Empirical solubility model

Notes-. The empirical solubility model used was log (M ) = a + h pH + c log M.j. + d log OM, where a is an empirical constant (intercept) and the other three coefficients reflect the dependence of solubility on pH, total soil metal content and organic matter (or carbon), respectively. 

Fig. 3. Distribution of metal-2 -deoxymugineic acid (DMA) in solution as a function of pH. Metal binding by the soil solid phase is simultaneously considered using empirically derived solubilities. For Cd, Zn, Cu, and Ni the empirical solubility model used was log (M"+) = a + b pH + c log Mj + d log OM, where a is an empirical constant (intercept) and the other three coefficients reflect the dependence of solubility on pH, total soil metal content and organic matter (or carbon), respectively. Fe(OH)j had an assumed solubility of log K = —2.1 (Lindsay, 1979). The total soil metal concentration was 10 mg kg , organic C was 10 g kg and DMA was 25 iM.

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. 

We have developed a two-step procedure for the in silico screening of compound libraries based on biopharmaceutical property estimation linked to a mechanistic simulation of GI absorption. The first step involves biopharmaceutical property estimation by application of machine learning procedures to empirical data modeled with a set of molecular descriptors derived from 2D and 3D molecular structures. In silico methods were used to estimate such biopharmaceutical properties as effective human jejunal permeability, cell culture permeability, aqueous solubility, and molecular diffusivity. In the second step, differential equations for the advanced compartmental absorption and transit model were numerically integrated to determine the rate, extent, and approximate GI location of drug liberation (for controlled release), dissolution, and absorption. Figure 17.3 shows the schematic diagram of the ACAT model in which each one of the arrows represents an ordinary differential equation (ODE). 

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. 

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. 

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,)... 

Solvent selectivity is a measure of the relative capacity of a solvent to enter into specific solute-solvent interactions, characterized as dispersion, induction, orientation and coaplexation interactions, unfortunately, fundamental aiq>roaches have not advanced to the point where an exact model can be put forward to describe the principal intermolecular forces between complex molecules. Chromatograidters, therefore, have come to rely on empirical models to estimate the solvent selectivity of stationary phases. The Rohrschneider/McReynolds system of phase constants [6,15,318,327,328,380,397,401-403], solubility... 

Mechanisms of dissolution kinetics of crystals have been intensively studied in the pharmaceutical domain, because the rate of dissolution affects the bioavailability of drug crystals. Many efforts have been made to describe the crystal dissolution behavior. A variety of empirical or semi-empirical models have been used to describe drug dissolution or release from formulations [1-6]. Noyes and Whitney published the first quantitative study of the dissolution process in 1897 [7]. They found that the dissolution process is diffusion controlled and involves no chemical reaction. The Noyes-Whitney equation simply states that the dissolution rate is directly proportional to the difference between the solubility and the solution concentration ... 

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]. 

If the pore-mechanism applies, the rate of permeation should be related to the probability at which pores of sufficient size and depth appear in the bilayer. The correlation is given by the semi-empirical model of Hamilton and Kaler [150], which predicts a much stronger dependence on the thickness d of the membrane than the solubility-diffusion model (proportional to exp(-d) instead of the 1 Id dependence given in equation (14)). This has been confirmed for potassium by experiments with bilayers composed of lipids with different hydrocarbon chain lengths [148], The sensitivity to the solute size, however, is in the model of Hamilton and Kaler much less pronounced than in the solubility-diffusion model. 

Influence of Organic Cosolvents. Rao et al. (49) have recently presented a solvophobic model for estimating the sorption of a hydrophobic solute from a mixed solvent. This model is based on the work of Yalkowsky et al. (27), who developed an empirical relationship between the solubility in a mixed solvent system, Sm, and that in pure water given by... 

In the 2nd period ranging from the 1930s to the 1950s, basic research on flotation was conducted widely in order to understand the principles of the flotation process. Taggart and co-workers (1930, 1945) proposed a chemical reaction hypothesis, based on which the flotation of sulphide minerals was explained by the solubility product of the metal-collector salts involved. It was plausible at that time that the floatability of copper, lead, and zinc sulphide minerals using xanthate as a collector decreased in the order of increase of the solubility product of their metal xanthate (Karkovsky, 1957). Sutherland and Wark (1955) paid attention to the fact that this model was not always consistent with the established values of the solubility products of the species involved. They believed that the interaction of thio-collectors with sulphides should be considered as adsorption and proposed a mechanism of competitive adsorption between xanthate and hydroxide ions, which explained the Barsky empirical relationship between the upper pH limit of flotation and collector concentration. Gaudin (1957) concurred with Wark s explanation of this phenomenon. Du Rietz... 

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... 

Alternatively, the structure-solubility relationship estimates solubility using equations that relate solubility to the molecular structures of solutes. The structure-solubility relationship is generally regarded as an empirical method. There is no doubt that an exact theoretical method is preferred over an empirical method forthe study of solubility phenomena. However, owing to the very complicated nature of molecular interactions and the various simpliLcations used in the development of mathematical models, exact thermodynamic approaches may not always provide accurate results without an extensive study of the compound of interest. At the present time, both theoretical and empirical approaches result in similar accuracy, and can be used equally well in the estimation of solubility. 

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