Comparative studies of calculation methods for symmetrical mixed electrolytes

Various methods used in the analysis of the activity coefficients for binary mixtures of symmetrical electrolytes are compared. The accuracies of these methods are examined through their standard deviations of the log fittings, maximun deviations max , and the number of fitted points n, which have exceeded the experimental tolerance. The reason for the different degree of accuracy obtained are discussed in terms of the complexity of the g₀ function.     

A new method for calculating activity coefficients of mixed electrolytes

In present work, a new method is developed from which activity coefficients for both electrolytes in admixture can be obtained simultaneously from the fitting of experimental activity coefficients of one of the electrolyte. The calculated results for the system HCl+KCl at 25°C are reported and discussed.     

All mixing coefficients and consistency test calculations for binary mixed electrolytes

Two new methods are reported from which the mixing activity coefficients of both electrolytes in a binary mixture can be computed simultaneously from fitting the activity coefficients of one of the electrolytes only and without using the derivatives of the parameters. Furthermore, variations caused by changing the fractional ionic strengths at fixed total ionic strength entails no assumptions about the ionic strength dependence of the mixing coefficients. The methods are shown to be superior to other methods. The results for the system HCl+KCl at 25°C are discussed.     

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.     

Soret coefficients of mixed electrolytes

Practical equations are developed which relate the Soret coefficients of mixed electrolytes to the entropies and enthalpies of transport. The derived equations together with published binary thermal diffusion data can be used to estimate the Soret coefficients of mixed electrolytes. The procedure is illustrated for the systems NaCl+HCl+ water and NaCl+MgCl₂+ water. Aqueous NaCl, like most salts, diffuses to the cold plate in binary Soret experiments. In aqueous HCl solutions, however, NaCl can diffuse to the warm plate, and the magnitude of its Soret coefficient can take values twice as large as those for binary solutions. The thermal diffusion of trace amounts of a salt in a solution containing a large excess of another salt is discussed. Exceptionally large Soret effects are predicted for traces of strong acids in aqueous salt solutions.     

Estimation of activity and osmotic coefficients of strong electrolytes in water at elevated temperatures

It was found over a wide concentration and temperature range that differences between osmotic coefficients of a given electrolyte and a standard electrolyte, - ^st , can be approximated by a linear relation. Sodium chloride, calcium chloride and sodium sulfate were chosen as standard electrolytes for 1:1, 2:1 and 1:2 electrolytes, respectively. Special numerical procedures were developed for the prediction and estimation of activity and osmotic coefficients at elevated temperatures based on data at two temperatures or on data at room temperature only. Reasonable agreement was found between activity coefficients estimated by the present procedure and those correlated by Pitzer's and Meissner's equations.     

Activity coefficients of single electrolytes in concentrated solutions derived from a quasi-lattice model

This paper describes a new model to calculate the mean activity coefficients of dissociated electrolytes in concentrated solutions. It is based on three assumptions: (i) a quasi-lattice arrangements of ions in solution; (ii) a contribution from ion-water interactions to the mean activity coefficients; (iii) a concentration dependence of the dielectric constant. The mean activity coefficients of thirteen strong electrolytes from moderately dilute solutions to saturated solutions are found to correlate well by this model. For dilute solutions, a limiting equation in which only ion-specific parameters are required is proposed. It is suggested that specific ionwater interactions might be the major source of the nonideality of strong electrolyte solutions at high concentrations.     

Activity coefficients of electrolytes in binary mixtures calculated using total molal quantities

Activity coefficients in binary mixed electrolytes are expressed in terms of the parameters from total molal quantities. Two versions of the calculations are presented and compared with the methods of Pitzer and Scatchard. For each method interrelations among the various parameters are examined. The system being tested is HCl+CoCl₂+H₂O at 25°C, for which new experimental data at low ionic strengths are included.     

Modification of the Pitzer model to calculate the mean activity coefficients of electrolytes in a water-alcohol mixed solvent solution

The approach tested in this work consists in adapting the Pitzer model, initially designed for aqueous solutions of electrolytes, to the case of solutions with a mixed solvent, without systematically readjusting the coefficients. This modified model was applied successfully to the calculation of the mean activity coefficients of NaBr in the mixed solvent H₂O+MeOH, H₂O+EtOH and compared with the experimental values obtained from electrode potential measurements.General D dielectric constant - G ^ex excess Gibbs energy - I ionic strength - k Boltzman's constant - m _i molality - N _o Avogadro's number - n _w number of kilograms of water - R gas constant - T temperature (K) - T _c critical temperature - T _cm critical temperature of mixed solvent - x _i molar fraction - z _i ionic charge - electronic charge - osmotic coefficient - ± mean activity coefficient of electrolyte - number of moles of ions given by one mole of electrolyte - _M number of moles of cations given by one mole of electrolyte - _X number of moles of anions given by one mole of electrolyte - _W density of water Debye- Hückel Model A Debye-Hückel parameter - a distance of closest approach of ions in solution - B Debye-Hückel parameter Pitzer Model b numerical parameter of model - numerical parameter of model - ₁, ₂ numerical parameters of model, used in the case of 2:2 electrolyte - _MX ⁽⁰⁾ numerical parameter of electrolyte MX - _MX ⁽¹⁾ numerical parameter of electrolyte MX - _MX ⁽²⁾ numerical parameter of 2:2 electrolyte MX - C _MX numerical parameter of electrolyte MX - binary interaction parameter - ternary interaction parameter     

Estimation of activity coefficients at different temperatures by using the mean spherical approximation

A method of estimating activity coefficients for a variety of electrolytes at different temperatures is presented. The MSA approximation is used to calculate the activity coefficients from experimental data available in the literature. This strategy provides suitable results within a wide range of temperatures, electrolyte stoichiometries and concentrations of investigated solutions.     

乙醇-环己烷体系中NaI活度系数的测定与计算

由于非水溶剂的应用日趋广泛,促使物理化学工作者对于溶剂和溶液性质进行研究,同时开展了有关物理化学数据的测定和积累工作,以利于指导实践[1]。目前文献报道含水混合溶剂中的电解质活度系数较多,但非水混合溶剂中电解质活度系数报道较少。电解质浓溶液活度系数的计算方法目前应用较广的是Pitzer半经验算法[2]。Pitzer的算法中具体物系的β(0)、β(1)等系数需从实测活度系数数据拟合求得。孙仁义等通过测定汽液平衡盐效应的方法研究了盐在混合溶剂中的活度系数[3-4]。最近孙仁义等[5]提出了双液比固定条件下含盐体系汽液平衡数据热力学一…     

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 of electrolytes from the emf of liquid membrane cells. IV: Revised activity coefficients of lanthanum hexacyanoferrate(III)

Lanthanum ferricyanide is so far the only 3–3 electrolyte whose activity coefficients have been studied carefully; however, the results have been acknowledged to be inconsistent below 1×10^–4 mol-kg^–1. New measurements have been made with an improved cell, proving that the wrong trend was due to chemical interference in the original cell. The new cell makes it possible to reach dilution levels of the order of 4×10^–6 mol-kg^–1. The salt behaves radically unlike Debye-Hückel's predictions, but agrees with other more refined treatments of the hard sphere models without needing any further hypotheses, such as e.g., association. The revised values of the activity coefficients are reported.     

Activity coefficients in binary electrolyte mixtures HCl + MgCl2 + H2O at 298.15°K

Activity coefficients of hydrochloric acid in aqueous mixed solutions with magnesium chloride have been determined at 298.15°K from electromotiveforce measurements of the cell Pt, H₂(g, 1 atm.)HCl(m_A), MgCl₂(m_B)AgClAg at constant total ionic strengths of 0.1, 0.5, 1.0, 2.0, and 3.0 moles-kg^–1. The data were interpreted in terms of Scatchard's and Pitzer's equations whereupon it was found that the former gave a better fit of the experimental data but the latter were reasonably adequate. Activity coefficients for magnesium chloride in the mixtures were derived using Pitzer's equations.     

Effect of ion solvation on the diffuse layer structure in mixed electrolytes

A “solvionic” model of a multicomponent electrochemical system (mixed electrolyte) is considered. An ion in the solution is considered as a point charge rigidly fixed inside its solvation shell. The corresponding equations for the diffuse layer on an ideally polarizable electrode are derived, and an effective method of their numerical solution is formulated. The calculations are performed in order to follow the changes in the diffuse layer structure with variations in the electrode charge and electrolyte composition. Far from the zerocharge potential of solution, the dependences of distributions of solution components over the diffuse layer on the electrode charge radically differ from those within the classic Gouy-Chapman theory. Analytical equations (asymptotics at large electrode charges) for concentrations of solvated ions in the plane of their maximum approach and for their “surface excesses” (diffuse adsorption) are determined. Results of numerical calculations for a 0.2 M LiCl + 0.05 M BaCl₂ solution are plotted.     

Thermodynamic properties of electrolyte solutions: An EMF study of the activity coefficients of KCl in the system KCl−KNO3−H2O at 25, 35 and 45°C

Electromotive force measurements were carried out on the system KCl–KNO₃–H₂O at constant total ionic strengths of 0.5, 1.0, 2.0 and 3.0 mol-kg^–1 and at 25, 35 and 45°C using a cell consisting of a potassium ionselective electrode and a Ag/AgCl electrode. The Harned coefficients and the Pitzer binary and ternary interaction parameters for the system have been evaluated at each temperature. The osmotic coefficients, excess free energies of mixing and heats of mixing of the system have been predicted at each of the experimental temperatures and ionic strengths. The solubility data at 25°C are also interpreted.     

Numerical calculation of the Onsager transport coefficients for isothermal binary electrolytes

The Ebeling-Falkenhagen diffusion equations are applied to calculate the Onsager transport coefficients as well as the electrical conductances, transference numbers, and mutual diffusion coefficients for isothermal binary electrolytes. For this purpose the hierarchy of diffusion equations is closed on the level of the binary distribution functions by the superposition approximation. The resulting system of common differential equations is solved by numerical methods. Hydrodynamic interactions are taken into account up to first order. Some results are given for symmetrically charged binary electrolytes with hard-core ions (restricted primitive interaction model). The model parameters (Bjerrum parameter and Debye screening length) are chosen to represent strong electrolytes up to the molar region.     

The application of the ion-interaction model to multicomponent 1-1 type electrolytes in mixed solvents

The ion-interaction model has been applied to published measurements for the multicomponent electrolytes HCl+MCl (M means Na or K) in mixed solvents (urea + water or methanol + water). The Pitzer parameters _HCl ⁽⁰⁾ , _HCl ⁽¹⁾ , C _HCl , ( _NaCl ⁽⁰⁾ + _NaH), _NaCl ⁽¹⁾ , _NaHCl in the HCl+NaCl + urea + water system were obtained by the method of least squares. A temperature and molality dependent equation for _HCl in this system was obtained. In the HCl+MCl + methanol + water system, the mixing parameter _HCl was obtained in terms of the Harned Rule. The relationship between Pitzer parameters and the composition of the mixed solvent was discussed.on leave from Department of Chemistry, Liaoning University Shenyang, China.     

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

Osmotic and activity coefficients of ammonium thiocyanate in aqueous solution at 25°C have been determined by the isopiestic vapor pressure method. The activity coefficients do not agree with values reported previously but are consistent with trends shown by activity coefficients of ammonium chloride and bromide.     

Electromotive-force studies of mixed electrolytes in mixed solvents. HCl+NH4Cl in methanol+water solvents at 25°C

Electromotive-force measurements of the cell Pt, H₂(g, 1 atm)|HCl(m₁), NH₄Cl(m₂), methanol(X%), Water(100–X)%|AgCl|Ag have been made at 25°C for m₁+m₂=1 mole-kg^–1 and X=0, 10, 20, 30, 40, and 50% methanol by weight. Hydrochloric acid obeys Harned's rule in aqueous solutions, but a quadratic term is required in the mixed solvents. The Harned coefficients for the acid vary with solvent composition, and this invalidates the applicability of Harned's method for estimating activity coefficients for single electrolytes in mixed solvents. This method is described and the reason for the inapplicability of the method is discussed in terms of ion-ion and ion-solvent interactions.