Lewis-Randall to McMillan-Mayer conversion for the thermodynamic excess functions of solutions. Part III. Common-ion mixtures of two electrolytes

Derivations are given for the equations expressing the thermodynamic coefficients that characterize the process of mixing two electrolytes with a common ion in the McMillan-Mayer system in terms of the coefficients for the corresponding process in the Lewis-Randall system, together with correction terms made up of various Lewis-Randall thermodynamic coefficients of the solutions. In the former case, the solutions are mixed at fixed molar ionic strength (i.e., fixed Debye kappa), fixed temperature, and fixed chemical potential of the solvent. In the latter case they are mixed at fixed molal ionic strength, fixed temperature, and fixed total pressure on the solutions.     

Thermodynamics of mixed electrolyte solutions. VI. An isopiestic study of a pseudo-ternary system: NaCl−KCl−MgCl2−H2O at 25°C

Activity coefficients for magnesium chloride in the aqueous pseudo-ternary system sodium chloride-potassium chloride-magnesium chloride were derived from isopiestic measurements at 25°C. The isopiestic data were treated by both McKay-Perring and Scatchard methods, and results obtained agree fairly well over the ionic strength range of 1–6. At constant ionic strength, the activity coefficient of MgCl₂ increased with addition of other salts. Interaction coefficients were obtained from Scatchard's and Friedman's formalisms. The excess free energy of mixing was calculated and compared with similar systems.     

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.     

Thermodynamics of multicomponent electrolyte solutions: Aqueous mixtures of two salts from among NaCl,KCl, NaH2PO4, and KH2PO4 at 25° C

Five of the six possible aqueous two-salt mixtures from among NaCl, KCl, NaH₂PO₄,and KH₂PO₄ have been studied by the isopiestic method at 25°C. The sixth mixture, NaCl–KCl, has been studied previously. The deviations from ideal mixing behavior are described by a series of coefficients which were found by regression analysis. The coefficients were used to calculate the excess Gibbs energies of mixing for equal ionic strength fractions of each salt and the trace activity coefficient of each salt at an ionic strength of 2 mode-kg^–1. The cross-square mixing rule is obeyed within experimental uncertainty for the excess Gibbs energies of mixing.     

Comment on “Factorizing of a concentration function for the mean activity coefficients of aqueous strong electrolytes into individual functions for the ionic species” by A. Ferse and H.O. Müller

A. Ferse and H.O. Müller have recently presented a mathematical method aimed at subdividing the activity coefficients of electrolytes into functions of individual ionic species; these functions are suggested to be the ionic activity coefficients. By examining the method, it is possible to verify that the peculiar mathematical structure of the functions in question really guarantees a unique result, unlike the usual subdivisions of electrolyte activity coefficients, which admit infinite possibilities for the ionic activity coefficients. But the subsequent step of the reasoning, i.e., that these functions have to be the activity coefficients of the ionic species, is an illation. And indeed, another kind of subdivision in individual functions can be exemplified, whose mathematical structure also guarantees results that are unique and perfectly compatible with all theoretical properties of the ionic activity coefficients. It is concluded that it is impossible to rely on mathematical method to pull the activity coefficients of ions out of the mean activity coefficients of the electrolytes. And hence, the individual functions for the ionic species determined by Ferse and Müller do not represent the ionic activity coefficients and do not have any particular utility.     

New forms of McKay-Perring equations for mixed electrolyte solutions

Pan, H. and Han, S., 1993. New forms of McKay-Perring equations for mixed electrolyte solutions. Fluid Phase Equilibria, 90: 289-306.

A rigorous derivation is given for new forms of the McKay-Perring equations and the partial differential equation relating the activity coefficients of two electrolytes in mixed electrolyte solutions. They all have simple and symmetrical forms when the independent variables are the total ionic concentration and the fraction of ionic concentration. However, the simple and symmetrical forms remain only when the electrolytes are of the same charge types and when the independent variables are ionic strength and the fraction of ionic strength. The method of surface fitting is introduced to evaluate the McKay-Perring equations. The calculated results for four systems are in good agreement with those from the Pitzer equations.     

Optical Response of Porous Titania‐Silica Waveguides to Surface Charging in Electrolyte Filled Pores

In this work, we present a novel method for in situ investigation of surface charging and ion transport inside nanopores of titania‐silica waveguide by means of the optical‐waveguide‐lightmode spectroscopy. Porous oxide waveguides show a strong optical response when exposed to electrolyte solutions, and this response is consistent with oxide surface charging due to changes in ionic strength and pH of the solution in contact with the waveguide. The optical response to pH or electrolyte concentration change is stabilized within several minutes when the solution ionic strength is sufficiently high (0.1M ), while it takes two orders of magnitude longer to reach stable optical response at very low ionic strengths (<0.1mM ). The relaxation times at the high ionic strength are still by several orders of magnitude slower than expected from bulk diffusion coefficients of electrolytes in water. Our results indicate that diffusion of electrolytes is severely hindered (and more so with decreasing ionic strength) in charged pores inside waveguides.     

Comparative analysis of the activity coefficients for the system NaBr+NaFormate+H2O at 25°C by the methods of scatchard,pitzer and lim

Activity coefficients for NaBr in the system NaBr+NaFormate+H₂O at 25°C were determined from emf measurements at different total ionic strengths. At each total ionic strength, the measurements were carried out at different Na-Formate/NaBr ionic strength ratios. The experimental activity coefficients were comparatively analyzed using Scatchard's, Pitzer's and Lim's methods. Although all these models can be successfully applied to the analysis of this mixed system, the All Mixing Coefficients (LA) and Consistency Test (LT) models lead to better fittings than the others.     

Löslichkeiten und Aktivitätskoeffizienten von H2S in Elektrolytmischungen

From solubility measurements on hydrogen sulfide in aqueous solutions of the composition [H⁺] = HM, [Na⁺] = (I — H) M = A M, [Cl^?] = I M at 25°C, the molar and molal activity coefficients of H₂S have been calculated. The activity coefficients of H₂S in the electrolyte mixtures have been found to be additive functions of the activity coefficients in the individual electrolyte solutions at the same ionic strength. This result is predicted by the internal pressure theory of salt effects on non-electrolyte activity coefficients, provided that the volume change upon mixing two electrolyte solutions of the same ionic strength is zero.     

Osmotic and Activity Coefficients of {yKCl+(1−y)MgCl2}(aq) at T=298.15 K

Isopiestic vapor-pressure measurements were made at the temperature 298.15 K for aqueous KCl + MgCl₂ solutions using KCl(aq) as the reference standard. The measurements for these ternary solutions were made at KCl ionic strength fractions of y=0.0, 0.1989, 0.3996, 0.5993, 0.7925 and 1.0 (with two additional sets at y=0.0, 0.2021, 0.3998, 0.6125, 0.8209 and 1.0) for the ionic strength range from 0.4014 to 6.2790 mol?kg^?1. Our results, and those from two previous isopiestic studies, were combined and used with previously determined parameters for KCl(aq) and those determined here for MgCl₂(aq) to evaluate mixing parameters for the Clegg-Pitzer-Brimblecombe model. These combined data were also used to determine the mixing parameters of the Scatchard model. Both sets of model parameters are valid for ionic strengths of I≤12.8 mol?kg^?1, where higher-order electrostatic effects have been included in the Clegg-Pitzer-Brimblecombe mixture model. The activity coefficients for KCl and MgCl₂ were calculated from these models and the results for KCl were compared to experimental data from Emf measurements. The Scatchard model interaction parameters were used for calculation of the excess Gibbs energy as a function of the ionic strength and ionic strength fraction of KCl. The Zdanovskii-Robinson-Stokes rule of linearity for mixing of isopiestic solutions was tested.     

NaCl-KCl-H2O体系的体积性质及其与Pitzer模型的相关性研究

本文用高精度数字式振荡管密度计测定了288K至323K温度范围内NaCl?KCl混合溶液的密度,溶液的离子强度范围从0.1到4 mol.kg_^–1。用密度实验值计算了三元体系的超额体积并拟合得到了实验温度和浓度范围内的Pitzer模型参数,模型计算值与实验值的偏差在±0.0004 g.cm_^–3以内。用Pitzer模型计算了不同离子强度下三元体系在298.15K下的混合体积。     

Thermodynamics of mixed electrolyte solutions. VIII. An isopiestic study of the ternary system KCl−MgCl2−H2O at 25°C

The osmotic coefficients of aqueous solutions of mixtures of potassium and magnesium chlorides were derived from isopiestic measurements at 25°C. The isopiestic data were treated by the methods of both Scatchard and Friedman, and the results obtained agree very well over the ionic strength range of 1–5. Interaction coefficients were obtained from both formalisms. Excess free energies of mixing were calculated and compared with those of similar systems.     

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.     

Calculating the thermodynamic properties of aqueous solutions of alkali metal carboxylates

A modified Robinson-Stokes equation with terms that consider the formation of ionic hydrates and associates is used to describe thermodynamic properties of aqueous solutions of electrolytes. The model is used to describe data on the osmotic coefficients of aqueous solutions of alkali metal carboxylates, and to calculate the mean ionic activity coefficients of salts and excess Gibbs energies. The key contributions from ionic hydration and association to the nonideality of solutions is determined by analyzing the contributions of various factors. Relations that connect the hydration numbers of electrolytes with the parameters of the Pitzer-Mayorga equation and a modified Hückel equation are developed.     

Development of a Modified Bromley's Methodology for the estimation of ionic media effects on solution equilibria: Part 3. Application to the construction of thermodynamic models

The development of the Modified Bromley's Methodology (MBM) is extended for the estimation of the activity coefficients of individual species in aqueous solution at 25°C in single and mixed ionic media. The estimation is compared with literature data of activity coefficients of mixtures of electrolytes in water and applied to (a) the prediction of the ionic product of water in aqueous solutions containing different salts which are commonly used as background electrolytes (NaCl, KNO₃ and NaClO₄) and (b) the equilibrium constants of the Cr(VI)–H₂O system.     

Activity measurements in the ternary system NaBr+NaClO4+H2O at 25°C

The activity coefficients of sodium bromide in the ternary system NaBr+NaClO₄+H₂O were determined at 25°C and constant ionic strength of 0.1, 0.5, 1, 2, and 3 mol-kg^?1 from emf of the cell without, liquid junction $$ISE - Na|NaBr(m_A ), NaClO_4 (m_B ), AgCl_{(s)} 1 Ag$$ The experimental activity coefficients were comparatively analyzed by using the Harned, Scatchard, Pitzer and Lim-HOLL treatments. All these methods are adequate for the analysis of the experimental data. The results have been compared with those of Lanier for the system: NaCl+NaClO₄+H₂O. The Gibbs excess energy of mixing was obtained and qualitatively interpreted in terms of ionic interactions.     

电动势法对LiCl-Li~2SO~4-H~2O体系25℃热力学性质研究

用自制的锂离子选择电极和经典Ag-AgCl电极,测定25℃时LiCl-Li~2SO~4-H~2O三元体系中离子强度0.01～6.0mol.kg^-1的LiCl平均活度系数.,由实验数据,用多元线性回归法求取Pitzer方程、Harned方程的离子作用参数和系数,并用上述方程计算LiCl在混合溶液中的平均活度系数,分别以Inγ~±LiCl和logγ~±LiCl的形式与实验值进行比较,标准偏差均小于0.008.本工作测得的LiCl平均活度系数的自然对数与等压法测定的渗透系数拟合的Pitzer方程参数计算值比较,标准偏差为0.0097.同时计算了Li~2SO~4在该体系中的平均活度系数和混合溶液的渗透系数以及混合超额自由能.     

Estimation of Pitzer's ion interaction parameters for electrolytes involved in complex formation using a chemical equilibrium model

Pitzer's ion interaction model has been widely accepted for calculating the thermodynamic properties for electrolytes at high ionic strength. For weak electrolytes, a better estimation can be obtained by combining the model with chemical equilibria. The method of calculation is to treat each individual species as a single, separated ion. The concentration of each ion will be constrained by the mass balance equation and its activity will be guarded by the stability constants. Including chemical equilibria in Pitzer's model provides not only a better estimation of the thermodynamic properties of weak electrolytes but also a better understanding of the equilibrium among the complexes. The results may be used for correcting the effect from high ionic strength solution when determining the stability constants. When considering chemical equilibria, some of the parameters reported by Pitzer may have to be reestimated. The method of estimation and comparison between final results are presented. The binary system of HF, and the ternary systems of CuCl₂ in NaCl and in HCl are used for demonstration.     

Variations of activity coefficients in concentrated electrolyte solutions at constant lonic strength

Measurements of different types on various (trace) electrolytes in HClO₄–Na(Li)ClO₄ solutions at several (constant) values of the ionic strength have been used to determine the variation of their activity coefficients with changing amount of perchloric acid in the solution. These variations (with respect to the hydrogen ion) differ considerably among different cations and anions. The results for the alkali metal ions and the anions are interpreted in the light of the recent work of Pitzer on short-range ionic interactions. The results for the cations with outerd-electrons and the alkaline earth metal ions are interpreted in terms of ion-solvent interactions. It is concluded that the use of HClO₄–NaClO₄ solutions of high ionic strength (rather than the use of HClO₄–LiClO₄ solutions) is advisable in studies where the variation in activity coefficients must be accounted for. Finally, it is shown that the usual interpretation of the influence of the salt medium in studies of complex equilibria and reaction kinetics is sometimes questionable.     

Activity coefficients for the system NaCl+Na2SO4+H2O at various temperatures. Application of Pitzer's equations

The mean activity coefficients of NaCl in the system NaCl+Na₂SO₄+H₂O at various compositions were determined in the temperature range 5–45°C from the emf of potentiometric cells. By processing the results using Pitzer's equations the mixing parameters describing the non-ideal behavior of electrolytes were calculated. The temperature coefficients of the mixing parameters were determined and found not to be significant. The mixing parameters and temperature coefficients calculated for the binary mixture can be used to describe the behavior of multicomponent systems containing NaCl and Na₂SO₄, and eventually sea water.