Aqueous activity coefficients

Opperhuizen, A. (1987) Relationships between octan-l-ol/water partition coefficients, aqueous activity coefficients and reversed phase HPLC capacity factors of alkylbenzenes, chlorobenzenes, chloronaphthalenes and chlorobiphenyls. Toxicol. Environ. Chem. 15, 349-364. 

Figure 3. The effect of dissolved organic carbon on the aqueous activity coefficient estimated from the octanol-water partition coefficient.

Some stability constants for ion pairs on Fe oxides are listed in Table 10.4. This model was applied by Davis and Leckie (1978, 1980) to adsorption of various cations and anions on ferrihydrite. The extended triple layer model of Sahai and Svenjensky (1997) incorporates recent advances in aqueous electrolyte chemistry which enable aqueous activity coefficients for electrolytes to be calculated over a wide range of ionic strengths. The model also considers the free energy of adsorption of an ion to be the sum of the contributions from an electrostatic term, a Born solvation term and a ion intrinsic term. This extended model has been applied to adsorption of Co and Cd on goethite. 

In addition, data for the thermodynamic properties of the species themselves are given as mentioned above for the primary master species (of course, no aqueous activity coefficients are required for solids and gases). 

Solubilities and Aqueous Activity Coefficients of Organic Liquids Solubilities and Aqueous Activity Coefficients of Organic Solids Solubilities and Aqueous Activity Coefficients of Organic Gases Illustrative Example 5.1 Deriving Liquid Aqueous Solubilities, Aqueous Activity Coefficients, and Excess Free Energies in Aqueous Solution from Experimental Solubility Data... 

Enthalpic and Entropic Contributions to the Excess Free Energy Molecular Picture of the Dissolution Process Model for Description of the Aqueous Activity Coefficient Box 5.1 Estimating Molar Volumes from Structure Illustrative Example 5.2 Evaluating the Factors that Govern the Aqueous Activity Coefficient of a Given Compound... 

Illustrative Example 5.3 Evaluating the Effect of Temperature on Aqueous Solubilities and Aqueous Activity Coefficients Dissolved Inorganic Salts... 

Illustrative Example 5.4 Quantifying the Effect of Inorganic Salts on Aqueous Solubility and Aqueous Activity Coefficients... 

Availability of Experimental Data Methods for Estimation of Aqueous Activity Coefficient and Aqueous Solubility... 

We will start our discussion by considering a special case, that is, the situation in which the molecules of a pure compound (gas, liquid, or solid) are partitioned so that its concentration reflects equilibrium between the pure material and aqueous solution. In this case, we refer to the equilibrium concentration (or the saturation concentration) in the aqueous phase as the water solubility or the aqueous solubility of the compound. This concentration will be denoted as Qf. This compound property, which has been determined experimentally for many compounds, tells us the maximum concentration of a given chemical that can be dissolved in pure water at a given temperature. In Section 5.2, we will discuss how the aqueous activity coefficient at saturation, y, , is related to aqueous solubility. We will also examine when we can use yf as the activity coefficient of a compound in diluted aqueous solution, y (which represents a more relevant situation in the environment). 

Solubilities and Aqueous Activity Coefficients of Organic Liquids... 

Now we can see a key result. The aqueous mole fraction solubility of an organic liquid is simply given by the inverse aqueous activity coefficient ... 

Obviously, we can also say that for a liquid compound, the aqueous activity coefficient at saturation is given by the inverse of its mole fraction solubility ... 

One may also see how the aqueous activity coefficient is related to solubility for organic substances that are solids ... 

It thus follows that the aqueous activity coefficient of a gaseous pure compound is related to the solubility by ... 

Let us now extend our molecular descriptor model introduced in Chapter 4 (Eqs. 4-26 and 4-27) to the aqueous activity coefficient. We should point out it is not our principal goal to derive an optimized tool for prediction of yw, but to develop further our understanding of how certain structural features determine a compound s partitioning behavior between aqueous and nonaqueous phases. Therefore, we will try to keep our model as simple as possible. For a more comprehensive treatment of this topic [i.e., of so-called linear solvation energy relationships (LSERs)] we refer to the literature (e.g., Kamlet et al., 1983 Abraham et al., 1990 Abraham, 1993 Abraham et al., 1994a and b Sherman et al., 1996). 

Having means to estimate relative solute sizes, we recognize that we can now estimate a new compound s aqueous activity coefficient and/or liquid solubility from... 

Illustrative Example 5.2 Evaluating the Factors that Govern the Aqueous Activity Coefficient... 

In summary, we can conclude that at moderate salt concentrations typical for seawater ( 0.5 M), salinity will affect aqueous solubility (or the aqueous activity coefficient) by a factor of between less than 1.5 (small and/or polar compounds) and about 3 (large, nonpolar compounds, n-alkanals). Hence, in marine environments for many compounds, salting-out will not be a major factor in determining their partitioning behavior. Note, however, that in environments exhibiting much higher salt concentrations [e.g., in the Dead Sea (5 M) or in subsurface brines near oil fields], because of the exponential relationship (Eq. 5-28), salting-out will be substantial (see also Illustrative Example 5.4). 

At 25°C phenanthrene is a solid. Because the free energy contributions of phase change (i.e., melting, or condensation in the case of a gas) to the overall free energy of solution are not affected by salts in the solution, it is the aqueous activity coefficient that is increased as salt concentration increases (Eq. 5-28). Hence, the actual solubility decreases by the same factor (Eq. 5-27). The Kf value of phenanthrene is 0.30 M 1 (Table 5.7). Since 34.2%o salinity corresponds to a total salt concentration of 0.5 M (see text), [salt]tot for 30%o is equal to 0.44 M. Insertion of these values into Eq. 5-28 yields ... 

Hence, this approach is very similar to the one used for describing the effect of salt on aqueous solubility and aqueous activity coefficient (Eqs. 5-27 and 5-28). Some example calculations using Eq. 5-30 or 5-31, respectively, are given in Illustrative Example 5.5. Finally, we should note that the mole fractions of two solvents in a binary mixture are related to the volume fractions by ... 

Any general approach (i.e, any approach that is not restricted to a confined set of structurally related compounds) for prediction of aqueous solubilities and/or aqueous activity coefficients has to cope with the intrinsic difficulty of describing precisely... 

Therefore, similar to the attempts made to estimate vapor pressure (Section 4.4) there have been a series of quite promising approaches to derive topological, geometric, and electronic molecular descriptors for prediction of aqueous activity coefficients from chemical structure (e.g., Mitchell and Jurs, 1998 Huibers and Katritzky, 1998). The advantage of such quantitative structure property relationships (QSPRs) is, of course, that they can be applied to any compound for which the structure is known. The disadvantages are that these methods require sophisticated computer software, and that they are not very transparent for the user. Furthermore, at the present stage, it remains to be seen how good the actual predictive capabilities of these QSPRs are. 

How is the aqueous activity coefficient of a compound related to the aqueous solubility, if the compound is (a) a liquid, (b) a solid, and (c) a gas under the prevailing conditions Comment on any assumptions that you make when answering this question. 

---