The semi-ideal solution theory for mixed ionic solutions at solid-liquid-vapor equilibrium

The semi-ideal solution theory has been presented to describe the changes in thermodynamic properties accompanying the process of mixing the nonideal electrolyte solutions M(i)X(i)-(NY)sat-H2O (i = 1 and 2) at constant activities of NY and H2O, including concentration, chemical potential, activities of all M(i)X(i), Gibbs free energy, enthalpy, entropy, thermal properties, and volumetric properties. The theory states that, under the conditions of equal activities of NY and H2O, the average hydration numbers characterizing the ion-solvent interactions have the same values in the mixture as in the subsystems and the process of mixing these nonideal electrolyte solutions is as simple as that of mixing the ideal solutions if the contributions from the ion-ion interactions to the solvent activity are assumed to be the same in the mixture as in its subsystems, which has been justified by the calculations of the Pitzer equation. Therefore, a series of novel linear equations are established for the thermodynamic properties accompanying the process of mixing these nonideal solutions as well as mixing the ideal solutions M(i)X(i)-(NY)sat-H2O (i = 1 and 2) of equal mole fractions of NY and H2O. From these equations, the widely applied empirical Zdanovskii's rule is derived theoretically, and the important constant in the McKay-Perring equation under isopiestic equilibrium is determined theoretically, which has been substantiated by comparisons with the experimental results for 18 mixtures reported in the literature. Isopiestic measurements have been made for the systems BaCl2-LaCl3-H2O, NaCl-BaCl2-LaCl3-H2O, and NaCl-LaCl3-BaCl2.2H2O(sat)-H2O at 298.15 K. The results are used to test the novel linear concentration relations, and the agreement is excellent. The novel predictive equation for the activity coefficient of M(i)X(i) in M1X1-M2X2-(NY)sat-H2O has been compared with the calculations of the Pitzer equation, and the agreement is good.     

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.     

308.15K下NaCl-CaCl_2-H_2O体系热力学性质的等压研究

采用等压法研究了308.15K下NaCl-H2O、CaCl2-H2O和NaCl-CaCl2-H2O体系离子强度分别为0.5666～5.9265molkg-1、0.3943～5.5573molkg-1和0.6524～16.6631molkg-1的等压平衡浓度和水活度,计算了渗透系数及饱和蒸汽压,获得了该体系渗透系数和饱和蒸汽压随离子强度的变化规律.应用Pitzer离子相互作用模型,用实验数据用多元线性回归拟合了308.15K下该体系的NaCl和CaCl2的纯盐参数β(0)、β(1)、Cφ分别为0.3181、1.5346、-0.0014和0.07972、0.3067、0.00075,拟合标准偏差分别为0.00072、0.0049;混合离子作用参数θNa,Ca、ψNa,Ca,Cl分别为0.06821、-0.0076,拟合标准偏差为0.0063和0.0064.用Pitzer模型计算的渗透系数与实验结果吻合.本研究为含钠钙海卤水体系热力学模型建立提供了重要的热力学基础数据.     

用Pitzer理论预测混合电解质溶液的偏摩尔体积

用Pitzer理论研究了混合电解质溶液的偏摩尔体积,建立了偏摩尔体积的预测方法,并利用所得电解质溶液的表观摩尔体积的Pitzer参数预测了HNO₃-UO₂(NO₃)₂-H₂O、KCl-Na₂SO₄-H₂O、NaCl-Na₂SO₄-H₂O、NaCl-CaCl₂-H₂O、KCl-CaCl₂-H₂O、KCl-MgCl₂-H₂O和KCl-NaBr-H₂O共7个系统4种类型的混合溶液的偏摩尔体积。     

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.     

等压法测定298.15K下LiCl-CaCl2-H2O体系的活度系数

The isopiestic method was used to determinate isopiestic molality and osmotic coefficients in single-salt solutions of LiCl-H2O(molality range from 0.5 to 9.0 mol· kg-1),CaCl2-H2O(molality range from 0.35 to 5.2 mol· kg-1) and multisalt solution LiCl-CaCl2-H2O(ionic strength range from 0.5 to 15.7 mol· kg-1) at 298.15K,from which Pitzer's interaction parameters of single salt ,mixed salts of the systems were obtained.The mean ionic activity coefficients of LiCl、 CaCl2 in pure and mixed solutions were reported.     

等压法测定298.15K下LiCl-CaCl2-H2O体系的活度系数

电解质水溶液热力学性质的研究一直是一个很活跃的研究领域.对含锂水盐体系热力学性质的研究不仅对电解质水溶液理论,而且对盐湖锂资源的开放利用都有非常重要的意义.姚燕等对ＬｉＣｌＫＣｌＨ2Ｏ[1],ＬｉＣｌＭｇＣｌ2Ｈ2Ｏ[2],ＬｉＣｌＭｇＳＯ4Ｈ2Ｏ[3,4],ＬｉＣｌＬｉ2ＳＯ4Ｈ2Ｏ[5]体系多温下热力学性质进行了研究,应用Ｐｉｔｚｅｒ电解质水溶液理论模型进行处理,计算出ＬｉＣｌ在不同体系中,很大的浓度范围内的活度系数.但在盐湖卤水中,ＣａＣｌ2的存在很普遍.对ＬｉＣｌＣａＣｌ2混合物在水溶液中的热力学性质研究对理解ＬｉＣｌ在盐…     

The Semi-ideal Solution Theory. 3. Extension to Viscosity of Multicomponent Aqueous Solutions

Viscosities were measured for the ternary aqueous systems NaCl–mannitol(C₆H₁₄O₆)–H₂O, NaBr–mannitol–H₂O, KCl–mannitol–H₂O, KCl–glycine(NH₂CH₂COOH)–H₂O, KCl–CdCl₂–H₂O, and their binary subsystems NaCl–H₂O, KCl–H₂O, NaBr–H₂O, CdCl₂–H₂O, mannitol–H₂O, and glycine–H₂O at 298.15 K. A powerful new approach is presented for theoretical modeling of the viscosity of multicomponent solutions in terms of the properties of their binary solutions. In this modeling, the semi-ideal solution theory was used to associate the solvation structure formed by each ion and its first solvation shell in a binary solution with the solvation structure of the same ion and its first solvation shell in multicomponent solutions. Then, the novel mechanism proposed by Omta et al. (Science, 301:347–349, 2003) for the effect of a single electrolyte on the viscosity of water was extended to describe the influence of solute mixtures on the viscosity of water, including electrolyte mixtures, nonelectrolyte mixtures, and mixtures of electrolytes with nonelectrolytes. The established simple equation was verified by comparison with measured viscosities and viscosities reported in literature. The agreements are very impressive. This formulation provides a powerful new approach for modeling this transport property in solutions. It can stimulate further research in establishing a dynamical analogue to that formulated for the thermodynamics of multicomponent solutions. It is also very important for the study of hydration of ions.     

Densities and Conductivities of Aqueous N,N,N-Alkyloctyldimethylammonium Chloride at Different Temperatures

The simple equations for predictions of the density and conductivity of mixed electrolyte solutions were extended to the related properties of mixed ionic liquid solutions. The densities and conductivities were measured for the ternary solutions OOAC (N,N,N-dioctyldimethylammonium chloride) + OPAC (N,N,N-octylpentyldimethylammonium chloride) + H₂O, OOAC + N,N,N-octylbutyldimethylammonium chloride (OBAC) + H₂O, OPAC + OBAC + H₂O and their corresponding binary subsystems OOAC + H₂O, OPAC + H₂O, and OBAC + H₂O at (298.15, 303.15, and 308.15) K, respectively. The results were used to test the predictability of the extended equations. Comparison of the results shows that these simple equations can be used to predict the density and conductivity of the mixed ionic liquid solutions from the properties of their binary subsystems of equal ionic strength.     

高溶解性盐水体系热力学模型预测能力的比较研究I: 二元体系

用原始Pitzer模型、扩展的Pitzer模型、Pitzer-Simonson-Clegg模型、S-MSA模型和BET模型分别对LiCl-H2O, LiBr-H2O, CaCl2-H2O, Mg(NO3)2-H2O, MnCl2-H2O和Mn(NO3)2-H2O等六种不同体系的热力学性质进行描述, 考察了各种模型的预测能力. 结果表明原始Pitzer模型不能准确描述高浓电解质溶液的性质; 扩展的Pitzer模型虽然能较准确地描述某些体系高浓度的热力学性质, 但预测能力不足; Pitzer-Simonson-Clegg模型对高浓盐水体系热力学性质具有一定的预测能力, 但拟合参数所用的最大浓度与溶解度相差很大时, 外推饱和点的热力学性质则会出现较大偏差; S-MSA模型虽然可以将拟合参数的浓度范围扩大到饱和, 但没有外推能力, 而且需要溶液的密度数据, 这限制了该模型的广泛应用; BET模型对这六种体系均体现出很强的预测能力, 预测结果准确, 且模型参数少, 物理意义明确, 该模型可用于熔盐水化物相变储能材料的设计.     

273.15K时LiCl-Li2SO4-H2O体系热力学性质的等压研究

0℃下用改进的等压设备和改进的实验方法测定了纯水溶液(LiCl 0.5～9.2mol·kg-1,Li2SO40.3～2.5mol·kg-1)以及混合水溶液(离子强度0.5～9.5mol·kg-1)的水活度和渗透系数.该体系的等水活度线与Zdanovskii规则非理想混合溶液表达式的标准偏差为0.0088,当Li2SO4溶液达到饱和后,用Zdanovskii规则扩展式计算,标准偏差为0.0027.根据Pitzer离子相互作用模型对实验数据进行了理论分析,用本文和不同来源的文献数据拟合求取了0℃下该体系的Pitzer纯盐参数和混合参数,计算值与实验值相吻合.     

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.     

Studies of Activity Coefficients for Ternary Systems: Water + 18-Crown-6 + Alkali Chlorides at 298.15 K

Osmotic vapor pressure measurements have been carried out for three ternary systems, H₂O + 0.2 m 18-crown-6 + LiCl, H₂O + 0.2 m 18-crown-6 + NaCl and H₂O + 0.2 m 18-crown-6 + KCl at 298.15 K using vapor pressure osmometry. Water activities for each ternary system were measured and used to calculate the activity coefficients of 18-crown-6 (18C6) and its salts following the methodology developed by Robinson and Stokes for isopiestic measurements. In the concentration range studied, it was found that (in NaCl and KCl solutions) there is considerable lowering of activity coefficients of one component in the presence of other solutes that has been attributed to the formation of the complexed 18C6:Na⁺ (or 18C6:K⁺) species in solution. The Gibbs energies of transfer of alkali chlorides from water to aqueous 18C6 solutions and that of 18C6 from water to aqueous electrolyte solutions have been calculated. These were further used to evaluate the pair and triplet interaction parameters. The calculation of thermodynamic equilibrium constants using the pair interaction parameter, g _NE (i.e., the nonelectrolyte–electrolyte pair interaction) for the studied complexation of cations yields values which are in good agreement with those reported in literature obtained by using ion-selective potentiometry and calorimetry. The results are discussed in terms of water structural effects, complex formation, and hydrophobic interactions.     

HNO3-UO2(NO3)2-H2O系统的活度系数的测定和计算

用H^+和NO3^-离子选择电极组成的电池用电势法测定了HNO3-UO2(NO3)2-H2O系统在25°C时的HNO3的平均活度系数, 求得了同时含有^E0和 ^S0-I关系式的Pitzer方程中的两粒子和三粒子作用参数(^s0(0), ^s(1),Ψ)。用Pitzer方程计算了该系统中水的活度, 并用Pitzer方程、Mckay-Perring方法和Harned方程分别计算了系统中HNO3和UO2(NO3)2的平均活度系数。     

Thermodynamic Characteristics of Phenacetin in Solid State and Saturated Solutions in Several Neat and Binary Solvents

The thermodynamic properties of phenacetin in solid state and in saturated conditions in neat and binary solvents were characterized based on differential scanning calorimetry and spectroscopic solubility measurements. The temperature-related heat capacity values measured for both the solid and melt states were provided and used for precise determination of the values for ideal solubility, fusion thermodynamic functions, and activity coefficients in the studied solutions. Factors affecting the accuracy of these values were discussed in terms of various models of specific heat capacity difference for phenacetin in crystal and super-cooled liquid states. It was concluded that different properties have varying sensitivity in relation to the accuracy of heat capacity values. The values of temperature-related excess solubility in aqueous binary mixtures were interpreted using the Jouyban–Acree solubility equation for aqueous binary mixtures of methanol, DMSO, DMF, 1,4-dioxane, and acetonitrile. All binary solvent systems studied exhibited strong positive non-ideal deviations from an algebraic rule of mixing. Additionally, an interesting co-solvency phenomenon was observed with phenacetin solubility in aqueous mixtures with acetonitrile or 1,4-dioxane. The remaining three solvents acted as strong co-solvents.     

Water Activities, Osmotic and Activity Coefficients and Some Correlation of Aqueous Mixtures of Alkaline-Earth and Ammonium Nitrates, NH4NO3-Y(NO3)2-H2O with Y ≡ Ba2+, Mg2+ and Ca2+ at T = 25 °C

The thermodynamic properties of the mixed aqueous electrolyte of ammonium and alkaline earth metal nitrates have been studied using the hygrometric method at 25?°C. The water activities of these {yNH₄NO₃+(1?y)Y(NO₃)₂}(aq) systems with Y ≡ Ba²⁺, Mg²⁺ and Ca²⁺ were measured at total molalities ranging from 0.10 mol?kg^?1 to saturation for different NH₄NO₃ ionic-strength fractions of y=0.20, 0.50 and 0.80. These data allow the calculation of osmotic coefficients. From these measurements, the ionic mixing parameters are determined and used to calculate the solute activity coefficients in the mixtures at different ionic-strength fractions. The results of these ternary solution measurements are compared with those for binary solutions of the alkaline earth nitrates of magnesium, calcium and barium with ammonium nitrates. The behavior of the aqueous electrolyte solutions containing mixtures of barium or calcium or magnesium with ammonium nitrates are correlated and show that ionic interactions are more important for the system containing Mg²⁺ than for Ca²⁺ or Ba²⁺. The trends are mainly due to the effects of the ionic size, polarizability and the hydration of the ions in these solutions.     

A new approach in modelling phase equilibria and gas solubility in electrolyte solutions and its applications to gas hydrates

This paper presents a new predictive model for phase equilibria and gas solubility calculations in the presence of electrolyte solutions. It treats salts as pseudo-components in an equation of state (EoS) by defining the critical properties and acentric factor for each salt. The water–salt, gas–salt and salt–salt binary interaction parameters (BIP) have been determined by using available experimental data on freezing point depression and boiling point elevation as well as gas solubility and salt solubility data in saline solutions.The methodology has been applied in modelling sodium chloride, potassium chloride and their mixtures, as well as solubility of methane and carbon dioxide in aqueous single and mixed electrolyte solutions.The developed model is capable of accurately predicting the phase behaviour, gas hydrate stability zone and potential salt precipitation in single and mixed electrolyte solutions. The model predictions are compared with available independent experimental data, including hydrate inhibition characteristics of single and mixed electrolyte solutions, and good agreement is demonstrated.     

Preferential interaction between DNA and small ions in mixed-size counterion systems: Monte Carlo simulation and density functional study

Competitive binding between counterions around DNA molecule is characterized using the preferential interaction coefficient of individual ion in single and mixed electrolyte solutions. The canonical Monte Carlo (MC) simulation, nonlinear Poisson-Boltzmann (PB) equation, and density functional theory (DFT) proposed in our previous work [Wang, Yu, Gao, and Luo, J. Chem. Phys. 123, 234904 (2005)] are utilized to calculate the preferential interaction coefficients. The MC simulations and theoretical results show that for single electrolyte around DNA, the preferential interaction coefficient of electrolyte decreases as the cation size is increased, indicating that the larger cation has less accumulation ability in the vicinity of DNA. For the mixed electrolyte solution, it is found that cation diameter has a significant effect on the competitive ability while anion diameter has a negligible effect. It proves that the preferential interaction coefficients of all ions decrease as the total ionic concentration is increased. The DFT generally has better performance than the PB equation does when compared to the MC simulation data. The DFT behaves quite well for the real ionic solutions such as the KCl-NaCl-H2O, NaCl-CaCl2-H2O, and CaCl2-MgCl2-H2O systems.     

Vapor-liquid equilibrium properties of sodium n-heptyl sulfonate in Water and in aqueous solutions of poly(ethylene glycol) at different temperatures

The vapor-liquid equilibria properties of sodium n-heptyl sulfonate (C₇SO₃Na) in pure water and in aqueous poly(ethylene glycol) (PEG) solutions were determined at different temperatures below and above the critical micelle concentration (CMC). Vapor-liquid equilibrium data such as water activity, vapor pressure, osmotic coefficient, activity coefficient and Gibbs free energies were obtained through isopiestic method. The concentration dependence of all investigated thermodynamic properties exhibit a change in slope at the concentration in which micelles are formed. It was found that the vapor pressure depression for a ternary aqueous C₇SO₃Na + PEG system is more than the sum of those for the corresponding binary solutions and, at higher temperatures, the higher concentration of PEG is in equilibrium with a certain concentration of surfactant.