solutes (3.20)
w is normally positive for a liquid solute
Since DH fus is always positive and DH ex
that exhibits a limited solubility in water (i.e., when g i >> 1), the solubility of
a solid solute in water (or other solvents) is usually much more sensitive to T
than that of a similar liquid solute.
The derivative of logg* s with T is similar to that of logg w with T:
* ex
dlogg s -D H s -D H s
= = (3.21)
dT 2.303 RT 2 2.303 RT 2
s is the molar excess heat of mixing of the liquid or supercooled-
in which DH ex
liquid solute with the organic-solvent phase (which is saturated by a certain
amount of water) at T and DH s is the molar heat of solution of the solute at
ex
T. Again, for solid solutes, DH s =DH s +DH fus. Thus, by combining Eqs. (3.16),
(3.17), and (3.21), one obtains

ex
ex
dlog K sw D H s - D H w D H s - D H w
= = (3.22)
dT 2.303 RT 2 2.303 RT 2
and thus,