Electrolytes, activity coefficients solubility

Once the composition of the aqueous solution phase has been determined, the activity of an electrolyte having the same chemical formula as the assumed precipitate can be calculated (11,12). This calculation may utilize either mean ionic activity coefficients and total concentrations of the ions in the electrolyte, or single-ion activity coefficients and free-species concentrations of the ions in the electrolyte (11). If the latter approach is used, the computed electrolyte activity is termed an ion-activity product (12). Regardless of which approach is adopted, the calculated electrolyte activity is compared to the solubility product constant of the assumed precipitate as a test for the existence of the solid phase. If the calculated ion-activity product is smaller than the candidate solubility product constant, the corresponding solid phase is concluded not to have formed in the time period of the solubility measurements. Ihis judgment must be tempered, of course, in light of the precision with which both electrolyte activities and solubility product constants can be determined (12). 

It is important to note that the solubility product relation applies with sufficient accuracy for purposes of quantitative analysis only to saturated solutions of slightly soluble electrolytes and with small additions of other salts. In the presence of moderate concentrations of salts, the ionic concentration, and therefore the ionic strength of the solution, will increase. This will, in general, lower the activity coefficients of both ions, and consequently the ionic concentrations (and therefore the solubility) must increase in order to maintain the solubility product constant. This effect, which is most marked when the added electrolyte does not possess an ion in common with the sparingly soluble salt, is termed the salt effect. 

There are several factors through which anions can influence the pathway and O2 reduction kinetics. The main factors are competition with O2 for surface sites changes in the activity coefficients of the reactants, intermediates, and transition states and the acidity and dielectric properties of the electrolyte side of the interface [Adzic, 1998]. For example, perfluoro acids have higher O2 solubility and lower adsorbability than... 

Similarly, concepts of solvation must be employed in the measurement of equilibrium quantities to explain some anomalies, primarily the salting-out effect. Addition of an electrolyte to an aqueous solution of a non-electrolyte results in transfer of part of the water to the hydration sheath of the ion, decreasing the amount of free solvent, and the solubility of the nonelectrolyte decreases. This effect depends, however, on the electrolyte selected. In addition, the activity coefficient values (obtained, for example, by measuring the freezing point) can indicate the magnitude of hydration numbers. Exchange of the open structure of pure water for the more compact structure of the hydration sheath is the cause of lower compressibility of the electrolyte solution compared to pure water and of lower apparent volumes of the ions in solution in comparison with their effective volumes in the crystals. Again, this method yields the overall hydration number. 

Salting-out Coefficients at 25°C. The effect of an electrolyte on the solubility or activity of a gas dissolved in an aqueous solution is commonly expressed as a salting out coefficient ... 

Gamsjager, H. Schindler, P. "Solubilities and Activity Coefficients of H2S in Electrolyte Mixtures," Helv. Chim. Acta,1969, 52, 1395-1402. 

Very few generalized computer-based techniques for calculating chemical equilibria in electrolyte systems have been reported. Crerar (47) describes a method for calculating multicomponent equilibria based on equilibrium constants and activity coefficients estimated from the Debye Huckel equation. It is not clear, however, if this technique has beep applied in general to the solubility of minerals and solids. A second generalized approach has been developed by OIL Systems, Inc. (48). It also operates on specified equilibrium constants and incorporates activity coefficient corrections for ions, non-electrolytes and water. This technique has been applied to a variety of electrolyte equilibrium problems including vapor-liquid equilibria and solubility of solids. 

The papers in the second section deal primarily with the liquid phase itself rather than with its equilibrium vapor. They cover effects of electrolytes on mixed solvents with respect to solubilities, solvation and liquid structure, distribution coefficients, chemical potentials, activity coefficients, work functions, heat capacities, heats of solution, volumes of transfer, free energies of transfer, electrical potentials, conductances, ionization constants, electrostatic theory, osmotic coefficients, acidity functions, viscosities, and related properties and behavior. 

By measuring the solubility, r, of the silver chloride in different concentration of added salt and extrapolating the solubilities to zero salt concentration, or better, to zero ionic strength, one obtains the solubility when v = 1. and from Eq. (29) K can be found. Then y can be calculated using this value of K and any measured solubility. Actually, this method is only applicable to sparingly soluble salts. Activity coefficients of ions and of electrolytes can be calculated from the Debye-HOckel equations. For a uni-univalent electrolyte, in water at 25 C, the equation for the activity coefficient of an electrolyte is... 

Nitric acid is a strong electrolyte. Therefore, the solubilities of nitrogen oxides in water given in Ref. 191 and based on Henry s law are utilized and further corrected by using the method of van Krevelen and Hofhjzer (77) for electrolyte solutions. The chemical equilibrium is calculated in terms of liquid-phase activities. The local composition model of Engels (192), based on the UNIQUAC model, is used for the calculation of vapor pressures and activity coefficients of water and nitric acid. Multicomponent diffusion coefficients in the liquid phase are corrected for the nonideality, as suggested in Ref. 57. 

The activity a2 of an electrolyte can be derived from the difference in behavior of real solutions and ideal solutions. For this purpose measurements are made of electromotive forces of cells, depression of freezing points, elevation of boiling points, solubility of electrolytes in mixed solutions and other characteristic properties of solutions. From the value of a2 thus determined the mean activity a+ is calculated using the equation (V-38) whereupon by application of the analytical concentration the activity coefficient is finally determined. The activity coefficients for sufficiently diluted solutions can also be calculated directly on the basis of the Debye-Hiickel theory, which will bo explained later on. 

It is a function expressing the effect of charge of the ions in a solution. It was introduced by -> Lewis and Randall [iii]. The factor 0.5 was applied for the sake of simplicity since for 1 1 electrolytes I = c (electrolyte). It is an important quantity in all electrostatic theories and calculations (e.g., - Debye-Huckel theory, - Debye-Htickel limiting law, - Debye-Huckel-Onsager theory) used for the estimation of -> activity coefficients, -> dissociation constants, -> solubility products, -> conductivity of -> electrolytes etc., when independently from the nature of ions only their charge is considered which depends on the total amount (concentration) of the ions and their charge number (zj). 

Extrathermodynamic methods represent powerful tools for the evaluation of single-ion solvation quantities, but the available data are rather low in accuracy. Accurate knowledge of solubility and salt activity coefficients is highly desirable. Estimation of liquid-liquid junction potentials (particularly at nonaqueous-aqueous electrolyte... 

Values of Activity Coefficients.—Without entering into details, it is evident from the foregoing discussion that activities and activity coefficients are related to chemical potentials or free energies several methods, both direct and indirect, are available for determining the requisite differences of free energy so that activities, relative to the specified standard states, can be evaluated. In the study of the activity coefficients of electrolytes the procedures generally employed are based on measurements of either vapor pressure, freezing point, solubility or electromotive force. The results obtained by the various methods arc... 

It is not certain that the theoretical arguments, which led to the introduction of the term C t, are completely satisfactory, but it seems to be established that the experimental data require a term of this type. The aggregation of solvent molecules in the vicinity of an ion is the factor responsible for the so-called salting-out effect, namely, the decrease in solubility of neutral substances frequently observed in the presence of salts the constant C is consequently called the salting-out constant. The activity coefficient of a non-electrolyte, as measured by its solubility in the presence of electrolytes, is often given by an expression of the form log / = CV this is the result to which equation (62) would reduce for the activity of a non-electrolyte, i.e., when z+ and z arc zero, in a salt solution of ionic strength... 

Activity Coefficients from Solubility Measurements.—The activity coefficient of a sparingly soluble salt can be determined in the presence of other electrolytes by making use of the solubility product principle. In addition to the equations already given, this principle may be stated in still another form by introducing the definition of the mean ionic concentration, i.e., c , which is equal to c+clr, into equation (109) this equation then becomes... 

The method of calculation will be described with reference to thallous chloride, the solubility of which has been measured in the presence of various amounts of other electrolytes, with and without an ion in common with the saturating salt. By plotting the values of c for the thallium and chloride ions in solutions of different ionic strengths and extrapolating to zero, it is found that which in this case is equal to V, is 0.01428 at 25 (Fig. 58). It follows, therefore, from equation (122) that the mean activity coefficient of thallous chloride in any saturated solution is given by... 

The estimation of transfer activity coefficients was reviewed by Popovych. One method for measurement of transfer activity coefficients for electrolytes or neutral molecules is by measurement of solubility. When the solubility is low, the effects of contamination by traces of water can be profound. Furthermore, reliable solubility values even in water are difficult to obtain. Nevertheless, if saturated solutions of a substance in water and another solvent are considered, and if each solution can be shown to be in equilibrium with the same solid, the value of y, is given by the ratio of the solubility products ( sp)water/( sp)soivent electrolyte producing n ions. For... 

Broadly considered, solubilities depend in part on nonspecific electrolyte effects and in part on specific effects. The nonspecific effects can be considered in terms of activity coefficients (Chapter 2). But activity-coefficient effects often are negligible compared with the uncertainties arising from disregarded or unknown side reactions and also with uncertainties arising from the crystalline state, the state of hydration, the extent of aging of the precipitate, and intrinsic solubility, all of which may contribute to the solubility of the precipitate. To the extent that each can be identified and measured, each can be accounted for. Nevertheless, the magnitude of unsuspected effects makes it expedient to assume activity coefficients of unity unless otherwise specifically indicated for relatively soluble salts or solutions containing moderate amounts of electrolytes. 

Equation (7-4) indicates that the solubility product includes an activity-coefficient term, a term which has been assumed to be unity up to this time. The introduction to this chapter pointed out that errors arising from neglect of the effects of the activity coefficient are usually small when compared with several uncertainties or side reactions. The activity coefficient in Equation (7-4) depends on the kind and concentration of all electrolytes in solution, not merely those involved directly with the precipitate. The correction to solubility calculations that must be made to account for the activity-coefficient effect is known as the diverse ion effect. The appropriate background is discussed in Chapter 2, and Problems 2-1,2-2, and 2-3 are examples of the calculations. For 1 1 electrolytes in solution, activity coefficients can usually be assumed to be unity when concentrations are much less than 0.1 M. Common ion and diverse ion effects can be significant at the same time, for example, when a large excess of common ion is added in a precipitation. The diverse ion effect is one of the reasons that the haphazard addition of a large excess of precipitant should be avoided. 

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