Solubility data, empirical

Solubility of 1-butene in 2,2,4-trimethyl-l,3-pentanediol monoisobutyrate. The solubility data were first modeled with the empirical equation [11] giving mole fraction of dissolved gas (x,)... 

A number of empirical relationships have been published which could be used to predict partition coefficients from solubility data [19-29, 65, 72, 78-97]. Comparisons among these relationships may be confusing since different sets of compounds and different solubility terms are used. A theoretical analysis of partition coefficient with reference to aqueous solubility is important because it illustrates the thermodynamic principles underlying the partitioning process. The objective of that relationship is its utility for both predicting and validating reported values for partition coefficients. 

The evaluation of the sublimation pressure is a problem since most of the compounds to be extracted with the supercritical fluids exhibit sublimation pressures of the order of 10 14 bar, and as a consequence these data cannot be determined experimentally. The sublimation pressure is thus usually estimated by empirical correlations, which are often developed only for hydrocarbon compounds. In the correlation of solubility data this problem can be solved empirically by considering the pure component parameters as fitting-parameters. Better results are obviously obtained [61], but the physical significance of the numerical values of the parameters obtained is doubtful. For example, different pure component properties can be obtained for the same solute using solubility data for different binary mixtures. 

Fragmental solubility constants can be determined empirically from experimental solubility data using regression techniques. In 1986, V fekita et al. (1986) studied the solubility of a large numberof nonhomologous compounds in water. In this study, fragmental solubility constants were determined... 

However, from the measurements of solubilities of oxygen (6,7) and carbon dioxide (8) in aqueous single-salt solutions over a wide range of salt concentration, it was found that data for many systems could not be correlated by the empirical Setschenow Equation. Therefore, the modified Setschenow Equation can not always be used to estimate satisfactorily the gas solubility data over a wide range of salt concentrations. 

Available literature solubility data of pure lipids belonging to major (fatty acids, mono-, di- and triacylglycerols, and fatty acid esters) and minor lipid classes (pigments, sterols, vitamins, and hydrocarbons) in SCCO2 were compiled (26, 27). These references (26, 27) contain exhaustive bibliography on lipid + SCCO2 binary systems. Literature data were correlated using Chrastil s equation, which is an empirical model used quite commonly to correlate the solubility of lipid components (30). This model is based on the formation of a solute-solvent complex on association of the solute and solvent molecules and establishes a linear relationship between In(solubility) and In(density) as follows ... 

The figures show that Eq. (4) coupled with the Flory-Huggins equation for the activity coefficient of water in polymer + water mixed solvents provides a minimum for the Henry constant at high (>95 wt%) polymer compositions. Because gas solubility data are not available for such high polymer compositions, one cannot determine whether this minimum is due to the empirical nature of the adjustable parameter x or reflects an experimental feature of the gas... 

Solubility is a complex property, and this complexity confounds our ability to develop computational models to predict it. Most computational solubility models are empirical QSPR models, trained on solubility data sets either sourced from the literature and corporate databases or generated specifically for the purposes of modeling. Hence, it is not surprising that the quality of the computational model depends on the quality of the data set of experimental measurements used to train the model. 

There are many empirical correlations and theoretical treatments for predicting solubility, diffusivity, and permeability constants. Table 2 shows the permeability and solubility data for gases in polystyrene and low-density polyethylene. In the extrusion process. 

Most published solubility studies of the cation-uranyl phosphates are inconsistent and/or poorly documented (cf. Grenthe et at. 1992). To avoid dealing with the questionable solubility data, tabulated AG/ values for the autunites are based on AG/(H-autunite) from this table and AG/ for the general exchange reaction H2(U02)2(TO4)2 + M = M (U02)2(P04)2 + 2H, where n = 1 and 2 for divalent and monovalent canons, respectively. The empirical ion exchange results are from Muto et al. (1968). 

Recomputed from the empirical solubility data in Hostetler and Garrels (1962) consistent with the data in diis table and with corrections for ion activities and complexes. AG/ computed assuming AG/ for the tyuyamunite/carnotite exchange reaction equals its value for the autunite/K-autunite exchange reaction. 

The ion-interaction model is a theoretically based approach that uses empirical data to account for complexing and ion pair formation by describing this change in free ion activity with a series of experimentally defined virial coefficients. Several philosophical difficulties have resulted from the introduction of this approach the lack of extensive experimental database for trace constituents or redox couples, incompatibility with the classical ion pairing model, the constant effort required to retrofit solubility data as the number of components in the model expand using the same historical fitting procedures, and the incompatibility of comparing thermodynamic solubility products obtained from model fits as opposed to solubility products obtained by other methods. 

In most time-lag experiments, the initial downstream penetrant concentration. C,. is zero tied the upstream concentration Cj is assumed to he established instantaneously at its equilibrium value. Although 6 is an additional parameter not requited to evaluate permeability and solubility data, it is wise, when possible, to verify that the lime lags obeerved experimentally are consistent with the ptedlclious of Fick s Law. To perfonn this lest, oue needs only to fit an empirical eqnelion to the D(C) versus C data shown in Fig- 20.3-6 and to perform the integration indicated. 17... 

Several papers report solubility data for this system (1-6). Empirical smoothing equations describing the temperature dependence of this solubility have also been reported (6,7). Solubility data for this system have also been reported as part of a study of multicomponent systems having KH.PO, as one component (8-24). Some of these values are clearly incorrect and were rejected immediately (8-10). The same is true for some of the solubility values reported for 323 K (11,12). In another report (13) the solubility of KH2P0 at 298 K is given as 20.3% and also as 21.6%. The latter value is an obvious error. All the other data from the studies of multicomponent systems were evaluated together with the data in refs. (1-6). 

The above approach is empirical. Thermodynamic models for describing solution behavior can also be employed to determine gas solubilities, and these models are amenable to the estimation of gas solubilities in multicomponent systems from sets of single salt data. The thermodynamic approach employed is known as the Pitzer species interaction model, and it is used to determine the activity coefficient of the gas from a summation of interaction terms with anions, cations, and neutral species [3, 10, 11]. These interaction parameters are determined empirically from solubility data in a range of electrolyte solutions and have been tabulated for a wide range of salts, permitting the solubility of oxygen to be determined in mixed electrolyte solutions over a wide range of temperature and concentrations. 

All that which has been said about empirical models based on the 1-octanol/water partition coefficients is also true for models based on the water solubilities (a) the measured water solubility data are of low precision (see TABLE 4), (b) there exists a wide variety of quantitative linear models correlating soil sorption coefficients and water solubility (Wijayaratne and Means 1984 Chiou et al. 1983 Banwart et al. 1982 Means et al. 1982 Briggs 1981 Kenaga and Goring 1980 Karickhoff etal. 1979), and (c) the statistical requirements for linear regression models are violated by the large errors in the experimental water solubility data. That some quantitative models (Wijayaratne and Means 1984 Banwart et al. 1982 Means et al. 1982) use non-molar units ( ig mL ) for water solubility data, further impedes their use. 

Thus one must rely on macroscopic theories and empirical adjustments for the determination of potentials of mean force. Such empirical adjustments use free energy data as solubilities, partition coefficients, virial coefficients, phase diagrams, etc., while the frictional terms are derived from diffusion coefficients and macroscopic theories for hydrodynamic interactions. In this whole field of enquiry progress is slow and much work (and thought ) will be needed in the future. 

The solubility of methyl parathion is not sufficient to pose a problem in runoff water as determined by an empirical model of Wauchope and Leonard (1980). Some recent monitoring data, however, indicate that methyl parathion has been detected in surface waters (Senseman et al. 1997). In a study to determine the residue levels of pesticides in shallow groundwater of the United States, water samples from 1,012 wells and 22 springs were analyzed for methyl parathion. No methyl parathion was detected in any of the water samples (Kolpin et al. 1998). In a study of water from near-surface aquifers in the Midwest, no methyl parathion was detected in any of the water samples from 94 wells that were analyzed for pesticide levels (Kolpin et al. 1995). Leaching to groundwater does not appear to be a significant fate process. 

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