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.     

Comparative studies of calculation methods for activity coefficients of unsymmetrical mixed electrolytes

Several methods for the calculation of activity coefficients for binary mixed electrolytes are compared. Their accuracies are analysed and the reasons for the different degrees of accuracies are given.     

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.     

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.     

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.     

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.     

HOLL All Mixing Coefficients method for binary mixed electrolytes

As an extension of the All Mixing Coefficients method which was developed in 1987, we have now incorporated the Higher Order Limiting Law into the method so that it satisfies the HOLL while it retains its high accuracy and other important features. One mixture each symmetrical and unsymmetrical were used for testing. The calculated results are analysed and compared with other well known methods. The superiority of the present method is shown.     

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.     

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.     

A thermodynamic approximation for the estimation of velocity correlation coefficients in binary liquid mixtures

An equation is derived using the relations of equilibrium thermodynamics to estimate limiting distinct diffusion coefficients, (or velocity cross-correlation coefficients) in binary non-electrolyte mixtures. It is tested against 13 mixtures. Good agreement is obtained with distinct diffusion coefficients derived experimentally in the case of near deal systems. For non-ideal mixtures the calculated values appear to follow the experimental coefficients to some extent. For this reason, the thermodynamic approximation is not as suitable for a reference equation as a structural approximation previously derived.     

Characteristics of the activity coefficients in binary solutions on chromatographic paper

The deviation from ideality of the characteristics of chromatographic binary solutions in paper chromatography is discussed.     

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.     

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.     

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.     

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.     

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.     

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.     

The application of the pitzer equations to 1-1 electrolytes in mixed solvents

Pitzer's equation for the activity coefficient has been applied to LiCl, NaCl, KCl, RbCl, CsCl, and HCl in methanol-water mixtures at 25°C. The two parameters, _MX ⁽⁰⁾ and _MX ⁽¹⁾ , were obtained by the method of least squares. The same values of b and as for aqueous systems could be used for the methanol-water mixtures without greatly affecting the standard deviation of the fit. _MX ⁽⁰⁾ was found to decrease with methanol content for the alkali metal chlorides whereas _MX ⁽¹⁾ was found to increase. For HCl, however, a slight maximum and a minimum were found in the values of _MX ⁽⁰⁾ while a maximum was observed in the values of _MX ⁽¹⁾ .     

Activity coefficients of electrolytes from the E.M.F. of liquid membrane cells. I. The method—Test measurements on KCl

A new electrochemical cell is described, in which two permselective liquid membranes, one anionic the other cationic, are interposed between the subsidiary electrodes and the solution of the electrolyte under examination By means of this kind of cell it is possible to measure activity coefficients of salts of cations and anions for which reversible electrodes are not available, with great accuracy even at high dilutions never accessible before (down to ≊10⁻⁴ mol-dm⁻³). The cell performance has been tested by measuring the activity coefficients of KCl for which accurate data are available in literature.     

Activity coefficients of DL-valine in aqueous solutions of KCl at 25°C. Measurement with ion selective electrodes and modelling

Electrochemical cells with two ion selective electrodes, a cation and an anion ion selective electrode, versus a double junction reference electrode were used to measure the activity coefficients of DL-valine at 298.15 K, up to 0.5 molality, in aqueous solutions of KCl up to 1.0 molality. The results obtained in this work are compared with those reported before for the activity coefficients of DL-valine in aqueous solutions of NaCl. The experimental data were correlated using the model proposed previously by Khoshkbarchi and Vera for the activity coefficients of amino acids in aqueous electrolytes solutions.