Models to predict solubility in ternary solvents based on sub-binary experimental data

The capability of the extended forms, of two well established cosolvency models, i.e. the combined nearly ideal binary solvent/Redlich-Kister equation and the modified Wilson model, used to predict the solute solubility in non-aqueous ternary solvent mixtures is presented. These predictions are based on the measured solubilities of anthracene in binary solvent mixtures. As a result the values of average percent deviations were less than 2% for the anthracene solubility in ternary mixtures. This work was also extended to other cosolvency models, ie. the extended Hildebrand solubility approach and the mixture response surface method, which are also commonly used for correlating solubility data in ternary solvents. The accuracy of the models is compared with each other and also with a published solubility model for ternary mixtures. The results illustrate that all models produced comparable accuracy.     

Predicting solubility of anthracene in non-aqueous solvent mixtures using a combination of Jouyban-Acree and Abraham models

Quantitative structure property relationships were proposed to calculate the binary interaction terms of the Jouyban-Acree model using coefficients of Abraham solvational models. The applicability of the proposed methods for reproducing solubility data of anthracene in binary solvents has been evaluated using 56 solubility data sets collected from the literature. The mean percentage deviation (MPD) of experimental and calculated solubilities, using predicted mole fraction solubility of anthracene in solvents 1 and 2, has been computed as a measure of accuracy and the MPD of the proposed methods were 5.5 and 4.2%. The accuracy of the method was compared with that of a previously reported method where the MPD was 14.4% and the mean differences between proposed and previous methods was statistically significant. To provide a predictive model, solubility of anthracene was computed using Abraham solvational models and employed to predict the solubility in binary solvents using derived model constants of Jouyban-Acree model and the obtained MPDs were 37.9 and 22.2%, respectively.     

Comparison of different algorithms to calculate electrophoretic mobility of analytes as a function of binary solvent composition

Ten different mathematical models representing the electrophoretic mobility of analytes in capillary electrophoresis in mixed solvents of different composition have been compared using 32 experimental data sets. The solvents are binary mixtures of water-methanol, water-ethanol and methanol-ethanol, respectively. Mean percentage deviation (MPD), overall MPD (OMPD) and individual percentage deviation (IPD) have been considered as comparison criteria. The results showed that a reorganized solution model, namely the combined nearly ideal binary solvent/Redlich-Kister equation, is the most accurate model among other similar models concerning both correlation ability and prediction capability.     

Solubility prediction of paracetamol in binary and ternary solvent mixtures using Jouyban-Acree model

The Jouyban-Acree model has been used to predict the solubility of paracetamol in water-ethanol-propylene glycol binary and ternary mixtures based on model constants computed using a minimum number of solubility data of the solute in water-ethanol, water-propylene glycol and ethanol-propylene glycol binary mixtures. Three data points from each binary solvent system and solubilities in neat solvents were used to calculate the binary interaction parameters of the model. Then the solubility at other binary solvent compositions as well as in a number of ternary solvents were predicted, and the mean percentage deviation (+/-S.D.) of predicted values from experimental solubilities was 7.4(+/-6.1)%.     

Solubility of pyrene in simple and mixed solvent systems

The solubility of pyrene was experimentally determined in simple and complex solvent systems (single, binary, ternary, quaternary and pentinary solvent systems) composed of benzene, ethylbenzene, hexane, hexanol and methylcyclohexane over a temperature range from 293 to 318 K. In addition, six models were used in this study to represent pyrene solubility in the different solvent systems. The interaction parameters for modified Wilson, NIBS/Redlich-Kister, UNIQUAC and NRTL models were estimated using the solubility data generated for pyrene in single, binary and ternary solvent systems. By re-adjusting the interaction parameters reported for Dortmund UNIFAC and ASOG models, a better representation of the solubility of pyrene was obtained compared to using reported values. Furthermore, a correction term is introduced for the ASOG model in this study to better improve pyrene solubility prediction in simple and mixed solvent systems. These estimated or re-adjusted interaction parameters for the different models, along with the reported parameters for Dortmund UNIFAC and ASOG models, were tested on complex solvent systems (quaternary and pentinary solvent mixtures), in order to check their validity and accuracy for such predictions.     

Solubility of Anthracene in Binary Carbon Tetrachloride + Alkane Solvent Mixtures

Abstract

Experimental solubilities are reported for anthracene in binary solvent mixtures containing carbon tetrachloride with n-hexane, n-heptane, n-octane, cyclohexane, methylcyclohexane and isooctane at 25°C. Results of these measurements, combined with the excess Gibbs free energies of the binary solvents, are used to test predictive expressions derived from the nearly ideal binary solvent (NIBS) model. Expressions based on a volume fraction average of solute properties in the two pure solvents predict anthracene solubilities to within a maximum deviation of 4.5% and an overall average deviation of 1.8%.     

A unified cosolvency model for calculating solute solubility in mixed solvents

Organic solvents are amongst the most powerful solubilization agents for a large number of water-insoluble drugs. A number of equations has been reported for mathematical representation of solute solubility in mixed solvents. The question is then posed--is there a mathematical difference between these models? To address this point, it has been demonstrated that all cosolvency models could be made equivalent by using algebraic manipulations. In order to familiarize the readers with the available cosolvency models, they are briefly reviewed. The models can be divided into two mathematical categories, i.e. linear and non-linear models. The linear models include: the log-linear, extended Hildebrand solubility approach, excess free energy equations, combined nearly ideal binary solvent/Redlich-Kister equation and Margule equations which can be converted to a general single model which expresses the logarithm of mole fraction solubility of a solute as a power series of volume fraction of the cosolvent. The non-linear models include the mixture response surface methods, two step solvation model and modified Wilson model which can be converted to a non-linear general form. Also, it has been shown that both the general single model and a non-linear general model are mathematically identical. To show the applicability of the models on real experimental data, 35 data sets have been collected from the literature. Both linear and nonlinear models produced comparable accuracies when an equal number of constant terms was employed in numerical analyses.     

Solubility of anthracene in binary alkane + ethanol solvent mixtures at 298.15 K

Experimental solubilities are reported for anthracene in six binary alkane?+?ethanol solvent mixtures at 298.15?K. The alkane solvents studied were hexane, heptane, octane, cyclohexane, methylcyclohexane and 2,2,4-trimethylpentane. Results of these measurements were used to test a mathematical representation based on the combined nearly ideal binary solvent (NIBS)/Redlich–Kister equation. For the six systems studied, the combined NIBS/Redlich–Kister equation was found to accurately describe the experimental data, with an average absolute deviation between measured and back-calculated values being approximately ±0.5%.     

Thermodynamic properties of ternary non-electrolyte solutions: Part 2. Prediction of infinite dilution activity coefficients and solubilities based on the various nibs and microscopic partition models

The limitations and applications of the various nearly ideal binary solvent (NIBS) and microscopic partition (MP) models for predicting the thermochemical properties of solutes dissolved in binary solvent mixtures are re-examined using published solute solubility and infinite dilution activity coefficient data for 48 systems. Expressions derived from the basic NIBS and extended NIBS models provide very reasonable predictions for anthracene and carbazole solubilities in systems containing both non-specific and specific interactions. For many of the systems considered, deviations between experimental values and NIBS predictions are of the order of 6% or less. In comparison, the two expressions derived from the MP model grossly overpredict the observed solubilities, with the average absolute deviations for several of the carbazole systems being 30% or more.     

Effect of pH, temperature and solvent mole ratio on solubility of disodium 5′-guanylate in water + ethanol system

Solubility of disodium 5′-guanylate in water + ethanol binary solvent mixtures was determined by a gravimetric method in the temperature range from 283.15 K to 323.15 K, pH range from 8 to 10 and at different water/ethanol mole ratios. The effects of pH, temperature and water/ethanol mole ratio on the solubility were investigated in detail. The modified Apelblat model and the combined nearly ideal binary solvent (CNIBS)/Redlich-Kister model were selected to correlate the experimental data. The results showed that the experimental data was satisfactorily correlated by the (CNIBS)/Redlich-Kister model, but for the modified Apelblat model, the correlation was not so satisfactory in some cases.     

Solubilities of families of heterocyclic polynuclear aromatics in organic solvents and their mixtures

The solubilities of anthracene, acridine, xanthene, thioxanthene, carbazole, dibenzofuran, and dibenzothiophene have been experimentally determined in benzene, cyclohexane, thiophene, and pyridine from ambient temperature to approximately 440 K. The results have been correlated using the classical equation for solid-liquid solubility to obtain the experimental activity coefficient of the solute in the solvent. These experimental activity coefficients have been regressed, using three common solution models, to find the binary interaction parameters needed in those models. The solubilities of biphenyl, dibenzofuran, and dibenzothiophene have been experimentally determined in five binary mixtures of the solvents. The experimental activity coefficients have been found and compared to the values predicted by the four solution models, using the binary interaction parameters obtained from the solubilities in the pure solvents and solventsolvent binary interaction parameters obtained from literature vaporliquid equilibria data. The effect of substituting various heteroatoms into the ring structure has been discussed.     

Solubility of anthracene in binary toluene + alcohol solvent mixtures at 298.15 K

Experimental solubilities are reported for anthracene in eight binary toluene?+?alcohol solvent mixtures at 298.15?K. The alcohol solvents studied were 1-propanol, 1-butanol, 1-pentanol, 1-hexanol, 2-propanol, 2-butanol, 2-methyl-1-propanol and 3-methyl-1-butanol. Results of these measurements were used to test a mathematical representation based on the combined nearly ideal binary solvent (NIBS)/Redlich–Kister equation. For the eight systems studied, the combined NIBS/Redlich–Kister equation was found to accurately describe the experimental data, with an average absolute deviation between the measured and back-calculated values being approximately ±0.4%.     

Solubility of Anthracene in Binary Alcohol + 1-chlorobutane Solvent Mixtures at 298.2 K

Abstract

Experimental solubilities are reported for anthracene dissolved in six binary alcohol + 1-chlorobutane solvent mixtures at 25°C. The alcohol cosolvents studied were 1-propanol, 2-propanol, 1-butanol, 2-butanol, 2-methyl-1-propanol and 3-methyl-1-butanol. Results of these measurements are used to test a mathematical representation based upon the combined Nearly Ideal Binary Solvent (NIBS)/Redlich-Kister equation. For the six systems studied, the Combined NIBS/Redlich-Kister equation was found to mathematically describe the experimental data, with overall average absolute deviations between measured and calculated values being approximately\pm 0.4%.     

An activity coefficient model for predicting salt effects on vapor–liquid equilibria of mixed solvent systems

In the present study, an activity coefficient model, based on the concept of local volume fractions and the Gibbs–Helmholtz relation, has been developed. Some modifications were made from Tan–Wilson model (1987) and TK–Wilson model (1975) to represent activity coefficients in mixed solvent–electrolyte systems. The proposed model contains two groups of binary interaction parameters. One group for solvent–solvent interaction parameters corresponds to that given by the TK–Wilson model (1975) in salt-free systems. The other group of salt–solvent interaction parameters can be calculated either from vapor pressure or bubble temperature data in binary salt–solvent systems. It is shown that the present model can also be used to describe liquid–liquid equilibria. No ternary parameter is required to predict the salt effects on the vapor–liquid equilibria (VLE) of mixed solvent systems. By examining 643 sets of VLE data, the calculated results show that the prediction by the present model is as good as that by the Tan–Wilson model (1987), with an overall mean deviation of vapor phase composition of 1.76% and that of the bubble temperature of 0.74 K.     

Solubility of Anthracene in Binary Alcohol + Butyl Acetate Solvent Mixtures at 298.2 K

Abstract

Experimental solubilities are reported for anthracene dissolved in six binary alcohol + butyl acetate solvent mixtures at 25° C. The alcohol cosolvents studied were 1-propanol, 2-propanol, 1-butanol, 2-butanol, 2-methyl-1-propanol and 3-methyl-1-butanol. Results of these measurements are used to test a mathematical representation based upon the combined Nearly Ideal Binary Solvent (NIBS)/Redlich-Kister equation. For the six systems studied, the Combined NIBS/Redlich-Kister equation was found to mathematically describe the experimental data, with overall average absolute deviations between measured and calculated values being approximately\pm 0.6%.     

Vapour-liquid-solid equilibrium of eicosanoic acid in one- and two-component solvents

Domańska, U., 1986. Vapour-liquid-solid equilibrium of eicosanoic acid in one- and two-component solvents. Fluid Phase Equilibria, 26: 201–220.Solubilities of eicosanoic acid in 14 pure solvents and in 18 pairs of binary solvent systems, at room temperature to temperatures near the melting point of the solid, and VLE along the saturation line in cyclohexane, heptane and ethanol have been determined. Five methods of calculation were applied: the Hilderbrand-Scatchard regular solution theory, the Wilson equation, the Redlich-Kister equation, the van Laar equation and the generalized solubility equation (λh). Mixed solvent systems were found to exhibit a synergistic effect on solubility. The best correlation was obtained with the λh equation.     

Thermochemical investigations of hydrogen-bonded solutions. Part 11. Expressions for predicting anthracene solubilities in alcohol+alkoxyalcohol mixtures based on mobile order theory

Experimental solubilities are reported for anthracene dissolved in eight binary mixtures containing 2-ethoxyethanol with 1-propanol, 2-propanol, 1-butanol, 2-butanol, 2-methyl-1-propanol, 1-pentanol, 3-methyl-1-butanol and 1-octanol, and also in binary 1-pentanol+2-methoxyethanol and 2-methyl-1-propanol+2-propoxyethanol solvent systems at 25°C. Results of these measurements, combined with previously reported anthracene solubility data in 22 different alcohol +2-alkoxyethanol (2-methoxyethanol, 2-propoxyethanol and 2-butoxyethanol) solvent mixtures, are used to test the limitations and applications of expressions derived from Mobile Order theory. The first predictive expression assumes only formation of homogeneous self-associated hydrogen-bonded species, whereas the second equation includes additional terms to account for heterogeneous complex formation between the dissolved alcohol and 2-alkoxyethanol solvent molecules. Both equations predict the observed anthracene solubilities to within an average absolute deviation of about 3%.     

Phase Equilibria in the Systems Ethyl 1,1-Dimethylethyl Ether + Benzene + 2,2,4-Trimethylpentane and Benzene + 2,2,4-Trimethylpentane at 94.00 kPa

Abstract

Consistent vapor-liquid equilibria data at 94.00 kPa have been determined for the ternary system ethyl 1,1-dimethylethyl ether + benzene + 2,2,4-trimethylpentane and for its constituent binary benzene + 2,2,4-trimethylpentane, in the temperature range 343 to 370 K. The systems exhibit slight positive deviations from ideal behavior and the system benzene + 2,2,4-trimethylpentane presents an azeotrope. The VLE data have been correlated with the mole fraction using the Redlich-Kister, Wilson, NRTL, UNIQUAC, and Tamir relations. These models, in addition to UNIFAC, allow good prediction of the VLE properties of the ternary system from those of the pertinent binary systems.     

Solvatochromic parameters for binary mixtures of 1-(1-butyl)-3-methylimidazolium tetrafluoroborate with some protic molecular solvents

The solvatochromic parameters (ET(N), normalized polarity parameter; pi*, dipolarity/polarizability; beta, hydrogen-bond acceptor basicity; alpha, hydrogen-bond donor acidity) were determined for binary solvent mixtures of 1-(1-butyl)-3-methylimidazolium tetrafluoroborate ([bmim]BF4) with water, methanol, and ethanol at 25 degrees C over the whole range of mole fractions. In nonaqueous solutions, the value of the mixture increases with mole the fraction of [bmim]BF4 and then decreases gradually to the value of pure [bmim]BF4. Positive deviation from ideal behavior was observed for the solvent parameters ET(N), pi*, and alpha, whereas the deviation of the beta parameter is negative. The applicability of the combined nearly ideal binary solvent/Redlich-Kister equation for the correlation of various solvatochromic parameters with solvent composition was proved too for the first time. This equation provides a simple computational model to correlate and/or predict various solvatochromic parameters for many binary solvent systems. The correlation between the calculated and the experimental values of various parameters was in accordance with this model. Solute-solvent and solvent-solvent interactions have been applied for interpretation of the results.