Water solubility empiric approach

We conclude this section by a few general remarks about extrathermodynamic approaches. These quantitative methods involve empirical approaches that cannot be derived strictly from thermodynamic theory. They are widely used to predict and/ or to evaluate partition constants and/or partition coefficients (see Box 3.2 for nomenclature) of organic compounds. There are many situations in which some of the data required to assess the partitioning behavior of a compound in the environment are not available, and, therefore, have to be estimated. For example, we may need to know the water solubility of a given compound, its partition coefficient between natural organic matter and water, or its adsorption constant from air to a natural surface. In all these, and in many more cases, we have to find means to predict these unknown entities from one or several known quantities. 

For our purpose here, we adopt the most simple empirical approach where we assume a log-linear relationship between activity coefficient (or mole fraction solubility) of a given compound and volume fraction of the CMOS over a narrow f%so[v-range (i.e., A/,jSolv = 0.2) confined by /v Solv and /v2solv. Hence, for a given organic solute i and a given CMOS/water system, we get (note that we omit the subscript solv to indicate the CMOS) ... 

Greaves AJ, Churchley JH, Hutchings MG, Philhps DAS, Taylor JA (2001) A chemometric approach to understanding the bioelimination of anionic, water-soluble dyes by a biomass using empirical and semi-empirical molecular descriptors. Water Res 35 1225-1239. http // www.doi.org/10.1016/S0043-1354(00)00388-2... 

The increased solubility in a surfactant solution of an organic substance, insoluble or sparingly soluble in water, is a phenomenon which has been applied empirically for a very long time it is only in the last century that an attempt at a rather less empirical approach to solubilization has been made. 

About one decade ago Bass et al. [13,14] proposed first that such approach could help in exploring the structure of water dissolved silicates. Following this initiative, recently we critically evaluated how the published FTIR and Raman assignments could be adopted for differentiating between the molecular structures of some commercially available sodium silicate solutions [7-9,15], In this paper we present comparative structural studies on aqueous lithium and potassium silicate solutions as well. According to some NMR studies, the nature of A+ alkaline ion and the A+/Si ratio barely affects the structural composition of dissolved silicate molecules [5], In contrast, various empirical observations like the tendency of K-silicate solutions to be less tacky and more viscous than their Na-silicate counterparts, the low solubility of silica films obtained from Li-silicate solutions compared to those made from other alkaline silicate solutions, or the dependence of some zeolite structures on the nature of A+ ions in the synthesis mixture hint on likely structural differences [16,17]. It will be shown that vibrational spectroscopy can indeed detect such differences. 

Much effort has been expended on models that can be used to predict the solubility behavior of solutes, with good success being attained using a semi-empirical, group contribution approach [75]. In this system, the contributions made by individual functional groups are summed to yield a composite for the molecule, which implies a summation of free energy contributions from constituents. This method has proven to be useful in the prediction of solubility in water and in water-cosolvent mixtures. In addition to the simplest methodology, a variety of more sophisticated approaches to the prediction of compound solubility have been advanced [68]. 

The extensions of the Hildebrand and Hansen approaches are both empirical. Afterthe solubility behavior has been evaluated in a series of solvent systems, regression analysis can be used to estimate the empirical coefLcients, including th fferm of the extended Hansen approach, and then the solubility can be estimated in a solvent system which has not been included in the experimental portion of the study. The problem with acknowledging the predictive power of these equations is that the solubility in many solvents must be determined before being able to predict the solubility in the solvent of choice. It is probably easier to simply perform the solubility study in the solvent of choice and eliminate the prediction equation altogether. On the other hand, in a study of binary solvent systems consisting of water and a cosolvent appropriate to parenteral products, the solubility maximum in that series can be readily estimated by the mathematical expression Lnally achieved. 

Attempts to model chemical weathering of catchments have used a variety of approaches and were originally designed to understand acidification processes. The BIRKENES code (Christophersen et al., 1982) was one of the first developed to model catchment stream chemistry. It used cation-anion charge balance, a gibbsite equilibrium solubility control for aluminum concentrations, a Gapon ion exchange for metals sorption, and rates for sulfate adsorption/ desorption in a two-reservoir model. The model was calibrated by input mass fluxes and output mass fluxes for the Birkenes catchment in Norway to provide the water flux information and to fit empirical parameters. 

In a subsequent paper Yalkowsky and Valvani (1980) related the solubility of non-electrolytes in water, polar as well as non-polar, to their distribution quotients between 1-octanol and water and, in the case of crystalline solutes, to their fusion temperatures, Tp, and entropies of fusion, Ap5. This approach was taken for the aqueous solubilities of dmg molecules and places the burden of explaining the interactions on the octanol/water distribution quotients, D°w, or on P°w = log T>°w, that have been dealt with extensively by Hansch and Leo (1979) among others. The empirical expression used for solubility at 25 °C was ... 

Clearly, the process of selecting the best surfactant or surfactants for the preparation of an emulsion has been greatly simplified by the development of the more or less empirical but theoretically based approaches exemplified by the HLB, solubility parameter, and PIT methods. Unfortunately, each method has its significant limitations and cannot eliminate the need for some amount of trial-and-error experimentation. As our fundamental understanding of the complex phenomena occurring at oil-water interfaces, and of the effects of additives and environmental factors on those phenomena, improves it may become possible for a single, comprehensive theory of emulsion formation and stabilization to lead to a single, quantitative scheme for the selection of the proper surfactant system. 

This section discusses theories and calculations that have been used in molecular modeling of primitive hydrophobic effects. There is a basic schism among approaches that have been pursued. One approach is to model hydrophobic effects empirically on the basis of experimental solubilities without direct consideration of solute-water molecular interactions. Hydrophobic effects extracted on the basis of empirical fitting of solubilities are often called hydrophobicities (see... 

The buzzword polarity , derived from the dielectric approach, is certainly the most popular word dealing with solvent effects. It is the basis for the famous rale of thumb ""similia similibus solvuntuf" ( like dissolves like"") apphed for discussing solubility and miscibility. Unfortunately, this rale has many exceptions. For instance, methanol and toluene, with relative permittivities of 32.6 and 2.4, respectively, are miscible, as are water (78.4) and isopropanol (18.3). The problem lies in exactly what is meant by a like solvent. Originally, the term polarity was meant to be an abbreviation of static dipolarity and was thus associated with solely the dielectric properties of the solvent. Later on, with the advent of the empirical solvent parameters, it has assumed a broader meaning, sometimes even that of the overall solvating power. With this definition, however, the term polarity is virtually superfluous. 

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