# Mean Activity Coefficient of Electrolyte Solutions

08 Mar 2007-Journal of Physical Chemistry B (American Chemical Society)-Vol. 111, Iss: 12, pp 3183-3191

TL;DR: A model of electrolyte solution is proposed that allows us to calculate gamma without using fitting parameters where the (upper) concentration exists at which the electrolyte solutions exhibits gamma = 1 (molality scale).

Abstract: In this paper, we deal with the mean activity coefficient, γ, of electrolyte solutions. The case γ ≤ 1 is investigated. As is generally recognized, the most accepted models (specific ion interaction/Pitzer theory) have the disadvantage of the dependence on semiempirical parameters. These are not directly accessible from experimental measurements, but can only be estimated by means of best-fitting numerical techniques from experimental data. In the general context of research devoted to the achievement of some reduction of complexity, we propose a model of electrolyte solution that allows us to calculate γ without using fitting parameters where the (upper) concentration exists at which the electrolyte solution exhibits γ = 1 (molality scale). In the remaining cases, we show that a unique parameter is required, that is, the concentration that should ideally give γ = 1 for the electrolyte. Compared to other models that do not require adjustable parameters, the present one is generally applicable over a wider...

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TL;DR: Electrochemical modeling and simulations to the discharge process of LiCoO2 cells reveal the underlying mechanisms of performance limitations due to thick electrode, high-rate operation, and large-sized active material particles as well as effects of charge transports.

Abstract: Underutilization due to performance limitations imposed by species and charge transports is one of the key issues that persist with various lithium-ion batteries. To elucidate the relevant mechanisms, two groups of characteristic parameters were proposed. The first group contains three characteristic time parameters, namely: (1) te, which characterizes the Li-ion transport rate in the electrolyte phase, (2) ts, characterizing the lithium diffusion rate in the solid active materials, and (3) tc, describing the local Li-ion depletion rate in electrolyte phase at the electrolyte/electrode interface due to electrochemical reactions. The second group contains two electric resistance parameters: Re and Rs, which represent respectively, the equivalent ionic transport resistance and the effective electronic transport resistance in the electrode. Electrochemical modeling and simulations to the discharge process of LiCoO2 cells reveal that: (1) if te, ts and tc are on the same order of magnitude, the species transports may not cause any performance limitations to the battery; (2) the underlying mechanisms of performance limitations due to thick electrode, high-rate operation, and large-sized active material particles as well as effects of charge transports are revealed. The findings may be used as quantitative guidelines in the development and design of more advanced Li-ion batteries.

110 citations

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Ajinomoto

^{1}TL;DR: The apparent dissociation constants of the amino acids lysine, histidine, arginine, glutamic acid, tyrosine, phenylalanine, tryptophan, and threonine were determined at various ionic strengths by potentiometric titration as mentioned in this paper.

Abstract: The apparent dissociation constants of the amino acids lysine, histidine, arginine, glutamic acid, tyrosine, phenylalanine, tryptophan, and threonine were determined at 283.1 K, 298.1 K, 313.1 K, and 333.1 K at various ionic strengths by potentiometric titration. The Davies equation was used to extrapolate the dissociation constants to zero ionic strength. The pK values of the carboxylic acid attached to the α-carbon and the pK of the carboxylic acid on the side chain of glutamic acid were almost independent of temperature. Conversely, the pK values of the amino groups attached to the α-carbon and those on the side chain of the basic amino acids varied substantially with temperature. van’t Hoff type plots of the pK values showed linear relationships indicating that the standard enthalpy changes of reaction are constant over this range of temperatures.

78 citations

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TL;DR: In this paper, a combination of simple physical theory and Monte Carlo (MC) simulations is used to obtain good fits up to 1 molal (m) concentration for a large number of salt solutions.

Abstract: The properties of bulk salt solutions over wide concentration ranges are explored by a combination of simple physical theory and Monte Carlo (MC) simulations. The corrected Debye–Huckel (CDH) theory which incorporates ion size effects in a linear response approximation is extended to yield free energy and other thermodynamic properties by integration of the chemical potential over concentration. Charging integration which is usually used to obtain an electrostatic contribution of total free energy of electrolytes is avoided in this new direct approach. MC simulations are performed with a modified Widom particle insertion method, which also provides directly the ionic activity coefficients. The validity of the CDH theory is tested by comparison with the MC simulation data for 1:1, 2:1, 2:2 and 3:1 restricted primitive model (RPM) electrolytes over a wide concentration range and at various ion sizes. Mean ionic activity and osmotic coefficients calculated by the CDH theory in RPM approximation of electrolyte are fitted to experimental data by adjusting only a mean ionic diameter. Good fits up to 1 molal (m) concentration are obtained for a large number of salt solutions. MC simulations data for unrestricted primitive model (UPM) of 1:1 and 2:1 electrolytes are also fitted to the experimental data by varying the cation radius while keeping the anion radius fixed at a crystallographic value. The success of this approach is found to be salt specific. For example good fits up to 2 and 3.5 m concentrations were obtained for LiCl and LiBr, respectively. However in the case of less dissociated salts such as NaCl and KI the experimental data could only be fitted up to one molal concentration. Possibility of extending the applicability range of the CDH theory to concentrations >2 m is explored by including a concentration dependent dielectric constant as measured in experiments. Mean ionic activity coefficients for a number of salts could successfully be fitted up to 3 m concentration by adjusting only a mean ionic diameter. Difficulties encountered in simultaneously fitting the mean ionic activity and osmotic coefficients at salt concentrations >2 m are discussed.

37 citations

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TL;DR: In this paper, the authors focused on the correlation of the thermodynamic properties of aqueous solutions across a temperature range from (273.15 to 523.15) K by a simple two-parameter model.

Abstract: In this paper, we focused on the correlation of the thermodynamic properties of aqueous solutions across a temperature range from (273.15 to 523.15) K by a simple two-parameter model. This model is based on the modified three-characteristic-parameter correlation (TCPC) model. The two parameters, b, distance of closest approach, and S, solvation parameter, represent the interactions between ions and ions-molecules, respectively. The results show that it can adequately correlate the activity coefficient and osmotic coefficient of the single electrolyte solutions. The set of two characteristic parameters for many electrolytes was obtained. We also obtained the temperature-dependent parameters for these electrolytes. In over 70 % of the cases, six to eight parameters are necessary for an electrolyte. Compared with the Pitzer model, our model also represented a good performance.

20 citations

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TL;DR: It is shown that deviations from the Nernst–Einstein relation are proportional to the inverse viscosity by exploring the finite-size effect on transport properties under periodic boundary conditions.

Abstract: Deviations from the Nernst-Einstein relation are commonly attributed to ion-ion correlation and ion pairing. Despite the fact that these deviations can be quantified by either experimental measurements or molecular dynamics simulations, there is no rule of thumb to tell the extent of deviations. Here, we show that deviations from the Nernst-Einstein relation are proportional to the inverse viscosity by exploring the finite-size effect on transport properties under periodic boundary conditions. This conclusion is in accord with the established experimental results of ionic liquids.

18 citations

##### References

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TL;DR: In this paper, the osmotic coefficients and mean activity coefficients of uni-univalent electrolytes in aqueous solutions at 25 °C were derived using the molality or weight basis.

Abstract: This paper gives values for the osmotic coefficients and mean activity coefficients of uni‐univalent electrolytes in aqueous solutions at 25 °C. The values are expressed on the molality or weight basis. The data available in the literature have been corrected to the presently accepted scales of atomic weights (1969) and temperature (IPST 1968) and, where necessary, to the absolute electrical units of 1969 and the fundamental constants of 1963. The selected values of osmotic coefficients and mean activity coefficients for individual electrolytes have been made internally consistent thermodynamically. In some cases estimated values are given; in other cases, references only are given when the data are sparse or unsuited to critical evaluation. Values of the osmotic coefficients and mean activity coefficients of 79 compounds are given together with the standard deviation, variance, and normalized standard deviation of their fit to equations which express these quantities as functions of electrolyte concentration. Finally, literature references are given to data on 51 additional uni‐univalent electrolytes.

1,066 citations

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TL;DR: In this article, a generalized analytic correlation is presented for activity coefficient, enthalpy coefficient, and heat capacity of single and multicomponent strong aqueous solutions, where a good correlation for each salt to an ionic strength of six is obtained by assigning a single parameter "B" value to each salt.

Abstract: A generalized analytic correlation is presented for activity coefficient. osmotic coefficient, enthalpy, and heat capacity of single and multicomponent strong aqueous solutions. A good correlation for each salt to an ionic strength of six is obtained by assigning a single parameter “B” value to each salt. These B values are well approximated by assigning two parameters for each ion. Values presented for the common ions at 25°C allow the estimation of activity and osmotic coefficients of many unmeasured salt solutions.

773 citations

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TL;DR: In this article, the dielectric constants and loss angles of a series of concentrated aqueous ionic solutions have been measured at wave lengths of 10 cm, 3 cm, and 1.25 cm.

Abstract: The dielectric constants and loss angles of a series of concentrated aqueous ionic solutions have been measured at wave‐lengths of 10 cm, 3 cm, and 1.25 cm. From these results the values of the static dielectric constant and relaxation time for these solutions have been calculated on the basis of the Debye formula, which appears to hold accurately. All salts show a lowering of the dielectric constant and a shift in the relaxation time of water. It is found that the dielectric constant e can be represented by a formula e=eω+2δc, where eω is the dielectric constant of water, c is the concentration in moles per liter, and δ has values between −7 and −15 for various salts in concentrations of up to 2 M.In Part I the measurements are described and the results discussed in relation to the structure of ionic solutions. In Part II the validity of the Debye‐Sack saturation theory of the dielectric constant and the effects of the fall of dielectric constant on the electrolytic properties of concentrated solutions ...

617 citations

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492 citations

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TL;DR: In this article, the thermodynamic properties and radial distribution function of a primitive model electrolyte are calculated in the Mean Spherical Model (MSM) approximation, where the system considered is formally described as a classical fluid of charged hard spheres.

Abstract: The thermodynamic properties and radial distribution function of a ``primitive model electrolyte'' are calculated in the Mean Spherical Model (MSM) approximation. The system considered is formally described as a classical fluid of charged hard spheres (hard sheets in one dimension). The interaction potential between an ion of species i and an ion of species j, vij(r) is the sum of a Coulomb part and a hard core part qij(r)=∞ for r Rij, β being the inverse temperature. In this paper, which is the first of two in this topic, we give the method of solution for this approximation and obtain Cij(r) for r < Rij as polynomials in r, which have a structure similar to that found in the PY approximation for a mixture of uncharged hard spheres. We give the solution up to a set of algebrai...

422 citations