Activity coefficient of electrolyte solutes

In 1923 Peter Debye and Erich HUckel published two remarkable papers that described an a priori method of calculating the activity coefficient of electrolytic solutes in dilute solution. Without doubt this was one of the major breakthroughs in electrolyte solution theory. 

Many different techniques can be used to measure activity coefficients of electrolytic solutes, many of which are electrochemical. Most of these methods are reviewed in standard references (e.g., Harned and Owen, 1958 Monk, 1961 Robinson and Stokes, 1968, Ch. 8). Solutions of geological interest can span considerable temperature ranges, and it has often proven simplest experimentally to measure the activity of the... 

Electromotive force (emf) measurements are frequently used to determine activity coefficients of electrolyte solutions. Equation (136a) relates the emf to the activities of the reacting cell components. From concentration-dependent measurements the standard potential E° of the cell reaction and the activity coefficients can be obtained. As an example, according to Eq. (136a), the emf of the Galvanic cell... 

The Debye-Hiickel theory provides an accurate limiting law for the activity coefficients of electrolyte solutes. A semi-empirical equation, the Davies equation, can provide usable estimates of electrolyte activity coefficients at larger concentrations. 

Further on, Kunz et al could show that this failure of the simplified dispersion model is not a consequence of the weakness of the Poisson-Boitzmann equation. More elaborate statistical mechanics, using the so-called hypernetted chain equation (HNC), yielded basically the same result. Obviously the problem comes from the neglect of ion-water interactions and their changes near the surface. To introduce such interactions in primitive model calculations, Bostrom et al [see also Refs. 13(b)-13(d)] used Jungwirth s water profile perpendicular to the surface as a basis to model a distance-dependent electrostatic function, instead of a static dielectric constant. Such ideas were used several times over the years, for instance to model activity coefficients of electrolyte solutions. ... 

Moggia, E. Bianco, B. (2007) Mean activity coefficients of electrolyte solutions. J. Phys. Chem. B 111, 12,3183-3191, ISSN 1089-5647... 

Equation (7.45) is a limiting law expression for 7 , the activity coefficient of the solute. Debye-Htickel theory can also be used to obtain limiting-law expressions for the activity a of the solvent. This is usually done by expressing a in terms of the practical osmotic coefficient

electrolyte solute, it is defined in a general way as... 

In view of the electrostatic nature of forces that primarily lead to deviation of the behaviour of electrolyte solutions from the ideal, the activity coefficient of electrolytes must depend on the electric charge of all the ions present. G. N. Lewis, M. Randall and J. N. Br0nsted found experimentally that this dependence for dilute solutions is described quite adequately by the relationship... 

A second type of ternary electrolyte systems is solvent -supercritical molecular solute - salt systems. The concentration of supercritical molecular solutes in these systems is generally very low. Therefore, the salting out effects are essentially effects of the presence of salts on the unsymmetric activity coefficient of molecular solutes at infinite dilution. The interaction parameters for NaCl-C02 binary pair and KCI-CO2 binary pair are shown in Table 8. Water-electrolyte binary parameters were obtained from Table 1. Water-carbon dioxide binary parameters were correlated assuming dissociation of carbon dioxide in water is negligible. It is interesting to note that the Setschenow equation fits only approximately these two systems (Yasunishi and Yoshida, (24)). 

Stokes, R. H. Thermodynamics of solutions. In Activity Coefficients in Electrolyte Solutions, Pytkowicz, R. M., Ed., Vol. I, CRC Press, Boca Raton, Florida, 1979 1-28. 

Johnson, K. S. Pytkowicz, R. M. Ion association and activity coefficients in multicomponent solutions. In Activity Coefficients in Electrolyte Solutions, Pytkowicz, R. M., Ed., Vol. II, CRC Press, Boca Raton, Florida, 1979 1-62. Millero, F. J. Effects of pressure and temperature on activity coefficients. In Activity Coefficients in Electrolyte Solutions, P5dkowicz, R. M., Ed., Vol. II, CRC Press, Boca Raton, Florida, 1979, pp. 63-151. 

I. 46. The magnitude of the coefficient reflects the electric charge distribution of the ionic species. A 0.1 molal solution of Al2(S04)3 has an activity coefficient of only 0.035. It should also be noted that, in dilute solutions, activity coefficients of electrolytes decrease in magnitude with increasing concentration. A minimum is reached and the coefficient then increases with concentration. See Activity Debye-Huckel Law Biomineralization... 

Mean activity coefficient of electrolyte B in solution is given by... 

Belveze, L.S., Brennecke, J.F., and Stadtherr, M.A., Modeling of activity coefficients of aqueous solutions of quaternary ammonium salts with the electrolyte-NRTL equation, Ind. Eng. Chem. Res., 43, 815, 2004. 

K. S. Pitzer, Ion Interaction Approach Theory and Data Correlation , Chapter 3 of Activity Coefficients in Electrolyte Solutions, 2nd Edition, K. S. Pitzer, Editor, CRC Press, Boca Raton, 1991, p. 82. 

Equations used to calculate L and 4>CP are taken from K. S. Pitzer, Ion interaction approach theory and data correlation , Chapter 3 in Activity Coefficients in Electrolyte Solutions, 2nd Edition, K. S. Pitzer, Editor, CRC Press, Boca Raton, Florida, 1991. Equations for calculating L, L2, Ju and J2 are summarized in K. S. Pitzer, J. C. Peiper, and R. H. Busey, Thermodynamic properties of aqueous sodium chloride solutions , J. Phys. Chem. Ref Data, 13, 1-102 (1984). 

Just as we discussed in Chapter 9, we can use measured activities of solvents (determined from vapor pressure, freezing-point depression, boiling-point elevation, or osmotic pressure) to determine activity coefficients of electrolytes in solution. For an ionic substance, the Gibbs-Duhem equation is... 

It follows from the last equation that the net work gained by the dilution of an actual solution of an ion concentration c (c > 1) to the state of an ideal solution, with concentration c = 1, equals the sum of two constituents. The term of the first constituent, RT In c, expresses the energy gained by the dilution of the ideal solution and the second one, RT In y, represents the work, required to overcome the effect of the interionic electrical forces. Since the last mentioned electrical work reduces tho value of the work W, which would l>e gained by the dilution of an ideal solution, the expression RT In y must have a negative value, or in other words the activity coefficient of actual solutions y < 1. It follows further from this conception that the potential of an electrolyte contained in an actual solution must be lower than the potential of the same substance in an ideal solution. 

As can be seen from these equations the specific nature of individual ions is not expressed any more in very diluted solutions and the activity coefficient is determined solely by the ionic strength and the valence type of the electrolyte. Assuming the solutions to be properly diluted, the activity coefficients of electrolytes of the same valence type are identical in all solutions of the same ionic strength. 

Millero, F.J. Effects of pressure and temperature on activity coefficients, Ch. 13, in Pytkowicz, R.M., ed. "Activity Coefficients in Electrolyte Solutions," CRC Press, W. Palm Beach, Florida (in press). 

Individual Ion Activities.—The methods described in Chap. V for the determination of the activities or activity coefficients of electrolytes, e well as those depending on vapor pressure, freezing-point or other osmotic measurements, give the nean values for b >th ions into which the solute A convenient form of this equat ion for approximate purposes is... 

Corresponding to each chemical potential there is an activity coefficient defined in terms of equation (20.4). By convention, the activity coefficients of electrolytes are always expressed in terms of the ideal dilute solution as standard reference state, cf. chap. XXI, 3. Thus in the case of an aqueous NaCl solution we may write... 

In discussing the relation between the activity coefficients of electrolytes and the concentration of the 4 90 solution, use is made of the ionic strength, defined by... 

In the foregoing method the mean ionic activity coefficient of the solute has been calculated from actual vapor pressure data. If the osmotic coefficients for a reference substance are known over a range of concentrations, the activity coefficients of another electrolyte can be derived from isopiestic measurements, without actually determining the vapor pressures. If w, and p refer to an experimental electrolyte and wr, 0r and vr apply to a reference electrolyte which is isopiestic (isotonic) with the former, then by equation (39.46)... 

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