Activity coefficients mean ion

Comparison of the concentrations of either the cation or the anion in the two phases thus has potential for evaluating the polyanion valence provided that estimates of the mean ion activity coefficient (y ) are available. Furthermore, as realized by Svensson [165], expression of the Donnan distribution of small ions in this manner has two advantages in that (i) Eq. 31 applies to each type of small ion in situations where the supporting electrolyte is not restricted to single cationic and anionic species and (ii) multivalence of a small ion is also accommodated. 

We define the mean ion activity coefficient as the geometric mean of the single-ion activity coefficients... 

The mean ion activity coefficient values can be obtained from experiments where the effect of electrolyte concentration on the A sp value for a salt is determined. The mean values are then compared with those for KCl under the same solution conditions. The single-ion activity coefficient for Ca " " can then be computed if an assumption is made about the individual values for and Cl. These ions have the same magnitude of charge and similar electronic configuration, ionic radii, and ionic mobilities. On the basis of these properties, the Macinnes convention (1919) states that... 

With the use of equation 6, a table of values for other ions can be built up from the appropriate mean ion activity coefficients for example, for a monovalent chloride. 

The simplest procedure based on the Br nsted-Guggenheim hypothesis gives rise to an equation for the mean ion activity coefficient that consists only of an electrostatic term and a statistical term linear in the salt concentration (see Whitfield, 1973, 1975b) ... 

Pitzer and co-workers (1973, 1974) have proposed a more detailed, but at the same time more complex, approach. Whitfield (1973, 1975) has applied these equations to seawater and has shown that this model gives good agreement with available experimental data for the osmotic coefficient and for the mean ion activity coefficient of the major electrolyte components. The results obtained yield numerical results similar to the predictions of the ion association model (see Table A6.2). 

The anion and cation may each have a different ionic activity in solution and it is not possible to determine individual ionic activities experimentally. It is therefore necessary to use combined terms, for example the combined activity term is the mean ionic activity, a . Similarly, we have the mean ion activity coefficient, and the mean ionic molality, m+. The relationship between the mean ionic parameters is then... 

Values of the mean ion activity coefficient may be determined experimentally using several methods, including electromotive force measurement, solubility determinations and colligative properties. It is possible, however, to calculate y+ in very dilute solution... 

Similarly, we may also define a mean ion activity coefficient, y, in terms of the individual ionic activity coefficients y and y ... 

We cannot measure the individual ion activity coefficients here, only their total effect on /f,p. It is convenient to lump this total effect in the geometric mean of the product of the individual activity coefficients and to call this the mean ion activity coefficient of the salt. Thus for a K2SO4 solution, by definition... 

In general, for an electrolyte that dissociates into a total of n ions, the mean ion activity coefficient equals, by definition,... 

The mean ion activity coefficients of several salts taken from tables in Robinson and Stokes (1970) are plotted against ionic strength in Fig. 4.1. For reasons discussed later in this chapter, y ... 

Define the mean ion activity coefficient of a salt and comment on its significance in a weak versus a strong electrolyte solution. 

If a binary electrolyte dissociates giving v ions of which v+ are positive and v are negative then the mean Ion activity coefficient may be defined by... 

Thus the relation of these mean ion activities and mean ion activity coefficients to the chemical potential of the electrolyte, fxa, is from equation (37)... 

This ft is the ion activity coefficient of the ion constituent i. To obtain a mean ion activity coefficient,, for a binary electrolyte we may use the relation, (34a), Chapter 6,... 

Here [Zn] and [Cl] represent the molalities of the constituents indicated and y is the mean ion activity coefficient. This equation can be rearranged to... 

Although one can usually only measure mean-ion activity coefficients for neutral combinations of ions, it is sometimes convenient to use expressions for single-ion activity coefficients which can then be combined to obtain mean-ion coefficients. For... 

Table II. Calculated mean-ion activity coefficients in a sample FGD solution.

Figure 3. Pitzer and effective Radian mean-ion activity coefficients of CaSOt when MgSOt is added to a 0.01 M CaSO( solution at 50°C. The dotted lines represent the behavior of pure CaSOi (extrapolated beyond saturation).

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