Chemistry Reference
In-Depth Information
It is well known (Prausnitz, Lichtenthaler, and Gomes de Azevedo 1999) that the
solubility can be calculated if the standard state properties and the activity coeffi-
cients of the solute(s) and solvent(s) are known. However, prediction of the activity
coefficients of solutes (such as gases and large molecules of biomedical and environ-
mental significance) in saturated solutions of multicomponent mixtures constitutes a
major difficulty. Generally speaking, the activity coefficient of a solute in a saturated
solution of a multicomponent mixture can be predicted using group-contribution
methods, such as UNIFAC and ASOG (Derr and Deal 1969; Fredenslund, Jones,
and Prausnitz 1975; Fredenslund, Gmehling, and Rasmussen 1977; Kojima and
Tochigi 1979; Gmehling 1995; Prausnitz, Lichtenthaler, and Gomes de Azevedo
1999; Jakob et al. 2006; Schmid and Gmehling 2012). However, the above group-
contribution methods cannot provide accurate results for the activity coefficients of
large molecules, such as those typically required for the study of drug or environ-
mental molecules in aqueous mixed solvents (Li, Doucette, and Andren 1994; Kan
and Tomson 1996; Wienke and Gmehling 1998; Bouillot, Teychene, and Biscans
2011; Diedrichs and Gmehling 2011; Mota et al. 2012).
Another method for predicting the solubility of gases and large molecules in a
mixed solvent involves the Kirkwood-Buff theory of solutions (Kirkwood and Buff
1951). This theory connects macroscopic properties of solutions, such as the iso-
thermal compressibility, the derivatives of the chemical potentials with respect to
concentration and the partial molar volumes, to their microscopic characteristics
in the form of spatial integrals involving the radial distribution functions. It provides
the opportunity to extract some microscopic characteristics of mixtures from mea-
surable thermodynamic quantities. We employed the Kirkwood-Buff theory of solu-
tion to obtain expressions for the derivatives of the activity coefficients in ternary
(Ruckenstein and Shulgin 2001b) and multicomponent (Ruckenstein and Shulgin
2003a) mixtures with respect to mole fractions. These expressions for the derivatives
of the activity coefficients were used to calculate the solubilities of various solutes in
aqueous mixed solvents, namely:
1. The solubilities of drugs and environmentally significant molecules in
binary and multicomponent aqueous mixed solvents (Ruckenstein and
Shulgin 2003b, 2003c, 2003d, 2004, 2005),
2. The solubilities of gases in binary and multicomponent aqueous mixed sol-
vents (Ruckenstein and Shulgin 2002b; Shulgin and Ruckenstein 2002b;
Ruckenstein and Shulgin 2003a; Shulgin and Ruckenstein 2003),
3. The solubilities of various proteins in aqueous solutions (Shulgin and
Ruckenstein 2005b; Ruckenstein and Shulgin 2006; Shulgin and Ruckenstein
20 06b).
Details regarding the applications of the KB theory of solutions to solubility can
be found in a recently published topic (Ruckenstein and Shulgin 2009). We also
mention here the contributions of Mazo and Smith (Mazo 2006, 2007; Smith and
Mazo 2008) to the application of the KB theory of solutions
to the solubility in
mixed solvents (see also Section 1.3.5 in Chapter 1 and Chapter 9).
