CHAPTER 10 . Equilibrium Analysis, the Ionic Medium Method and Activity Factors
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ing is very convenient for the estimation of the Pitzer parameter /1[f!) for reactions,
because it only requires the value of the sum of squared charges of the ions participating in the reaction, /1Z2. One can show that for isocoulombic reactions, where
/1Z 2 = 0, the proposed result is consistent with /1[f!) = o.
Using the data in Table 10.2 we can now estimate the values of Xl and X2,
c.f. Example 2, for the protonation of sulphate, for which we obtain Xl = -0.11 ±0.07
and X2 = -1.35 ±0.05, in good agreement with the results in Table 1004Equation 10.25 was obtained by neglecting the contribution of the terms for higherorder electrostatic unsymmetrical mixing. By including these terms, the slope of the
function Y is changed somewhat, particularly for ions of charge 3 or higher.
Because the determination of the Pitzer parameters for a reaction (or for complexes)
from logK data is an ill-conditioned problem, it is rarely possible to determine more
than one interaction parameter. We therefore suggest the following strategy when using logK data determined in 1-1 electrolyte ionic media to determine the Pitzer parameters for complexes:
1. Use the SIT equation to obtain logK>.
2. Estimate X2 from the /1Z 2 value for the reaction if the charge of the reactants/products do not exceed 2 and calculate Xl using X2 as a fixed parameter. The terms
m 2 /11 Z 1 C NX and higher-order electrostatic unsymmetrical mixing terms for the ionic
medium ions should be included for data at high ionic strength.
3. Calculate the Pitzer parameters for the complexes from the values of with /1[f0) and
with /1[fI) and the corresponding quantities [f0) and [f!) for the reactants.
4. In order to describe equilibrium data at higher ionic strengths or mixed electrolyte
systems, it is necessary to determine additional interaction parameters. This can only
be achieved by additional equilibrium constant measurements under these conditions.
10.6
Determination of Interaction Parameters
The interaction parameters in the two models must be determined from experimental mean activity coefficients, osmotic coefficients and/or concentration equilibrium
constants. The accuracy of these data are typically ±0.005 in log y± or C/J, and ten to fifty
times lower for concentration equilibrium constants. These constants have usually been
determined at only a few ionic strengths. For the users of thermodynamic data, it is
essential to be aware of the limitations of the methods used to make activity corrections and the consequences of approximations in the models. It is useful to find relationships, c.f. Eq. 10.22, between the interaction parameters in the two models and
between the corresponding quantities for reactions. This is practical when one wishes
to use the extensive compilations of Pitzer parameters for strong electrolytes together
with the compilation of SIT parameters for complexes.
Examples of the use of the specific ion interaction models are in equilibrium analysis.
In the following, I will present three examples of the use of specific ion interaction
methods.
277
ing is very convenient for the estimation of the Pitzer parameter /1[f!) for reactions,
because it only requires the value of the sum of squared charges of the ions participating in the reaction, /1Z2. One can show that for isocoulombic reactions, where
/1Z 2 = 0, the proposed result is consistent with /1[f!) = o.
Using the data in Table 10.2 we can now estimate the values of Xl and X2,
c.f. Example 2, for the protonation of sulphate, for which we obtain Xl = -0.11 ±0.07
and X2 = -1.35 ±0.05, in good agreement with the results in Table 1004Equation 10.25 was obtained by neglecting the contribution of the terms for higherorder electrostatic unsymmetrical mixing. By including these terms, the slope of the
function Y is changed somewhat, particularly for ions of charge 3 or higher.
Because the determination of the Pitzer parameters for a reaction (or for complexes)
from logK data is an ill-conditioned problem, it is rarely possible to determine more
than one interaction parameter. We therefore suggest the following strategy when using logK data determined in 1-1 electrolyte ionic media to determine the Pitzer parameters for complexes:
1. Use the SIT equation to obtain logK>.
2. Estimate X2 from the /1Z 2 value for the reaction if the charge of the reactants/products do not exceed 2 and calculate Xl using X2 as a fixed parameter. The terms
m 2 /11 Z 1 C NX and higher-order electrostatic unsymmetrical mixing terms for the ionic
medium ions should be included for data at high ionic strength.
3. Calculate the Pitzer parameters for the complexes from the values of with /1[f0) and
with /1[fI) and the corresponding quantities [f0) and [f!) for the reactants.
4. In order to describe equilibrium data at higher ionic strengths or mixed electrolyte
systems, it is necessary to determine additional interaction parameters. This can only
be achieved by additional equilibrium constant measurements under these conditions.
10.6
Determination of Interaction Parameters
The interaction parameters in the two models must be determined from experimental mean activity coefficients, osmotic coefficients and/or concentration equilibrium
constants. The accuracy of these data are typically ±0.005 in log y± or C/J, and ten to fifty
times lower for concentration equilibrium constants. These constants have usually been
determined at only a few ionic strengths. For the users of thermodynamic data, it is
essential to be aware of the limitations of the methods used to make activity corrections and the consequences of approximations in the models. It is useful to find relationships, c.f. Eq. 10.22, between the interaction parameters in the two models and
between the corresponding quantities for reactions. This is practical when one wishes
to use the extensive compilations of Pitzer parameters for strong electrolytes together
with the compilation of SIT parameters for complexes.
Examples of the use of the specific ion interaction models are in equilibrium analysis.
In the following, I will present three examples of the use of specific ion interaction
methods.