Handbook of Solvents - George Wypych - ChemTech - Ventech!

288 Kenneth A. Connors
Solute Solvent
gA, � 2 molecule -1
Calculated Observed
4-Nitroaniline DMSO 101 86
4-Nitroaniline Acetonitrile 30 29
We now encounter a curious observation. The parameter gA is constrained, in the nonlinear
regression fitting program, to be constant as x 2 varies over its entire range from 0 to 1.
We have identified A as the nonpolar surface area of the solute (though it may actually be
the corresponding area of the solvent cavity, and so may show some cosolvent dependency,
which we have ignored). The quantity g can then be estimated. For example, from Table
5.5.2 for naphthalene (A = 147 � 2 molecule -1 ), g varies from 0.29 (for 2-propanol) to 0.86
(for DMSO). Yet how can g possess these different values in different cosolvents, maintain
its constancy as x 2 varies, and then collapse to the unique value it must possess in water, the
reference solvent for all systems? An independent calculation gives g = 0.41±0.03 in water. 8
Some tentative explanations for this puzzle have been offered, 8 and we return to this issue in
Section 5.5.4.
Turning to the K 1 and K 2 parameters, we have observed that these are relatively insensitive
to the identity of the solute, but that they depend upon the cosolvent, whose polarity is
a controlling factor. Table 5.5.3 gives some empirical correlations that provide routes to the
prediction of K 1 and K 1K 2. In Table 5.5.3, P M is the 1-octanol/water partition coefficient of
the pure cosolvent, 12 and E T is the Dimroth-Reichardt solvatochromic polarity parameter. 13
We thus have the capability of predicting gA, K 1, and K 1K 2, which extends the utility of eq.
[5.5.23] from the merely descriptive to the predictive.
Table 5.5.3. Empirical relationships for estimating solvation constants
Equation n r Restrictions
log K1 = -0.0316 ET + 2.24 10 0.91 -
log (K1/K2) = 0.0171 ET - 9.23 4 0.98 ET >51
log (K1/K2) = -0.0959 ET + 4.60 6 0.85 ET -1.0
5.5.3.2 Surface tension
In the development of the basic phenomenological model, eq. [5.5.23], we derived a relationship
for the surface tension of the solvation shell. Combining eqs. [5.5.16] and [5.5.18]
yields
2
⎡ Kxx 1 1 2 + 2KK
1 2x2 γ = γ + γ′
1 ⎢ 2
⎣x1
+ K x x + K K x
1 1 2 1 2
2
2
⎤
⎥
⎦
[5.5.26]
where γ′ = ( γ2 −γ1)/
2. Now if we identify the solute-solvation shell system with the air-solvent
interface, we are led to test eq. [5.5.26] as a description of the composition dependence