Handbook of Solvents - George Wypych - ChemTech - Ventech!

300 Kenneth A. Connors
that the composition dependence of the product �Âγ is being accounted for without claiming
that we can independently assign composition dependencies to the separate factors in
the product.
5.5.4.3 Interpretation of parameter estimates
Eq. [5.5.54] constitutes the basis for the resolution of the logical problem, described earlier,
in which different cosolvents, with a given solute, yield different gA values, although gA
had been assumed to be independent of composition. As eq. [5.5.54] shows, gA is determined
by a difference of two fixed quantities, thus guaranteeing its composition independence,
and at the same time permitting gA to vary with cosolvent identity.
Eq. [5.5.53] is therefore conceptually sounder and physically more detailed than is eq.
[5.5.23]. Eq. [5.5.53] shows, however, that in the absence of independent additional information
(that is, information beyond that available from the solubility study alone) it is not
possible to dissect the quantity (g2γ2A2 -g1γ1A1) into its separate terms. In some cases such
additional information may be available, and here we discuss the example of naphthalene
solubility in mixed aqueous-organic binary mixtures. Table 5.5.8 lists the values of
gA(γ2-γ1) obtained by applying eq. [5.5.23] to solubility data in numerous mixed solvent
systems. 8 In an independent calculation, the solubility of naphthalene in water was written
as eq. [5.5.55],
( 0)
*
ΔG x = = ΔG
+ g A γ [5.5.55]
soln
2 cryst 1 1 1
which is equivalent to eq. [5.5.4]. ΔG cryst was estimated by conventional thermodynamic arguments
and ΔG solv was omitted as negligible, 24 yielding the estimate g 1A 1γ 1 =4.64x10 -20 J
molecule -1 . With eq. [5.5.54] estimates of g 2A 2γ 2 could then be calculated, and these are
listed in Table 5.5.8.
Table 5.5.8. Parameter estimates and derived quantities for naphthalene solubility in
water-cosolvent mixtures at 25 o C a
Cosolvent γ2, erg cm -2
10 20 gA(γ2-γ1), J molecule -1
10 20 g2A2γ2, J molecule -1
Methanol 22.4 -3.11 +1.53
Ethanol 21.8 -2.70 1.94
Isopropanol 20.8 -2.19 2.45
Propylene glycol 37.1 -2.46 2.18
Ethylene glycol 48.1 -2.24 2.22
Acetone 22.9 -3.37 1.27
Dimethylsulfoxide 42.9 -3.67 0.97
a Data from ref. (8); γ1 = 71.8 erg cm -2 ,g 1A 1γ 1=4.64x10 -20 J molecule -1 .
Observe that g 1A 1γ 1 and g 2A 2γ 2 are positive quantities, as expected; gA(γ 2-γ 1) is negative
because of the surface tension difference. It is tempting to divide each of these quantities
by its surface tension factor in order to obtain estimates of gA, g 1A 1, and g 2A 2, but this
procedure may be unsound, as proposed subsequently.