A nonelectrolyte local composition model and its application in the correlation of the mean activity coefficient of aqueous electrolyte solutions

The local composition models have been widely used for the correlation of activity coefficient of nonelectrolyte and electrolyte solutions. A new equation for the excess Gibbs energy function is developed based on the local composition expression of Wilson and the random reference state. This new function, the nonelectrolyte Wilson nonrandom factor (N-Wilson-NRF) model, is presented in the form of a molecular framework so that it can be used for both nonelectrolyte and electrolyte solutions. Without any particular assumptions for ionic solutions, the new function is used to described the short-range contribution of the excess Gibbs energy of electrolyte solutions. The long-range contribution is represented by Pitzer–Debye–Hückel model. With two adjustable parameters per electrolyte, the new model is applied to correlate the mean activity coefficients of more than 150 binary aqueous electrolyte solutions at 25 °C. The results are compared with various local composition models such as the electrolyte-NRTL, electrolyte NRF-Wilson and electrolyte-NRTL-NRF models. The comparison of the results with experiment demonstrates that the new model can correlate the experimental data accurately. Moreover, the model shows high precision of predictability for the osmotic coefficient of binary electrolyte solutions.     

Aqueous solutions of ionic liquids. Description of osmotic coefficients within the Binding Mean Spherical Approximation

The Binding Mean Spherical Approximation (BiMSA) is used to describe osmotic coefficients of aqueous solutions of salts containing imidazolium cations and bulky anions over the whole concentration range at temperature in the range (25 to 60) °C. A total of 13 salts have been considered altogether. The ion diameters, the permittivity of solution and the association constant were taken as adjustable parameters. Ionic liquids are described as being weakly associated in water, and association constants values obtained within the BiMSA model are in good agreement with those from the literature. Diameter values were assigned to 1-alkyl-3-methylimidazolium cations. The adjusted values obtained for the cation diameters increased with the number of carbons on the alkyl chain. For all systems studied, average relative deviations were found to be satisfactory.     

Activity behaviour of electrolyte solutions: Evaluation of temperature effects by means of the quasi-random lattice model

The paper presents some applications of the Moggia–Bianco (quasi-random lattice) model for the calculation of mean activity and osmotic coefficients of electrolyte solutions, with emphasis on temperature effects. Aqueous uni-univalent and uni-divalent electrolytes from 0 °C to 100 °C are considered. Results show that the model is in general applicable over wide ranges of concentrations and temperatures, despite its dependence on a unique fitting parameter (which is, sometimes, experimentally known).Some theoretical aspects of the model are investigated. Hydration diameters are evaluated for uni-univalent systems. Concerning uni-divalent systems, charge-asymmetry effects are accounted for more rigorously than in previous works, starting from a better assessment of the relationship between the behaviour of the electrolyte at very low concentrations and the behaviour occurring at high concentrations.     

Measurement and modeling of osmotic coefficients of aqueous solution of ionic liquids using vapor pressure osmometry method

Osmotic coefficients of binary mixtures containing an ionic liquid, (1-butyl-3-methylimidazolium tetrafluoroborate, [BMIm]BF₄, 1-ethyl-3-methylimidazolium ethyl sulfate, [EMIm]ES, and 1-butyl-3-methylimidazolium methyl sulfate, [BMIm]MS) with water were measured until about 3 molal concentrations using vapor pressure osmometry method (VPO) at temperature ranges 298.15–328.15 K and modeled using different electrolyte excess Gibbs free energy models including electrolyte non-random two liquids (NRTL), modified NRTL (MNRTL), mean spherical approximation NRTL (MSA-NRTL), non random factor (NRF), and extended Wilson models. The results show that osmotic coefficient data increase with increasing temperature. The calculated standard deviations of the studied systems show that the applicability of these models for the correlation of VLE properties of ionic liquid solutions. The average standard deviations for the models have the order σ(?) MNRTL < σ(?) Wilson < σ(?) NRTL < σ(?) MSA-NRTL < σ(?)NRF. The results show MNRTL model is able to reproduce experimental osmotic coefficients of aqueous solution of studied ionic liquids with good precision.     

On the prediction of equilibrium phase behavior of amino acids in aqueous and aqueous-electrolyte solutions using SAFT equation of state

We present an approach based on the statistical associating fluids theory (SAFT) to predict the solubility of amino acids in aqueous and aqueous-electrolyte solutions. This approach can describe the association interactions and their effects on the solubility of amino acids. Using the experimental data of activity coefficients of amino acids in water, the parameters of SAFT model for amino acids are obtained. The solubility of several amino acids in the temperature range of 273.15–373.15 K is predicted. Results obtained from the model are in a good accordance with the experimental data. Also, we examine the effect of pH on the solubility of dl-methionine. Addition of an extra amino acid to the binary solution of amino acid + water makes the system more complex. To check the accuracy of model, we study the ternary solution of dl-serine + dl-alanine + water and dl-valine + dl-alanine + water. Predicted results depict that the proposed model has the ability to describe the ternary solution of amino acids, accurately. Finally, the solubility of amino acids in aqueous-electrolyte solutions is investigated. The long-range interactions caused by the presence of ions affects the solubility of amino acids, leading them to be salted in or out. To treat this kind of interaction, the restrictive primitive mean spherical approximation (RP-MSA) is coupled with the SAFT equation of state. The proposed model can accurately predict the solubility of amino acids in aqueous-electrolyte solutions.     

Osmotic and activity coefficients of ammonium thiocyanate in aqueous solutions at 25°C

Osmotic and activity coefficients of ammonium thiocyanate determined by the isopiestic vapor pressure method are compared with the data recently reported by Covington and Matheson. Activity coefficients calculated using the Pitzer equation are now in much better agreement although a systematic difference is evident in the two sets of data.Comment to the paper by Covingtonet al. (see ref. 2).We thank Mr. P. Kordes for programming.     

Isopiestic determination of the osmotic and activity coefficients of aqueous Lu2(SO4)3 at 25°C

Osmotic coefficients have been measured for aqueous Lu₂(SO₄)₃ solutions from 0.12402 to 0.89631 mol-kg^–1 at 25°C by use of the isopiestic method; these measurements extend into the supersaturated molality region. Since there was a lack of activity data for Lu₂(SO₄)₃ solutions at lower molalities, they were approximated by equating them to results for La₂(SO₄)₃ from freezing temperature depression measurements. The combined osmotic coefficients were then used to derive mean molal activity coefficients for Lu₂(SO₄)₃ solutions. The osmotic coefficients decrease to 0.307 as their minimum value and the mean molal activity coefficients decrease to 0.0069. When these activities were combined with our previously reported solubility of 0.6260±0.0017 mol-kg^–1 for Lu₂(SO₄)₃·8H₂O, a thermodynamic solubility product of 2.3×10^–10 was obtained. This value yields the Gibbs energy of formation G _f ^° (Lu₂(SO₄)₃·8H₂O, cr)=–5518.9±16.4 kJ-mol^–1.     

Isopiestic determination of osmotic and activity coefficients of aqueous solutions of aliphatic polyols at 298.15 K

The osmotic coefficients of 1,2-butanediol (12BD), 1,3-butanediol (13BD), 1,4-butanediol (14BD), 2,3-butanediol (23BD), 1,2,4-butanetriol (124BT) and 1,2,3,4-butanetetrol (1234BT) in water were measured by the isopiestic method at 298.15 K. Experimental osmotic coefficients were used to calculate water activity, solute activity coefficients and the pairwise Gibbs energy coefficients for solute–solute interactions.     

Effect of temperature on the behavior of osmotic and activity coefficients of amides in aqueous solutions

The osmotic coefficients of acetamide, propionamide and butyramide in water were measured at 293.15, 298.15 and 308.15 K using the isopiestic method. The activity coefficients were calculated for the aliphatic amides and the pairwise free energy coefficients for solute-solute interactions were determined according to the McMillan-Mayer theory. The osmotic and activity coefficients of amides are discussed in terms of solute-solute interactions.     

A new model for the activity coefficients of individual ions in aqueous electrolyte solutions

In this study, the individual ion activity coefficient in an aqueous solution is modeled with a new model. This model contains two physical significant ionic parameters regarding the ionic solvation and the closest distance of approach between ions in a solution. The present model was evaluated by the estimation of the individual activity coefficients of the ions of thirty electrolytes in aqueous solutions. The results showed that this model suitably predicts the individual ion activity coefficients in aqueous two-electrolyte solutions consisting of the binary pairs of electrolytes of NaCl, KCl, KBr and CaCl₂ in a temperature range from 298.15 to 243.15 K. The results by this model were compared to the literature values. The average absolute relative deviations of vapor pressures showed acceptable agreement between experimental data and the results of this model.     

Specific interactions and single-lon activity coefficients in mixed electrolyte solutions

A reexamination of Guggenheim's theory of specific interactions for dilute aqueous electrolyte solutions shows that the parameters of the theory should include terms for interactions between like-charged ions. The equations developed are analogous to those in Pitzer's treatment of concentrated solutions, and the inclusion of ion-solvent interaction parameters allows comparison with the Stokes and Robinson hydration theory treatment. As with hydration theory, specific-interaction theory predicts differences in single-ion activity coefficients.     

关于苯及其衍生物在盐水溶液中的活度系数的研究

摘录了25℃时苯,甲苯,邻位、间位、对位二甲苯,间位、对位二氯苯及萘在NaF,LiCL,NaBr,NEt~4Br等25种盐的水溶液中的活度系数f,它们的lgf-c~s的关系符合Setchenow盐效应公式。计算了苯及其衍生物在上述25种盐水溶液中的各种盐效应理论的k~s,主要有:1)Debye-macAulay静电理论;2)Conway-Desnoyers-Smith静电理论;3)Masterton-Lee定标粒子理论;4)McDevit-Long内压力理论;5)改进的内压力理论;6)改进的Bockris色散力理论。对各种理论值比较后可以看到改进后的内压力理论k~s值与实验k~s值较为吻合。Bockris色散力理论经改进后计算比较简单,可以判断盐效应符号,盐效应顺序也基本正确。     

Partial molar volumes and activity coefficients of the water in aqueous polyol solutions and the osmotic pressures of these solutions

The freezing-point depression and density of aqueous polyol (alditol) solutions were measured, and the osmotic pressure and the partial molar volume of the water of these solutions were calculated. The osmotic pressures calculated from the freezing-point depression data were compared with those calculated with van't Hoff's equation and fairly good agreement was found. The partial molar volumes of the water in the solutions were equal or almost equal to the molar volume of pure water up to the highest concentrations examined. Also, the activity coefficient of the water was unity or almost unity up to the highest concentrations examined.     

利用吉布斯吸附等温式探索求解电解质溶液活度的新方法

以吉布斯吸附等温式积分式为基础,数学推证表面势的表达式,并应用表面势的数学表达式探求了一种测算电解质溶液活度系数的新方法.选取KIM计算电解质溶液溶质的活度系数公式为新方法的活度系数经验关系式的具体表达形式,利用实验直接测得的不同浓度下的表面张力数据,采用最优化拟合的方法,求算出活度系数经验关系式中的待定系数,从而可以求得不同浓度下的电解质溶液中的溶质的活度系数和活度.计算结果与KIM文献值对比,活度系数曲线在不同的坐标尺度下有很好的一致性,这使得通过测定电解质溶液表面张力测算其活度成为可能.     

Density and activity of pertechnetic acid aqueous solutions at T = 298.15 K

The previous isopiestic investigations of HTcO₄ aqueous solutions at T = 298.15 K are believed to be unreliable, because of the formation of a ternary mixture at high molality. Consequently, published isopiestic molalities for aqueous HTcO₄ solutions at T = 298.15 K were completed and corrected. Binary data (variation of the osmotic coefficient and activity coefficient of the electrolyte in solution in the water) at T = 298.15 K for pertechnetic acid HTcO₄ were determined by direct water activity measurements. These measurements extend from molality m = 1.4 mol · kg⁻¹ to m = 8.32 mol · kg⁻¹. The variation of the osmotic coefficient of this acid in water is represented mathematically. Density variations at T = 298.15 K are also established and used to express the activity coefficient values on both the molar and molal concentration scale. The density law leads to the partial molar volume variations for aqueous HTcO₄ solutions at T = 298.15 K, which are compared with published data.     

Modeling aqueous electrolyte solutions. Part 2. Weak electrolytes

In this work the ePC-SAFT model is applied to weak electrolytes, such as weak acids or salts that do form ion pairs. Considering an association/dissociation equilibrium accounts for the fact that the electrolytes are not fully dissociated. Applying this approach, modeling the mean ionic activity coefficients (MIAC) as well as the water activity coefficients (WAC) is in very good agreement with experimental data for the aqueous HF system as well as for solutions of cadmium halides or alkali acetates. Experimental MIACs of ZnBr₂ and ZnI₂ reveal the formation of more than one complex in aqueous solutions. Implementing a simultaneous two-step ion-pairing mechanism also allows the modeling of the MIAC of these zinc salts in water.     

Osmotic and activity coefficients of aqueous lithium sulfate solutions at 40°C

The osmotic coefficients for aqueous lithium sulfate solutions were experimentally determined at 40°C. Sodium chloride served as the isopiestic standard for the calculation of osmotic coefficients. The molality ranges covered in this study correspond to about 0.1–2.5 mol-kg^–1. The system of equations developed by Hamer-Wu and Pitzer were used to fit each set of osmotic coefficients. The parameters obtained from the fit were used to calculate the activity coefficients.     

含锂水盐体系热力学性质研究:LiCl-MgCl~2-H~O体系渗透系数和活度系数的等压测定

25℃下,用等压法测定了单盐水溶液(浓度范围分别为0.5-19.8mol.kg^-1,0.3-6.0mol.kg^-1)以及混合水溶液(离子强度范围为0.6-19.4mol.kg^-1)的水活度和渗透系数,同时测定了LiCl的溶解度.该体系的实验等水活度线符合本工作推导出的Zdanovskii规则扩展式,用Gibbs-Duhem方程和改进的Mckay-perring方法计算了单盐和混合盐水溶液的活度系数.由本实验获得的渗透系数拟合了Pitzer单盐和混合作用参数,检验了Pitzer方程对该体系渗透系数、活度系数和溶解度预测的适用性.用Pitzer方程取本工作得到的参数计算的溶解度与文献实验值基本一致.     

Prediction of activity coefficients of electrolytes in aqueous mixed electrolyte solutions

A method is proposed for calculating the activity coefficient of constituent electrolytes in aqueous mixed electrolyte solutions. The equations derived from the knowledge of Λ^*, the overall reduced ionic activity coefficient in a mixture, are found to predict activity coefficients accurately up to an ionic strength of 12 mol kg⁻¹ and a temperature of 473 K.