Activity coefficients of ions

In the preceding section, a theoretical approach to the evaluation of ionic activity coefficients was developed and was based on the Debye-Huckel theory, which was experimentally verified in dilute solutions of electrolytes. In solutions of ionic strengths greater than 0.15 to 0.2, empirical values of activity coefficients must replace those calculated from Equation 3-8 to provide an adequate accuracy. 

Activity coefficients of single ions cannot be measured directly. Instead, on the basis of experiments in which the free energy of an electrolyte is determined by various methods (such as by measuring freezing point depressions of solutions or by the measurement of the e.m.f. s of cells), a quantity called the mean ionic activity coefficient is obtained. For an electrolyte the mean ionic activity coefficient is defined as follows  

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Table 8.1 Individual Activity Coefficients of Ions In Water at 25°C 8.3...

Values for the activity coefficients of ions in water at 25°C are given in Table 8.1 in terms of their effective ionic radii. 

Here Yi and y2 are the activity coefficients of ions in solution, y, and y2 are the coefficients of resin activity, cx and c2 are ion concentrations in solution, ntj and m2 are fixed ion concentrations (exchange or weight concentrations) and Ks is the concentration constant of ion exchange, the selectivity constant. 

If one of the partners in a second-order reaction is not an ion, then in ideal solutions there will be little effect of added salts on the rate. The activity coefficient of a nonelectrolyte does not depend strongly on ionic strength the way that the activity coefficients of ions do. In a reaction with only one participating ion, it and the transition... 

The beginning of the twentieth century also marked a continuation of studies of the structure and properties of electrolyte solution and of the electrode-electrolyte interface. In 1907, Gilbert Newton Lewis (1875-1946) introduced the notion of thermodynamic activity, which proved to be extremally valuable for the description of properties of solutions of strong electrolytes. In 1923, Peter Debye (1884-1966 Nobel prize, 1936) and Erich Hiickel (1896-1981) developed their theory of strong electrolyte solutions, which for the first time allowed calculation of a hitherto purely empiric parameter—the mean activity coefficients of ions in solutions. 

The formal Galvani potential, described by Eq. (22), practically does not depend on the concentration of ions of the electrolyte MX. Since the term containing the activity coefficients of ions in both solutions is, as experimentally shown, equal to zero it may be neglected. This results predominantly from the cross-symmetry of this term and is even more evident when the ion activity coefficients are replaced by their mean values. A decrease of the difference in the activity coefficients in both phase is, in addition, favored by partial hydration of the ions in the organic phase [31 33]. Thus, a liquid interface is practically characterized by the standard Galvani potential, usually known as the distribution potential. 

The original Debye-Huckel expression for the calculation of the activity coefficients of ions is... 

The most significant chemical equilibria present in flue gas scrubbing slurries are outlined. Expressions for temperature dependent equilibrium constants are presented that are suitable for the temperature ranges encountered in scrubbing applications. Expressions for activity coefficients of ions and ion-pairs are presented that are suitable for the ranges of ionii strengths encountered for this type of applications. 

Kielland, J. "Individual Activity Coefficients of Ions in Aqueous Solutions," J. Amer. Chem. Soc., 1937, j>9, 1675-78. 

The ratio of the activity coefficients of ion pairs JA and KA was assumed equal to one. 

For aqueous solutions of salts, lt, (P, 7) represents the chemical potential of pure ions. This chemical potential cannot be measnred experimentally. Instead of nsing this hypothetical standard state, the activity coefficients of ions often are normalized by introducing the asymmetrical activity coefficient, y,, defined as... 

Gibbs Energies of Transfer and Transfer Activity Coefficients of Ions... 

Tab. 2.7 Transfer activity coefficients of ions from water to non-aqueous solvents [log yt (i,W— S)] ... 

Activity coefficients of ions are determined using electromotive force, freezing point, and solubility measurements or are calculated using the theoretical equation of Debye and Htickel. 

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... 

Plot the activity coefficients of ions with charges 1, 2, 3, and 4 versus the ionic strength at 0 °C. Repeat these calculations at 25 °C and 40 °C... 

Activity coefficients of ions and the pH s of solutions can also be obtained from electrochemical measurements. 

In the context of RTILs the criterion (3) raises considerable problems since the concept of activity and activity coefficients of ions is largely unexplored in such media. Accordingly, validation of the applicability of the Nernst equation in such media is a non-simple exercise, given that RTILs are likely to exhibit gross non-ideality. Rather, electrochemical measurements based on otherwise validated reference electrodes, may likely in the future provide a methodology for the study of RTIL non-ideality. 

Figure 2.1. Relationship between solution ionic strength and single-ion activity coefficients of ions with different valencies. Calculated utilizing the extended Debye-Huckle equation) (from Skoog and West, 1976, with permission).

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