Predicting the Solubility of Drugs in Solvent Mixtures: Multiple Solubility Maxima and the Chameleonic Effect

Abstract— An approach to reproduce the solubility profile of a drug in several solvent mixtures showing two solubility maxima is proposed in this work. The solubility of sulphamethoxypyridazine was determined at 25°C in several mixtures of varying polarity (hexane: ethyl acetate, ethyl acetate:ethanol and ethanol: water). Sulphamethoxypyridazine was chosen as a model drug because of its proton-donor and proton-acceptor properties. A plot of the mole fraction of the drug vs the solubility parameter of the solvent mixtures shows two solubility peaks. The two peaks found for sulphamethoxypyridazine demonstrate the chameleonic effect as described by Hoy and suggest that the solute-solvent interaction does not vary uniformly from one mixture to another. The different behaviour of the drug in mixtures of two proton-donor and proton-acceptor solvents (alcohol and water), and in mixtures of one proton acceptor (ethyl acetate) and one proton donor-proton acceptor (ethanol) is rationalized in terms of differences in the proton donor-acceptor ability of the solvent mixtures. An approach based on the acidic and basic partial solubility parameters together with the Hildebrand solubility parameter of the solvent mixtures is developed to reproduce the experimental results quantitatively. The equation predicts the two solubility maxima as found experimentally, and the calculated values closely correspond to the experimental values through the range composition of the solvent mixtures. These results show that the chameleonic effect can be described in a quantitative way in terms of Lewis acid-base interactions; this approach can assist the product formulator to choose the proper solvent mixture for a new drug. A good solvent blend should result in a solubility parameter close to that of the drug; the acidic and basic partial solubility parameter values should provide maximum acid-base interaction of the mixed solvent with the drug. The failure in one of these conditions results in decreased solubility. Solubility parameters as well as the acidic and basic parameters are tabulated or they can be obtained from group contribution methods, making easier the evaluation of the best solvent mixture for a drug.     

Solubility Prediction of Satranidazole in Aqueous N,N-dimethylformamide Mixtures Using Extended Hildebrand Solubility Approach

The solubility of satranidazole in several water–N,N-dimethylformamide mixtures was analysed in terms of solute–solvent interactions and data were treated on the basis of extended Hildebrand solubility approach. The solubility profile of satranidazole in water–N,N-dimethylformamide mixtures shows a curve with a solubility maxima well above the ideal solubility of drug. This is attributed to solvation of the drug with the water–N,N-dimethylformamide mixture, and indicates that the solute–solvent interaction energy (W) is larger than the geometric mean (δ₁δ₂) of regular solution theory. The new approach provides an accurate prediction of solubility once the interaction energy (W) is obtained. In this case, the energy term is regressed against a polynomial in δ₁ of the binary solvent mixture. A quartic expression of W in terms of solvent solubility parameter was found for predicting the mole fraction solubility of satranidazole in the studied mixtures. The method has potential usefulness in preformulation and formulation studies during which solubility prediction is important for drug design.     

Thermodynamics of cosolvent action: phenacetin, salicylic acid and probenecid

The solubility of phenacetin, salicylic acid, and probenecid in ethanol-water and ethanol-ethyl acetate mixtures at several temperatures (15-40 degrees C) was measured. The solubility profiles are related to medium polarity changes. The apparent thermodynamic magnitudes and enthalpy-entropy relationships are related to the cosolvent action. Salicylic acid and probenecid show a single peak against the solubility parameter delta(1) of both solvent mixtures, at 40% (delta(1) = 21.70 MPa(1/2)) and 30% (delta(1) = 20.91 MPa(1/2)) ethanol in ethyl acetate, respectively. Phenacetin displays two peaks at 60% ethanol in ethyl acetate (23.30 MPa(1/2)) and 90% ethanol in water (delta(1) = 28.64 MPa(1/2)). The apparent enthalpies of solution display a maximum at 30% (phenacetin and salicylic acid) and 40% (probenecid) ethanol in water, respectively. Two different mechanisms, entropy at low ethanol ratios, and enthalpy at high ethanol ratios control the solubility enhancement in the aqueous mixture. In the nonaqueous mixture (ethanol-ethyl acetate) enthalpy is the driving force throughout the whole solvent composition for salicylic acid and phenacetin. For probenecid, the dominant mechanism shifts from entropy to enthalpy as the ethanol in ethyl acetate concentration increases. The enthalpy-entropy compensation plots corroborate the different mechanisms involved in the solubility enhancement by cosolvents.     

Solubility behavior of polymorphs I and II of mefenamic acid in solvent mixtures

The dissolution profile and solubility of two polymorphic forms of mefenamic acid were studied in solvent mixtures of ethanol-water and ethyl acetate-ethanol. The solubility parameter (delta) was used to study the effect of polarity on the solubility behavior of the two polymorphs. Differential scanning calorimetry and infrared spectroscopy were performed on the original powders and on the solid phases after contact with the solvent systems for the characterization and identification of the polymorphs. The dissolution rates of both polymorphs is greater in the less polar mixtures (ethyl acetate-ethanol) of lower solubility parameter values. Form II showed larger dissolution rates and saturation concentrations than Form I in all the solvent systems studied. The solid phase of Form II converts totally to Form I after equilibration with the solvents. The rate of conversion was faster in the least polar mixtures. The solubility of both polymorphs reaches a single maximum at 80% ethyl acetate in ethanol, delta = 20.09 MPa1/2. The modified extended Hildebrand method was used to predict the solubility profile of each polymorph. A single equation was obtained for both polymorphs which includes the solubility parameter of the mixtures and the logarithm of the solubility mole fraction of each polymorph in water. The Hildebrand solubility parameter of mefenamic acid is independent of the crystalline form and was determined from two methods giving quite similar values, delta 2 = 20-21 MPa1/2.     

Solubility behaviour of griseofulvin in fatty acids

The solubility of griseofulvin in the straight-chain alkanoic acids from C₂ to C₂₂ and in the C₄ and C₅ alkanoic acids branched at C-2 was measured at various temperatures. The enthalpy of fusion of griseofulvin, measured by differential scanning calorimetry, was 39.39 kJ mol^?1 at the melting point (495.15 K) and 36.95 kJ mol^?1 at 373.15 K. The standard Gibbs free energy (ΔG°), standard enthalpy (ΔH°) and standard entropy (ΔS°) of solution were calculated at 373.15 K, from the van't Hoff plot of the temperature dependence of the mole fraction solubility in terms of the pure supercooled liquid solute as the standard state. With increasing chain length of the alkanoic acid solvents, ΔG° increased in parallel with the increase in pK_a of the acids in water, suggesting that the solubility behaviour involves specific solute-solvent proton interactions, while ΔH° and ΔS° fluctuated but tended to decrease in parallel with the corresponding decreases in their enthalpies and entropies of ionization, respectively. The fluctuations in ΔH° and ΔS° may be attributed to the different solid adducts containing griseofulvin and the solvent. An observed non-linear (logarithmic) decrease in solubility with decreasing molality of the carboxyl group in the liquid solvent on ascending the homologous series is attributed to the disturbing influence of the hydrocarbon chains on the specific solute-solvent hydrogen bonding. Chain-branching of the solvent at C-2 gave a reduced solubility of griseofulvin and higher ΔG°, ΔH° and ΔS° values compared with the corresponding straight chain acid.     

Solubility Prediction of Satranidazole in Propylene Glycol-Water Mixtures Using Extended Hildebrand Solubility Approach

Extended Hildebrand solubility approach is used to estimate the solubility of satranidazole in binary solvent systems. The solubility of satranidazole in various propylene glycol-water mixtures was analyzed in terms of solute-solvent interactions using a modified version of Hildebrand-Scatchard treatment for regular solutions. The solubility equation employs term interaction energy (W) to replace the geometric mean (δ₁δ₂), where δ₁ and δ₂ are the cohesive energy densities for the solvent and solute, respectively. The new equation provides an accurate prediction of solubility once the interaction energy, W, is obtained. In this case, the energy term is regressed against a polynomial in δ₁ of the binary mixture. A quartic expression of W in terms of solvent solubility parameter was found for predicting the solubility of satranidazole in propylene glycol-water mixtures. The expression yields an error in mole fraction solubility of ~3.74%, a value approximating that of the experimentally determined solubility. The method has potential usefulness in preformulation and formulation studies during which solubility prediction is important for drug design.     

Thermodynamics-based mathematical model for solubility prediction of glibenclamide in ethanol–water mixtures

Abstract

Temperature-dependent solubility data of glibenclamide (GBN) in various ethanol–water mixtures is not reported in literature so far. Therefore, the aim of this study was to determine the mole fraction solubility of GBN in various ethanol–water mixtures at the temperature range of 293.15 to 318.15?K. The solubility of GBN was determined by reported shake flask method and the experimental data was fitted in thermodynamics-based modified Apelblat model. The solubility of GBN was found to be increased with increase in temperature and mass fraction of ethanol in ethanol–water mixtures. The experimental data of GBN was well correlated with the modified Apelblat model at each temperature range with correlation coefficient of 0.9940–1.0000. The relative absolute deviation (AD) was found to be less than 0.1% except in pure ethanol and water. The positive values of enthalpies and entropies for GBN dissolution indicated that its dissolution is endothermic and an entropy-driven process.     

A Modification of the Extended Hildebrand Approach to Predict the Solubility of Structurally Related Drugs in Solvent Mixtures

Abstract— A modification of the extended Hildebrand equation is proposed to estimate the solubility of an organic drug in solvent mixtures. The equation accurately reproduces the solubility of four sulphonamides in dioxane-water mixtures without requiring the heat of fusion of the solute. A single equation is obtained for predicting the solubility of related drugs using the solubilities of the drugs in the pure solvents, dioxane and water, and solute-solvent interaction terms consisting of the solubility parameter, δ₂, of the solute and the solubility parameter, δ₁, and basic partial solubility parameter, δ_1b, of the solvent mixture. By this procedure a single equation was obtained to estimate the solubilities of three xanthines in dioxane-water and another equation to obtain the solubilities of four sulphonamides. The equation obtained for sulphonamides is able to predict the experimental solubilities of two parent compounds, sulphasomidine and sulphathiazole, and the solubilities of a drug of different structure, p-hydroxybenzoic acid. This suggests that the intermolecular solute-solvent interaction of sulphonamides and p-hydroxybenzoic acid are similar. The results indicate that the solubility behaviour of drugs having different structures may be modelled using a common equation provided that they show similar solute-solvent interactions.     

Thermodynamics of Solutions I: Benzoic Acid and Acetylsalicylic Acid as Models for Drug Substances and the Prediction of Solubility

Purpose. To investigate the solution process of drug substances (exemplified by benzoic acid, BA, and acetylsalicylic acid, ASA), particularly the interrelation between enthalpic and entropic terms of Gibbs energy, in different solvents. To develop an approach for the estimation of standard solution enthalpies based on a self-consistent thermochemical scale. Method. Two independent methods, solubility experiments (concentrations of saturated solutions) and solution calorimetry (standard solution enthalpies) in aliphatic alcohols and individual organic solvents were used. Correlation between the thermodynamic functions in various solvents were analyzed by standard statistical methods. Multiple regression analysis between H ⁰ _sol values and the parameters of the solvents was run on the Koppel-Palm equation. Results. Based on experimental data, a compensation effect between thermodynamic functions was observed. Correlation was found between H ⁰ _sol (BA) and H ⁰ _sol (ASA) [where the H ⁰ _sol (BA)-values were used as a self-consistent thermochemical scale]. Furthermore, H ⁰ _sol correlated with the Koppel-Palm basicity of the solvents. Conclusions. The model based on solubility and solution experiments might be useful for the prediction of solubility or solvation of drug substances in different media. The regression equation based on the self-consistent thermochemical scale makes it possible to approximate the ability to solvate a drug substance in comparison with structure-relative substances.     

Influence of solvent composition on the solid phase at equilibrium with saturated solutions of quinolones in different solvent mixtures

The dissolution profiles and solubilities of three quinolonic drugs (oxolinic, pipemidic, and nalidixic acids) in different solvent mixtures were studied. The behavior of the solid phase, during solubility experiments was in-depth investigated with the aim of detecting possible crystalline modifications, such as polymorphic transitions or solvate formations, that might modify drug stability and/or solubility properties. In order to test the influence of both the nature and polarity of the co-solvents, aqueous and non-aqueous binary mixtures have been prepared by using Lewis base (dioxane and ethyl acetate) and amphiprotic co-solvents (ethanol and water). Differential scanning calorimetry (DSC), hot stage microscopy, IR spectroscopy and X-ray powder diffraction were used in combination with solubility and dissolution studies to characterize and investigate the solid state properties of the original powders and the corresponding ones at equilibrium with the different pure solvents and solvent mixtures examined. The solid phases of nalidixic and oxolinic acids did not show any change after equilibration with the various pure solvents or binary solvent mixtures, regardless the chemical nature of the examined solvents. On the contrary, in the case of pipemidic acid, the different analytical techniques used to characterize the drug solid state enabled identification of a solvated form at equilibrium with pure dioxane and a trihydrated form in aqueous mixtures of water with both ethanol (amphiprotic) or dioxane (Lewis base) in a concentration range from 10 to 100% water.     

姜黄素-邻苯二酚共晶溶度积的研究

目的 以姜黄素为药物活性成分,邻苯二酚为共晶形成物,研究姜黄素-邻苯二酚共晶在不同溶剂（甲醇和乙酸乙酯）中和不同温度下形成的热力学。方法 通过固态研磨法制备姜黄素-邻苯二酚共晶,并用X射线衍射表征,测定其在不同溶剂（甲醇、乙酸乙酯）、不同温度下的溶解度,采用络合模型计算共晶的溶度积（K_sp）和络合常数（K₁₁）。结果 姜黄素-邻苯二酚共晶在甲醇溶剂中符合1：1溶液络合模型,随着温度的升高,K_sp逐渐增大,K₁₁逐渐减小。在乙酸乙酯溶剂中符合无溶液络合模型,K_sp随温度升高而逐渐增加。结论 比较共晶在2种溶剂中的溶度积,发现其在甲醇中容易络合。该热力学研究为姜黄素-邻苯二酚共晶的制备条件优化奠定了一定的理论和应用基础。     

Solubility Enhancement of a Bisnaphthalimide Tumoricidal Agent,DMP 840, Through Complexation

ABSTRACT

The purpose of this research was to enhance the aqueous solubility of DMP 840 by complexation with water-soluble and nontoxic agents, and to understand the nature of the interactions involved in complex formation using nuclear magnetic resonance (¹H-NMR). The solubility of DMP 840 in water, saline, acetate buffers, and cosolvent mixtures was determined by high-performance liquid chromatography, and the effect of nicotinamide and pyridoxine concentrations on the solubility of DMP 840 was examined by the phase solubility method. ¹H-NMR spectra were acquired in deuterated acetate buffer at 400 MHz on a Varian Unity-400 spectrometer. The aqueous solubility of DMP 840 was sensitive to the presence of chloride and acetate anions in solution, and did not improve in the presence of cosolvents. The use of the nontoxic and water-soluble complex-forming agents nicotinamide and pyridoxine, however, resulted in a linear increase in the aqueous solubility of DMP 840 with both ligands. The solubilization appears to be due to formation of 1:1 complexes between DMP 840 and the bioorganic ligands. The complexation constants were 15.57 M^-1 for the DMP 840:nicotinamide complex and 13.36 M^-1 for the DMP 840:pyridoxine complex. The NMR results indicate that the interaction is a result of vertical or plane-to-plane stacking and the complexation constants were in agreement with that obtained by phase solubility. The results suggest that the aqueous solubility of a poorly water soluble drug substance such as DMP 840 can be significantly enhanced by its complexation with water-soluble and nontoxic agents.     

Thermodynamic origin of the solubility profile of drugs showing one or two maxima against the polarity of aqueous and nonaqueous mixtures: niflumic acid and caffeine

The purpose of this work was to investigate the origin of the different solubility profiles of drugs against the polarity of solvent mixtures with a common cosolvent. Niflumic acid and caffeine where chosen as model drugs. The solubilities were measured at five or six temperatures in aqueous (ethanol-water) and nonaqueous (ethyl acetate-ethanol) mixtures. The enthalpies of solution were obtained at the harmonic mean of the experimental temperature. Solid phase changes were analyzed using differential scanning calorimetry and thermomicroscopy. A single solubility maximum was obtained for niflumic acid against the solubility parameter of both mixtures that is not related to solid phase changes. In contrast, caffeine displays two maxima and anhydrous-hydrate transition occurs at the solubility peak in the amphiprotic mixture. The apparent enthalpies of solution of both drugs show endothermic maxima against solvent composition that are related to hydrophobic hydration. A general explanation for the cosolvent action in aqueous mixtures is proposed. The dominant mechanism shifts from entropy to enthalpy at a certain cosolvent ratio dependent on the hydrophobicity and the solubility parameter of the drug. Niflumic acid and caffeine show enthalpy-entropy compensation in ethanol-water, and this relationship is demonstrated for the first time in nonaqueous mixtures. The results support that enthalpy-entropy compensation is a general effect for the solubility of drugs in solvent mixtures. The shape of the solubility curves is correlated with the compensation plots. The solubility peaks separate different enthalpy-entropy relationships that also differentiate the solubility behavior of the hydrate and the anhydrous forms of caffeine.     

Extended Hildebrand solubility approach: sulfonamides in binary and ternary solvents

The extended Hildebrand solubility approach is used to estimate the solubility of sulfonamides in binary and ternary solvent systems. The solubility of sulfisomidine in the binary solvent, dioxane-water, shows a bell-shaped profile with a solubility maximum well above the ideal solubility of the drug. This is attributed to solvation of the drug with the dioxane-water solvent, and indicates that the solute-solvent interaction energy (W) is larger than the geometric mean (delta 1 delta 2) of regular solution theory. The solubilities of sulfadiazine, sulfisomidine, sulfathiazole, and sulfamethoxazole were determined in mixtures of dimethylacetamide, glycerol, and water, and the solubility profiles were well reproduced by use of the extended Hildebrand solubility approach. Since the solubility parameter (delta 1 = 11) of the solvent (dimethylacetamide) was approximately equal to the solubility parameters of the sulfonamides, and because of the powerful solvating power of dimethylacetamide, the solubility profiles did not exhibit peaks as observed for sulfisomidine in dioxane-water. When sulfisomidine was dissolved in a ternary mixture, i.e., butyl acetate (delta 1 = 8.5), dimethylacetamide (delta 1 congruent to 11), and methanol (delta 1 = 14.5), a spike was produced in the solubility profile at the solubility parameter of dimethylacetamide. This sharply peaked profile suggests that the two branches be treated as separate solubility curves, which are then independently well reproduced by the extended Hildebrand solubility approach. None of the four sulfonamides yielded log-linear relationships in the ternary mixtures.     

Transdermal Delivery of Levonorgestrel. V. Preparation of Devices and Evaluation in Vitro

Transdermal devices were prepared and evaluated for their ability to codeliver levonorgestrel and the permeation enhancers ethyl acetate and ethanol in vitro. The 24-hr devices were prepared with membranes composed of ethylene vinyl acetate (EVAc) copolymers. The vinyl acetate (VAc) content of the membranes (50 ± 10 or 100 ± 10 µm thick) was varied from 12 to 25% to give a range of permeabilities toward the enhancers. The reservoir used was ethyl acetate/ethanol (7:3, v/v; 0.5 ml) containing excess solid levonorgestrel and gelled with 2% hydroxypropyl cellulose. The higher VAc content membranes (18 and 25%) exhibited relatively high release rates of EtAc and EtOH leading to depletion of ethyl acetate and ethanol from the reservoir by the end of 24 hr. As a result, the transdermal flux of levonorgestrel, evaluated using rat skin, reached a maximum at about 8 hr and thereafter diminished to zero by 24 hr. The less permeable membranes (12 and 15% VAc content) led to a more sustained release of enhancers, but due to lower solvent delivery to the skin, levonorgestrel flux was substantially lower. There was a direct relationship between drug delivery through skin and the amount of solvent delivered until release of the enhancers had diminished. The potential use of ethyl acetate in transdermal drug delivery is also discussed.     

Molecular Dynamics Simulation of Amorphous Indomethacin-Poly(Vinylpyrrolidone) Glasses: Solubility and Hydrogen Bonding Interactions

Amorphous drug dispersions are frequently employed to enhance solubility and dissolution of poorly water-soluble drugs and thereby increase their oral bioavailability. Because these systems are metastable, phase separation of the amorphous components and subsequent drug crystallization may occur during storage. Computational methods to determine the likelihood of these events would be very valuable, if their reliability could be validated. This study investigates amorphous systems of indomethacin (IMC) in poly(vinylpyrrolidone) (PVP) and their molecular interactions by means of molecular dynamics (MD) simulations. IMC and PVP molecules were constructed using X-ray diffraction data, and force-field parameters were assigned by analogy with similar groups in Amber-ff03. Five assemblies varying in PVP and IMC composition were equilibrated in their molten states then cooled at a rate of 0.03 K/ps to generate amorphous glasses. Prolonged aging dynamic runs (100 ns) at 298 K and 1 bar were then carried out, from which solubility parameters, the Flory-Huggins interaction parameter, and associated hydrogen bonding properties were obtained. Calculated glass transition temperature (T_g) values were higher than experimental results because of the faster cooling rates in MD simulations. Molecular mobility as characterized by atomic fluctuations was substantially reduced below the T_g with IMC–PVP systems exhibiting lower mobilities than that found in amorphous IMC, consistent with the antiplasticizing effect of PVP. The number of IMC–IMC hydrogen bonds (HBs) formed per IMC molecule was substantially lower in IMC–PVP mixtures, particularly the fractions of IMC molecules involved in two or three HBs with other IMC molecules that may be potential precursors for crystal growth. The loss of HBs between IMC molecules in the presence of PVP was largely compensated for by the formation of IMC–PVP HBs. The difference (6.5 MPa^1/2) between the solubility parameters in amorphous IMC (25.5 MPa^1/2) and PVP (19.0 MPa^1/2) suggests a small, positive free energy of mixing, although it is close to the criterion for miscibility (< 7 MPa^1/2). In contrast to the solubility-parameter method, the calculated Flory-Huggins interaction parameter (? 0.61 ± 0.25), which takes into account the IMC–PVP interaction energy, predicts complete miscibility at all PVP compositions, in agreement with experimental observations. These results from MD simulations were combined with experimental values for the crystalline γ-polymorph of IMC and amorphous IMC to estimate the solubility of IMC in amorphous PVP dispersions and the theoretical enhancement in the aqueous solubility of IMC molecularly dispersed in PVP at various volume fractions. © 2012Wiley Periodicals, Inc. and the American Pharmacists Association J Pharm Sci 102:876–891, 2013     

Solution thermodynamics and solubility prediction of glibenclamide in Transcutol + water co-solvent mixtures at 298.15–333.15 K

Solution thermodynamics and solubility of glibenclamide (GBN) in binary co-solvent mixtures of Transcutol + water at temperature range of 298.15–333.15 K were investigated in present study. The modified Apelblat model was used to predict the solubility of GBN in co-solvent mixtures at various temperatures. The highest and lowest solubility of GBN were observed in pure Transcutol and pure water, respectively. Moreover, all co-solvent mixtures had highest solubility at 333.15 K. The experimental solubility data of GBN was correlated well with the modified Apelblat model at each temperature studied with relative absolute deviation in the range of 0.008–5.903 %. The correlation coefficients in co-solvent mixtures were observed in the range of 0.995–0.999 which indicated good fitting of experimental data with calculated one. The enthalpies and entropies for GBN dissolution were observed in the range of 2.012–38.215 kJ mol^?1 and 6.748–114.709 J mol^?1 K^?1, respectively indicating its dissolution is endothermic and an entropy-driven process. These results indicated that Transcutol can be used as a co-solvent in preformulation studies and formulation development of GBN.     

Thermodynamics of solutions: II. Flurbiprofen and diflunisal as models for studying solvation of drug substances

Three independent methods (sublimation, solubility and solution calorimetry) were used to study the dissolution and solvation processes of diflunisal (DIF) and flurbiprofen (FBP). Thermodynamic functions for the sublimation of DIF and FBP were obtained. Concentrations of saturated solutions and standard solution enthalpies of DIF and FBP in aliphatic alcohols and individual organic solvents were measured. Correlation analysis between: (a) the thermodynamic functions for a substance in various solvents, and (b) the same functions for different compounds was carried out. The investigated substances can be arranged with increasing Gibbs energy of solvation as follows: benzoic acid_H) and in terms of entropies (_S) was analyzed. Based on the experimental data, a compensation effect of thermodynamic solubility functions of the investigated substances both in alcohols and in organic solvents was found.     

The Estimation of Solubility in Binary Solvents: Application of the Reduced 3-Suffix Solubility Equation to Ethanol–Water Mixtures

The reduced 3-suffix solubility equation (R3SSE) is applied to the characterization of solubility in the ethanol–water system. The data needed are the solubility of the compound in each of the pure solvents and at one ethanol–water composition. This composition has been estimated from solubility data to be 0.56 volume fraction of ethanol. The solubility obtained at this volume fraction is used to estimate the ternary solute–solvent interaction constant, C ₂. The R3SSE, with the C ₂ thus obtained, predicts the mixed solvent solubilities of the compounds tested, as accurately as that obtained from several volume fractions. The superiority of the R3SSE over two related equations—a simple second-degree polynomial equation and a simplified form of the R3SSE which neglects contributions to solubility from the solvent mixture—is also demonstrated for a number of solutes.