Handbook of Solvents - George Wypych - ChemTech - Ventech!

286 Kenneth A. Connors
Figure 5.5.1. Solvent effect on the solubility of
diphenylhydantoin. Cosolvents, top to bottom: glycerol,
methanol, ethanol. The smooth lines were drawn
with eq. 5.5.23. (Reproduced with permission from the
Journal of Pharmaceutical Sciences reference 1.)
Figure 5.5.2. Solvent effect on the solubilities of barbituric
acid derivatives in ethanol-water mixtures. Top to
bottom: metharbital, butabarbital, amobarbital. The
smooth lines were drawn with eq. 5.5.23. (Reproduced
with permission from the Journal of Pharmaceutical
Sciences, reference 1.)
The free energy of solution per molecule is then calculated with eq. [5.5.1], δMΔ G
* is
found with eq. [5.5.22], and δMΔ G
* as a function of x2 is fitted to eq. [5.5.23] by nonlinear
regression, with gA, K1, and K2 being treated as adjustable parameters. 9 Figures 5.5.1 and
5.5.2 show some results. 1
Clearly eq. [5.5.24] possesses the functional flexibility to describe the data. (In some
systems a 1-step (2-state) equation is adequate. To transform eq. [5.5.24] to a 1-step version,
set K2 = 0 and let γ′ = γ2 −γ1
.) The next step is to examine the parameter values for their possible
physical significance. It seems plausible that K1 and K2 should be larger than unity, but
not “very large,” on the basis that the solutes are organic and so are the cosolvents, but the
cosolvents are water-miscible so they are in some degree “water-like.” In fact, we find that
nearly all K1 and K2 values fall between 1 and 15. Likewise the gA values seem, in the main,
to be physically reasonable. Earlier estimates of g (reviewed in ref. 1 ) put it in the range of
0.35-0.5. A itself can be estimated as the solvent-accessible surface area of the solute, and
many of the gA values found were consistent with such estimates, though some were considerably
smaller than expected. Since gA arises in the theory as a hydrophobicity parameter,
it seemed possible that A in the equation represents only the nonpolar surface area of the