Handbook of Solvents - George Wypych - ChemTech - Ventech!

5.5 The phenomenological theory of solvent effects 301
5.5.4.4 Confounding effects
Solute-solute interactions
It is very commonly observed, in these mixed solvent systems, that the equilibrium solubility
rises well above the dilute solution condition over some portion of the x2 range. Thus so-
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lution phase solute-solute interactions must make a contribution to ΔGsoln. To some extent
these may be eliminated in the subtraction according to eq. [5.5.22], but this operation cannot
be relied upon to overcome this problem. Parameter estimates may therefore be contaminated
by this effect. On the other hand, Khossravi 25 has analyzed solubility data for
biphenyl in methanol-water mixtures by applying eq. [5.5.23] over varying ranges of x2;he found that gA(γ2-γ1) was not markedly sensitive to the maximum value of x2 chosen to define
the data set. In this system the solubility varies widely, from x3 =7.1x10 -7 (3.9 x 10 -5
M) at x2 =0tox3= 0.018 (0.43 M) at x2 =1.
Coupling of general medium and solvation effects
In this theory the general medium and solvation effects are coupled through the solvation
exchange constants K1 and K2, which determine the composition of the solvation shell surrounding
the solute, and thereby influence the surface tension in the solvation shell. But the
situation is actually more complicated than this, for if surface tension-composition data are
fitted to eq. [5.5.26] the resulting equilibrium constants are not numerically the same as the
solvation constants K1 and K2 evaluated from a solubility study in the same mixed solvent.
Labeling the surface tension-derived constants K′ 1 and K′ 2 , it is usually found that K′ 1 >K1 and K′ 2 >K2. The result is that a number attached to γ at some x2 value as a consequence of a
nonlinear regression analysis according to eq. [5.5.23] will be determined by K1 and K2, and
this number will be different from the actual value of surface tension, which is described by
K′ 1 and K′ 2 . But of course the actual value of γ is driving the general medium effect, so the
discrepancy will be absorbed into gA. The actual surface tension (controlled by K′ 1 and K′ 2 )
is smaller (except when x2 = 0 and x2 = 1) than that calculated with K1 and K2. Thus gapparent =
gtruex γ( K′ 1 , K′ 2 )/γ(K1,K2). This effect will be superimposed on the curvature correction factor
that g represents, as well as the direct coupling effect of solvation mentioned above.
The cavity surface area
In solubility studies of some substituted biphenyls, it was found (see 5.5.3.1) that gA evaluated
via eq. [5.5.23] was linearly correlated with the nonpolar surface area of the solutes
rather than with their total surface area; the correlation equation was gA = 0.37 Anonpolar. It
was concluded that the A in the parameter gA is the nonpolar surface area of the solute. This
conclusion, however, was based on the assumption that g is fixed. But the correlation equation
can also be written gA = 0.37 FnonpolarAtotal, where Fnonpolar=Anonpolar/Atotalis the fraction of
solute surface area that is nonpolar. Suppose it is admitted that g may depend upon the solute
(more particularly, it may depend upon the solute’s polarity); then the correlation is consistent
with the identities A = Atotal and g = 0.37 Fnonpolar. Thus differences in gA may arise from differences in solute polarity, acting through g.
But A may itself change, rather obviously as a result of solute size, but also as a consequence
of change of solvent, for the solvent size and geometry will affect the shape and size
of the cavity that houses the solute.