An Empirical Approach for Estimating the Density of Multicomponent Aqueous Solutions Obeying the Linear Isopiestic Relation

An empirical approach is presented for the density of aqueous multicomponentsolutions conforming to the linear isopiestic relation. This approach can be usedto estimate the densities of multicomponent systems from data on the constituentbinary subsystems at the same water activity. Predicted and measured densitiesfor 22 mixtures have been compared, using the simple Young's rule, theisopycnotic mixing rule of Teng and Lenzi, and the present method. The present methodand Young's rule give the most accurate predictions for strong electrolyte mixtureswithout common ions and for the mixtures with strong ion complexes, respectively.There is no universal best method for the strong electrolyte mixtures with commonions. An extensive comparison has also been given between apparent molarvolume predictions by Young's rule and by the new method. The two rules arerelatively better for the strong electrolyte mixtures without common ions andmixtures containing the transition metal chlorides, respectively. However, neitheris universally better for mixtures of strong common-ion electrolytes.     

Semi-ideal solution theory. 2. Extension to conductivity of mixed electrolyte solutions

Conductivities were measured for the ternary systems NaCl-LaCl(3)-H(2)O and KCl-CdCl(2)-H(2)O and their binary subsystems NaCl-H(2)O, KCl-H(2)O, CdCl(2)-H(2)O, and LaCl(3)-H(2)O at 298.15 K. The semi-ideal solution theory for thermodynamic properties of aqueous solutions of electrolyte mixtures was used together with the Eyring absolute rate theory to study conductivity of mixed electrolyte solutions. A novel simple equation for prediction of the conductivity of mixed electrolyte solutions in terms of the data of their binary solutions was established. The measured conductivities and those reported in literature were used to test the newly established equation and the generalized Young's rule for conductivity of mixed electrolyte solutions. The comparison results show that the deviation of a ternary solution from the new conductivity equation is closely related to its isopiestic behavior and that the deviations are often within experimental uncertainty if the examined system obeys the linear isopiestic relation. While larger deviations are found in the system with large ion pairing effect, the predictions can be considerably improved by using the parameters calculated from its isopiestic results. These results imply that the previous formulation of the thermodynamic properties of aqueous solutions of electrolyte mixtures has a counterpart for transport properties.     

Modified McKay–Perring Equation and Its Two Particular Solutions

Zdanovskii’s rule is the simplest isopiestic molality relation of mixed electrolyte aqueous solutions and the McKay–Perring equation is a differentio-integral equation particularly suitable for calculating solute activity coefficients from isopiestic measurements. However, they have two unsolved problems, which have puzzled solution chemists for several decades: (1) Zdanovskii’s rule has been verified by precise isopiestic measurements. But, several scientists suggested that the rule contradicts the Debye–Hückel limiting law for extremely dilute unsymmetrical mixtures. (2) In the McKay–Perring equation, a solute activity coefficient is multiplied by a solute composition variable. Different scientists have suggested that the composition variable may be the total ionic strength, common ion concentration, total ionic concentration, or an additive function with arbitrary proportionality constants. But, the different choices of the composition variable may lead to different activity coefficient results. Here, I derive a modified McKay–Perring equation in which the composition variable has the exclusive physical meaning of total ionic concentration for mixed electrolyte solutions (or of total solute particle concentration for the mixed solutions containing nonelectrolyte solutes). I also demonstrate that Zdanovskii’s rule is consistent with the Debye–Hückel limiting law for extremely dilute unsymmetrical mixtures. I derive two particular solutions of the modified McKay–Perring equation: one for the systems obeying Zdanovskii’s rule and another for the systems obeying a limiting linear concentration rule. These theoretical results have been verified with literature experiments and model calculations.     

超额自由能型汽液相平衡混合规则

较全面地介绍了近几年来发展的各种典型的超额自由能型汽液相平衡混合规则。该类混合规则吸取了状态方程法和活度系数法在相平衡预测方面的优点,并将对于极性体系预测能力非常强的活度系数模型直接应用于状态方程法的相平衡预测中,实现了向高温区的良好外推和对超临界和亚临界组分的连续准确描述。依次发展的HV型、WS型和TC型三个大类的超额自由能型混合规则中,TC型混合规则的预测精确度要略高于HV型、WS型混合规则的预测精确度,而HV型、WS型混合规则的预测精确度大致相当。从发展的角度看,这些超额自由能型混合规则还要接受三元以上体系的汽液相平衡和液液相平衡预测的考验。另外,如何将超额自由能型混合规则扩展到多参数方程来提高相平衡预测精度,也是超额自由能型混合规则的一个值得关注的发展方向。     

H2O+KCl(饱和)+NaCl+NH4Cl的等压研究

Isopiestic measurements have been carried out at 298.15 K for the quaternary aqueous solution H2O+KCl(sat)+NaCl+NH4Cl saturated with potassium chloride and its ternary sub systems H2O+KCl (sat)+NaCl and H2O+KCl(sat)+NH4Cl. Taking sodium chloride (aq) or calcium chloride (aq) as reference solutions, osm otic coefficients and water activities of the aqueous solution were determined. The experiment results show that the isopiestic actions of the quaternary system related to its ternary sub-systems are in excellent agreement with the ideal like solution model.     

Reassessment of the binary, ternary, and quaternary interactions in mixed electrolytes from thermodynamic quantities: The systems with uncommon ions containing hydrophobic character

Accurate estimates of the binary, ternary, and quaternary interactions in aqueous ionic mixtures with uncommon ions with hydrophobic character are presented. For this purpose, the values of the excess Gibbs free energy of mixing, Delta m G(E), obtained from our earlier isopiestic osmotic coefficients (Kumar, A. J. Phys. Chem. B2003, 107, 2808) for the mixtures of NaCl with four guanidinium (Gn+) salts-CH3COOGn, GnNO3, GnClO4, and Gn2SO4-are analyzed with the help of the method developed by Leifer and Wigent. The methodology of Leifer and Wigent is based on the equations of Scatchard-Rush-Johnson and Friedman's cluster integral expansion theory. The Scatchard-Rush-Johnson theory explicitly considers the quaternary and higher-order ionic interactions in the mixtures as compared to the specific ion interaction theory of Pitzer, which accounts for binary and ternary interactions only. The contributions due to binary, ternary, and quaternary interaction terms to total Delta m G(E) are estimated and discussed critically. Also, the interaction between the same two cations, for example, Gn+ - Gn+, is estimated and found significant, which otherwise cannot be obtained by the use of Pitzer's theory. The information obtained from the analysis of Delta(m)G(E) is also supported by the newly measured excess volumes of mixing, Delta m V(E), at 298.15 K. The individual contributions of the binary, ternary, and quaternary interaction terms to total Delta m V(E) are described. The binary, ternary, and quaternary interaction terms for both Delta m G(E) and Delta m V(E) are analyzed in terms of Friedman's cluster integral expansion theory.     

The correlation of activity coefficients for the electrolyte-nonelectrolyte mixed solution —the thermodynamics of the liquid solid phase equilibria in (NH2)2CO-NaCl-NH4Cl-H2O system

Based on the various thermodynamic models for concentrated electrolyte and nonelectrolyte solutions, the correlation equations of activity coefficeints and methods of solubility prediction for ternary and quarternary systems have been developed. Only a few of experimental data are needed to calculate the interaction parameters. This method can be used to calculate the solubilities of the components for a given concentration of the unsaturated ones, the predicted solubilities agree with experimental data quite well.     

Thermodynamics of mixed electrolyte solutions. X. An isopiestic study of the quaternary system NaCl−KCl−MgCl2−H2O at 25°C

Activity coefficients in the aqueous quaternary system sodium chloridepotassium chloride-magnesium chloride were derived from isopiestic measurements at 25°C. The isopiestic data were treated by the various procedures of Scatchard, Friedman, and Reilly, Wood, and Robinson, and results obtained agreed fairly well with those obtained by pseudoternary transforms. Interaction parameters obtained indicated the preponderance of pairwise interactions. Excess Gibbs free energies of mixing were calculated.     

A new molecular thermodynamic model for multicomponent Ising lattice

A new molecular thermodynamic model is developed for multicomponent Ising lattice based on a generalized nonrandom factor from binary system. Predictions of the nonrandom factor and the internal energy of mixing for ternary and quaternary systems match accurately with simulation results. Predictions of liquid-liquid phase equilibrium for ternary systems are in nearly perfect agreement with simulation results, and substantially improved from Flory-Huggins theory and the lattice-cluster theory. The model also satisfactorily correlates the experimental data of real ternary systems. The concise expression and the accuracy of the new model make it well suited for practical engineering applications.     

Thermodynamics of mixed electrolyte solutions. XI. An isopiestic study of the quaternary system NaCl−KCl−CaCl2−H2O at 25°C

Osmotic and activity coefficients in the aqueous quaternary system sodium chloride-potassium chloride-calcium chloride were derived from isopiestic measurements at 25°C. The isopiestic data were treated by the various procedures of Scatchard, Friedman, and Reilly, Wood, and Robinson. The results obtained showed good agreement with those obtained by pseudo-ternary transforms. Interaction parameters obtained indicated the preponderance of pairwise interactions. Excess Gibbs free energies of mixing were calculated.     

Activity Coefficient Prediction for Binary and Ternary Aqueous Electrolyte Solutions at Different Temperatures and Concentrations

The mean spherical approximation (MSA) model, coupled with two hard sphere models, was used to predict the activity coefficients of mixtures of electrolyte solutions at different temperatures and concentrations. The models, namely the Ghotbi-Vera-MSA (GV-MSA) and Mansoori et al.-MSA (BMCSL-MSA), were directly used without introducing any new adjustable parameters for mixing of electrolyte solutions. In the correlation step, the anion diameters were considered to be constant, whereas the cation diameters were considered to be concentration dependent. The adjustable parameters were determined by fitting the models to the experimental mean ionic activity coefficients for single aqueous electrolytes at fixed temperature. The results showed that the studied models predict accurately the activity coefficients for single electrolyte aqueous solutions at different temperatures. In the systems of binary aqueous electrolyte solutions with a common anion, the GV-MSA model has slightly better accuracy in predicting the activity coefficients. Also, it was observed that the GV-MSA model can more accurately predict the activity coefficients for ternary electrolyte solutions with a common anion, especially at higher concentrations.     

Comparison of different mixing rules for prediction of density and residual internal energy of binary and ternary Lennard–Jones mixtures

Mixing rules are necessary when equations of state for pure fluids are used to calculate various thermodynamic properties of fluid mixtures. The well-known van der Waals one-fluid (vdW1) mixing rules are proved to be good ones and widely used in different equations of state. But vdW1 mixing rules are valid only when molecular size differences of components in a mixture are not very large. The vdW1 type density-dependent mixing rule proposed by Chen et al. [1] is superior for the prediction of pressure and vapor–liquid equilibria when components in the mixture have very different sizes. The extension of the mixing rule to chain-like molecules and heterosegment molecules was also made with good results. In this paper, the comparison of different mixing rules are carried out further for the prediction of the density and the residual internal energy for binary and ternary Lennard–Jones (LJ) mixtures with different molecular sizes and different molecular interaction energy parameters. The results show that the significant improvement for the prediction of densities is achieved with the new mixing rule [1], and that the modification of the mixing rule for the interaction energy parameter is also necessary for better prediction of the residual internal energy.     

硝酸盐型卤水体系的综合热力学模型与多温相图预测

硝酸盐型卤水是盐湖卤水、 硝酸盐工业、 废水处理中普遍遇到的电解质溶液体系. 硝酸盐具有极高的溶解度, 实现硝酸盐型复杂电解质体系物性和相平衡的精准热力学表达依然具有挑战性. 以煤化工废水的典型体系Na⁺//NO₃^- , Cl^-, SO₄^{2 -} -H₂O为对象, 以改进的eNRTL模型为基础, 由活度系数模型、 溶液物性模型、 物种热力学模型和固液相平衡模型构成了电解质体系的综合热力学模型. 利用二元体系的冰点、 饱和蒸汽压、 等压摩尔热容、 活度系数和渗透压系数等物性数据和三元体系等温相平衡数据, 采用多目标优化方法, 获得了表达研究体系的多温特性的12组液相特征参数和7个固相物种的热力学参数. 据此完成了3个二元体系、 3个三元体系等温相平衡的准确计算和三元、 四元完整相图的预测, 适用温度达到实验所及的全部温度范围(254.65~543.15 K); 适用浓度达到饱和程度, 其中NaNO₃的浓度高达226.88 mol/kg. 三元、 四元体系的多温相图预测结果与实验数据相吻合, 并给出了9个三元、 5个四元体系零变点的完整信息.     

Thermodynamic modeling of saturated liquid compositions and densities for asymmetric binary systems composed of carbon dioxide,alkanes and alkanols

The present study mainly focuses on the phase behavior modeling of asymmetric binary mixtures. Capability of different mixing rules and volume shift in the prediction of solubility and saturated liquid density has been investigated. Different binary systems of (alkane + alkanol), (alkane + alkane), (carbon dioxide + alkanol), and (carbon dioxide + alkane) are considered. The composition and the density of saturated liquid phase at equilibrium condition are the properties of interest. Considering composition and saturated liquid density of different binary systems, three main objectives are investigated. First, three different mixing rules (one-parameter, two parameters and Wong–Sandler) coupled with Peng–Robinson equation of state were used to predict the equilibrium properties. The Wong–Sandler mixing rule was utilized with the non-random two-liquid (NRTL) model. Binary interaction coefficients and NRTL model parameters were optimized using the Levenberg–Marquardt algorithm. Second, to improve the density prediction, the volume translation technique was applied. Finally, Two different approaches were considered to tune the equation of state; regression of experimental equilibrium compositions and densities separately and spontaneously. The modeling results show that there is no superior mixing rule which can predict the equilibrium properties for different systems. Two-parameter and Wong–Sandler mixing rule show promoting results compared to one-parameter mixing rule. Wong–Sandler mixing rule in spite of its improvement in the prediction of saturated liquid compositions is unable to predict the liquid densities with sufficient accuracy.     

Isopiestic Study of Water + Mannitol(sat) + Sodium Chloride + Ammonium Chloride + Barium Chloride at <Emphasis Type="Italic">T</Emphasis> = 298.15 K and Comparison with the Ideal-Like Solution Model

Isopiestic measurements have been carried out at the temperature 298.15 K for the quinary system (water + mannitol(sat) + sodium chloride + ammonium chloride + barium chloride) saturated with mannitol and its ternary sub-systems (water + mannitol(sat) + sodium chloride), (water + mannitol(sat) + ammonium chloride) and (water + mannitol(sat) + barium chloride). Taking aqueous sodium chloride as reference solutions, osmotic coefficients of the other aqueous solutions were determined. The experimental results show that the isopiestic activities of the quinary system in relation to its ternary sub-systems are in excellent agreement with the ideal-like solution model.     

Modification of PSRK mixing rules and results for vapor–liquid equilibria, enthalpy of mixing and activity coefficients at infinite dilution

The predictive Soave–Redlich–Kwong (PSRK) equation of state (EOS) is a well-established method for the prediction of thermodynamic properties required in process simulation. But there are still some problems to be solved, e.g. the reliability for strong asymmetric mixtures of components which are very different in size. The following modifications are introduced in the PSRK mixing rules: the Flory–Huggins term in the mixing rule for the EOS parameter a, and the combinatorial part in the UNIFAC model are skipped simultaneously; a nonlinear mixing rule for the EOS parameterb, instead of the linear mixing rule, is proposed. With these two modifications better results are obtained for vapor–liquid equilibria and activity coefficients at infinite dilution for alkane–alkane systems, specially for asymmetric systems. In order to obtain better results for enthalpy of mixing, temperature-dependent parameters are used. Group interaction parameters have been fitted for several groups, and the results are compared with the Modified UNIFAC (Dortmund), and the PSRK methods.     

Correlation of liquid-liquid equilibria in aqueous and organic systems using a modified Wilson model

A modified Wilson model is extended to involve three ternary parameters per ternary to allow the model to represent ternary liquid-liquid equilibria accurately. The calculated results for 19 ternary systems obtained from the present modification are compared with the previous results obtained from other modified Wilson models. The model is further extended to treat quaternary liquid-liquid equilibria for six aqueous systems and one nonaqueous system using binary, ternary, and quaternary parameters. Mutual solubilities for 19 systems over a wide temperature range are represented with the model having temperature-dependent energy parameters.     

Phase Behavior of Aqueous Na–K–Mg–Ca–Cl–NO<Subscript>3</Subscript> Mixtures: Isopiestic Measurements and Thermodynamic Modeling

A comprehensive model has been established for calculating thermodynamic properties of multicomponent aqueous systems containing the Na⁺, K⁺, Mg²⁺, Ca²⁺, Cl⁻ and NO₃⁻ ions. The thermodynamic framework is based on a previously developed model for mixed-solvent electrolyte solutions. The framework has been designed to reproduce the properties of salt solutions at temperatures ranging from the freezing point to 300 °C and concentrations ranging from infinite dilution to the fused salt limit. The model has been parameterized using a combination of an extensive literature database and new isopiestic measurements for thirteen salt mixtures at 140 °C. The measurements have been performed using Oak Ridge National Laboratory’s (ORNL) previously designed gravimetric isopiestic apparatus, which can also detect solid phase precipitation. In addition to various Na–K–Mg–Ca–Cl–NO₃ systems, results are reported for LiCl solutions. Water activities are reported for mixtures with a fixed ratio of salts as a function of the total apparent salt mole fraction. The isopiestic measurements reported here simultaneously reflect two fundamental properties of the system, i.e., the activity of water as a function of solution concentration and the occurrence of solid–liquid transitions. The thermodynamic model accurately reproduces the new isopiestic data as well as literature data for binary, ternary and higher-order subsystems. Because of its high accuracy in calculating vapor–liquid and solid–liquid equilibria, the model is suitable for studying deliquescence behavior of multicomponent salt systems.     

Structure-composition relationships in ternary solvents containing methylbenzoate

Thermophysical properties of the hexane+1-chlorohexane (or hexanoic acid or diisopropylether)+methylbenzoate ternary systems and their binary constituents are reported at 298.15 K and 0.1 MPa over the whole composition range. The properties and the optimized geometry of the gas-phase components were appraised from the density functional theory. To find out the causal link between the thermophysical measurements and the molecular level features, the derived mixing and excess functions of the ternary systems were looked into according to the scaled particle and Kirkwood-Buff analyses. The hydrogen bonding and dipole interactions along with the geometry effects brought about by the very different size and shape of the components give rise to complex mixed structures. Application of semiempirical models and use of simple cubic equations of state combined with a one-parameter van der Waals mixing rule has led to prediction of the ternary properties with variable degree of precision.