Yalkowsky equation

Aqueous solubility is a direct measure of the hydrophobicity of a substance. Therefore, perhaps the most practical way of estimating the intrinsic water solubility (logS) for structurally diverse organic substances is through the use of the Yalkowsky equation [47], which uses regression-derived correlation with logPQ w and melting point (MP) for solids ... 

Among the recent reviews, the most comprehensive one is by Dearden [15]. In his review, he discusses the fundamentals of aqueous solubility, which lead to the Yalkowsky equation. Dearden also reviews the oldest approaches of predicting aqueous solubility, from a very simple fragment-based approach of 1924 to the numerous approaches post-1990, for which he made an extensive tabular comparison. 

A series of studies has been made by Yalkowsky and co-workers. The so-called general solubility equation was used for estimating the solubility of solid nonelectrolytes [17, 18]. The solubility log S (logarithm of solubility expressed as mol/L) was formulated with log P logarithm of octanol/water partition coefficient), and the melting point (MP) as shown in Eq. (11). This equation generally... 

Yang G, Ran Y and Yalkowsky SH. Prediction of the aqueous solubility comparison of the general solubility equation and the method using an amended solvation energy relationship. J Pharm Sci 2002 91 517-33. 

Sanghvi, T., Jain, N Yang, G., Yalkowsky, S. Estimation of aqueous solubility by the general solubility equation (GSE) the easy way. QSAR Comh. Sci. 2003, 22, 258-262. 

It is advantageous with a new drug substance to be able to estimate what its solubility will be prior to carrying out dissolution experiments. There are several systems of solubility prediction, most notably those published by Amidon and Yalkowsky [14-16] in the 1970s. Their equation for solubility of p-aminobenzo-ates in polar and mixed solvents is a simplified two-dimensional analog of the Scatchard-Hildebrand equation and is based on the product of the interfacial tension and the molecular surface area of the hydrocarbon portion of a molecule. 

Ran, Y., Jain, N., Yalkowsky, S.H. Prediction of aqueous solubility of organic compounds by the general solubility equation (GSEJ./. Chem. Inf. Comput. Sci. 2001, 41, 1208—1217. 

Several computational methods require the user to input experimental parameters in order to make predictions. Examples include Yalkowsky s general solvation equation [18], which requires melting points, and Abraham s method [19], which requires five experimentally derived parameters. These methods are not useful for cases before the compounds are synthesized (e.g., in library design or virtual screening), and so they will not be considered further here. 

Yalkowsky and Roseman (1981) and Rubino and Yalkowsky (1987) suggest the following equations for relating solubility of a nonpolar solute (SJ in a binary mixture of an organic solvent and water to that in pure water (S ) ... 

The other term frequently occurring in such equations is the octanol-water partition coefficient, logP. It describes the lipophilicity of the compound. It is related to water solubility by Yalkowski s general solubility equation (GSE) ]33, 34] ... 

Ran, Y. and Yalkowsky, S.H. (2001) Prediction of drug solubility by the general solubility equation (GSE). Journal of Chemical Information and Computer Sciences, 41, 354—357. 

A comprehensive review of this field is beyond the scope of this chapter. As for vapour pressure, the aim is to give easy-to-use tools for non-specialists in the field. The general solubility equation, initially introduced by Yalkowski and Valvany [47], then revised by the same team [48], is probably the simplest ... 

Solubility-Partition Coefficient Relationships A critical review on the applicability of empirically derived solubility -Kow models has been given by Yalkowsky et al. [24], Isnard and Lambert [26], Lyman [1], and Muller and Klein [27]. Equations 10.4.3 to 10.4.5 are examples of solubility-Kow models. Isnard and Lambert developed a model based on 300 structurally diverse compounds. The model equation for liquids (Tm < 25°C) is... 

With the estimation of the molecular surface area available for speciLc and nonspeciLc interactions, the solubility in water of aliphatic compounds has been successfully related to molecular surface area by Equation 3.45 (Amidon et al., 1974,1975 Valvani and Yalkowsky, 1976) ... 

There are also empirical equations available that can be used for solubility estimation. Yalkowsky and Valvani (1980) developed the following equation by considering the transfer of a solute from the solid state to octanol followed by its transfer to the aqueous phase ... 

Other attempts at characterizing the deviation from ideal solubility theory have been made. Anderson et al. [50] showed that solubilities that could not be rationalized from the regular solution theory could be rationalized by assuming the formation of speciLc solute-solvent complexes. Yalkowsky et al. [51,52] showed that the deviation from the ideal solubility equation could be expressed in terms of interfacial tension and surface area. In equation form,... 

In Rubino s [9] review of approaches to predicting solubility in cosolvent systems, Yalkowsky and Roseman [60] proposed one of the simplest and most useful methods. Their equation,... 

Yalkowsky and Roseman [60] investigatethrough partition coefL dents. Since partition coefL-cients are really adivities of a compound in an organic phase, usually odanol, relative to an aqueous phase or other phase, the above equation can be rewritten as... 

Yalkowsky, Rubino, and others [63-67] have further studied log-linear cosolvent solubilization. For organic solutes in propylene glycol-water mixtures, Yalkowsky and Rubino found that the following equation... 

Similarly, Li and Yalkowsky [67] determined that for ethanol-water mixtures where the fraction of ethanol is less than 0.6, the following equation could be used to calculate solubility proL les of an organic solute ... 

Yalkowsky (1981) has developed equations describing water solubility as a function of both hydrophobicity (locP) and crystal lattice forces. Jain and Yalkowsky (2001) have offered a new general solubility equation, where the molar solubility, %) of a nonelectrolyte can be estimated by... 

Along with the drive to obtain increased accuracy (with more sophisticated estimation equations and special rules) is a tendency to forget the simplest methods — admittedly less accurate — which are very easy to use and can be considered useful guides in an estimation process which may employ two or more methods. (Examples of such methods are those of Banks [1939] and Burnop [1938] which rely primarily on the molecular weight, and the equations using melting point developed by Yalkowsky et al. [1994] and Walters et al. [1995].)... 

Grain (1982) presented several methods for estimating the vapor pressure of a wide variety of organic chemicals in an earlier handbook. He recommended the Antoine equation for liquids with vapor pressures above 1(H kPa and the modified Watson method for solids and liquids with vapor pressures above 10 7 kPa. Section 3.2 discusses both methods in detail. Lyman (1984) recommended the Grain-Watson method and a method that Mackay and coworkers (1982) developed. Myrdal and Yalkowsky (1997) used a method similar to... 

Solutes that, whatever their state of aggregation, undergo solvation interactions with the solvent beyond those due to dispersion forces, exhibit specific contributions to the solubility, that can be attributed to dipole-dipole and dipole-induced dipole interactions and electron-pair or hydrogen bond donation by the solvent to the solute or vice versa. Equations (2.10), (2.14) and (2.15) must then be modified to take these interactions into account by the addition of appropriate terms. Various approaches have been proposed for such additional interactions, and here the following is adopted, following Yalkowski (Yalkowski 1988) ... 

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