Solubility correlations

In the multimedia models used in this series of volumes, an air-water partition coefficient KAW or Henry s law constant (H) is required and is calculated from the ratio of the pure substance vapor pressure and aqueous solubility. This method is widely used for hydrophobic chemicals but is inappropriate for water-miscible chemicals for which no solubility can be measured. Examples are the lower alcohols, acids, amines and ketones. There are reported calculated or pseudo-solubilities that have been derived from QSPR correlations with molecular descriptors for alcohols, aldehydes and amines (by Leahy 1986 Kamlet et al. 1987, 1988 and Nirmalakhandan and Speece 1988a,b). The obvious option is to input the H or KAW directly. If the chemical s activity coefficient y in water is known, then H can be estimated as vwyP[>where vw is the molar volume of water and Pf is the liquid vapor pressure. Since H can be regarded as P[IC[, where Cjs is the solubility, it is apparent that (l/vwy) is a pseudo-solubility. Correlations and measurements of y are available in the physical-chemical literature. For example, if y is 5.0, the pseudo-solubility is 11100 mol/m3 since the molar volume of water vw is 18 x 10-6 m3/mol or 18 cm3/mol. Chemicals with y less than about 20 are usually miscible in water. If the liquid vapor pressure in this case is 1000 Pa, H will be 1000/11100 or 0.090 Pa m3/mol and KAW will be H/RT or 3.6 x 10 5 at 25°C. Alternatively, if H or KAW is known, C[ can be calculated. It is possible to apply existing models to hydrophilic chemicals if this pseudo-solubility is calculated from the activity coefficient or from a known H (i.e., Cjs, P[/H or P[ or KAW RT). This approach is used here. In the fugacity model illustrations all pseudo-solubilities are so designated and should not be regarded as real, experimentally accessible quantities. 

Saldana MDA, Tomberli B, Guigard SE, Goldman S, Gray CG and Temelli F. 2007. Determination of vapor pressure and solubility correlation of phenolic compounds in supercritical CO2. J Supercrit Fluids 40(1) 7—19. 

Murthy CN, Geckeler KE (2001) Solubility correlation of Cm fullerene in different solvents. Fullerenes Nanotechnol. Carbon Nanostruct. 9 477 186. 

A Avdeef, CM Berger, C Brownell. pH-Metric solubility correlation between the acid-base titration and the saturation shake-flask solubility-pH methods. Pharm. Res. 17 85-89 (2000). 

The solubility of a supercritical fluid is influenced by its temperature, pressure, and density. Solubility correlates better to density than to pressure. An empirical equation can be used to predict solubility [22] ... 

Dandge, D. K., Heller, J. P., Wilson, K. V., Structure Solubility Correlations Organic Compounds and Dense Carbon Dioxide Binary Systems, 24 162-166 (1985)... 

The previous considered methods usually depend on linear methods (MLR, PLS) to establish structure-solubility correlations for prediction of solubility of molecules. The work of Goller et al. [51] used a neural network ensemble to predict the apparent solubility of Bayer in-house organic compounds. The solubility was measured in buffer at pH 6.5, which mimics the medium in the human gastrointestinal tract. The authors used the calculated distribution coefficient log/1 (at several pH values), a number of 3D COSMO-derived parameters and some 2D descriptors. The final model was developed using 4806 compounds (RMSE = 0.72) and provided a similar accuracy (RMSE = 0.73) for the prediction of 7222 compounds that were not used to develop the model. The method, however, is quite slow, and it takes about 15 seconds to screen one molecule on an Intel Xeon 2.8 GHz CPU. 

Solubility correlated well with hydrophobicity. Less correlation was observed with the dielectric constant and the solubility parameter, and no correlation with... 

Dandge DK, Heller JP, Wilson KV. Structure-solubility correlations organic compounds and dense carbon dioxide binary systems. Ind Eng Chem Prod Res Dev 1985 24 162-166. 

Given the limited data base from which solubility correlations can be drawn, it is essential to measure the solubility directly for the system of interest during process development. Since process conditions often favor operation with high concentrations of solute, such systems are often thermodynamically nonideal. It is necessary to measure the solubility in the solvent system(s) of interest in order to optimize the yield and the purity. To accomplish the latter relies upon the ability to measure the solubility of the key impurities as well as the product of interest. This requires the availability of both the key impurities and product however, the impurities often are not available as isolated solids. In that case, the solubility of impurities must be deduced from the purity profile of mother liquors taken from crystallizations of the actual process stream. It is often simplest and always fastest to measure the solubility and carry out crystallizations in a single-solvent system. However, working in multiple-solvent systems increases the likelihood of improving the yield, the separation factor, and the prospects of observing more of the possible crystal forms that may exist. 

In addition to equation 3.4, a number of semi-empirical equations have been proposed for solubility correlation purposes, some of which are based on thermodynamic relationships relating to phase equilibria. Examples of some of the expressions that have found favour, at one time or another, are... 

It should also be noted that aqueous solubility is a thermodynamic quantity closely related to the octanol-water partition coefficient A ow As a result of the considerable A ow data compilations and analyses by Hansch, Leo, and co-workers (72), there exists the capability of calculating A ow froni a knowledge of molecular structure. These calculated values can then be used to deduce a value for the solubility. There have been several A ow-solubility correlations, notably those of Chiou et al. (4), but more recent correlations that include an entropy of fusion term are now more accurate (2, 25, 41),... 

Abraham et al. [14] have reported solubility correlations for a wide variety of systems that follow Henry s law. Gas/liquid partition coefficients for biofluids are modelled by a suitable combination of gas/water and gas/oil partition coefficients, thus allowing for the hydrophobicity of a given biological tissue or fluid. This method is furthermore able to provide a measure for the tissue/blood distribution of non-electrolytes (which may also be estimated using octanol-water partition coefficients [15]). 

Above the CMC of each surfactant, linear enhancements in HCB solubility were observed, similar to trends reported for HOCs in micellar solutions (7,5,75). The corresponding WSR values for Tween 60, Tween 80 and Triton X-100, calculated using Equation 1, were 0.59 g/kg, 0.63 g/kg and 0.35 g/kg, respectively. The lower HCB solubilization capacity of TritonX-100 is consistent with solubility correlations developed by PenneU et al. (5) for a range of surfactants and HOCs. This behavior is attributed to the greater alkyl chain length, and hence larger micelle size of Tween 60 and Tween 80 relative to that of Triton X-100. 

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