272
i. Grenthe
X and Yare known quantities that depend only on the charge type of the electrolyte, the ionic strength/molality and A,p. The linear function Y of X has the intercept
(f3fJL - €y(M,L) /2) and the slope 13m. The functions Y(X) are plotted in Fig. 10.2 for I1,2-1 and 3-1 ion combinations.
The linearity is very good, indicating that the SIT-model is approximatelr equivalent to the Pitzer model without the C charge type. The relationships between the two sets of parameters given in Table 10.1
for different ion combinations may be used to convert the large set of er. values already
available (Pitzer 1991, Guggenheim 1935) for complexes, into {f0) and If!) values. Note
that e values, not e}' are tabulated in Pitzer (1991) and Guggenheim (1935); the relationship between them is ey= eln (10). The difference is due to the use of decadic and
e logarithms, respectively.
The estimated values of If 0 for 3-1 and 4-1 interactions (If!) = 4.3 for 3-1 and 1-3,
and If 0 = 8.9 for 4-1 and 1-4 interactions) seem to be slightly lower than the "averaged"
values from Pitzer (1991), If!) = 5.2 ±1.2 and If 0 = 11 ±2, respectively.
It is not straightforward to determine Pitzer parameters from experimental mean
activity factors, and osmotic coefficient data. The interaction parameters are often
strongly correlated, and different experiments may not always give concordant results.
It is therefore advisable to investigate how sensitive the calculated activity coefficients
are for variations in the Pitzer parameters. Example 1 demonstrates the use of the two
models for a simple protolytic equilibrium and also how sensitive the Pitzer model is
for the numerical values of the parameters.
Use of the Pitzer model in equilibrium analysis. Here we are faced with slightly different problems from those described above. Pitzer parameters for complexes can rarely
be determined from mean activity coefficients; they have to be deduced from the ionic
strength/ionic medium dependence of equilibrium constants. This requires a very large
experimental effort and very precise values of the equilibrium constants. Very few data
of this type are available. A simplifying factor for the Pitzer analysis is when the reactants/products are present in such a low concentration that the main ion-ion interactions are those between the medium ions themselves and between the medium ions
and the reactants/products.
Complex formation equilibria are in general described using concentration equilibrium constants; these are "true" thermodynamic quantities as long as concentrations and activities for reactants/products are proportional to one another in the ionic
medium used. Each ionic medium may thus be considered as a particular solvent. A
practical way to compare equilibrium constants obtained in different ionic media is
to use one reference medium, usually pure water. A simplified Pitzer model for the
Table 10.1. Quantitative
(fP-£/2l
rP)
relationship between the
Ion combination
Pitzer parameters {f0) and
{fl) and the SIT parameter
M+,X0.035
0.34 = 0.3
Erfor different ion combinaM 2 +, X- and M+, X20.150
1.56 = 1.6
tions
M 3 +, X- and M+, X 3 -
0.366
4.29 ",,4.3
M 4 +, X- and M+, X 4 -
0.754
8.89",,8.9
i. Grenthe
X and Yare known quantities that depend only on the charge type of the electrolyte, the ionic strength/molality and A,p. The linear function Y of X has the intercept
(f3fJL - €y(M,L) /2) and the slope 13m. The functions Y(X) are plotted in Fig. 10.2 for I1,2-1 and 3-1 ion combinations.
The linearity is very good, indicating that the SIT-model is approximatelr equivalent to the Pitzer model without the C charge type. The relationships between the two sets of parameters given in Table 10.1
for different ion combinations may be used to convert the large set of er. values already
available (Pitzer 1991, Guggenheim 1935) for complexes, into {f0) and If!) values. Note
that e values, not e}' are tabulated in Pitzer (1991) and Guggenheim (1935); the relationship between them is ey= eln (10). The difference is due to the use of decadic and
e logarithms, respectively.
The estimated values of If 0 for 3-1 and 4-1 interactions (If!) = 4.3 for 3-1 and 1-3,
and If 0 = 8.9 for 4-1 and 1-4 interactions) seem to be slightly lower than the "averaged"
values from Pitzer (1991), If!) = 5.2 ±1.2 and If 0 = 11 ±2, respectively.
It is not straightforward to determine Pitzer parameters from experimental mean
activity factors, and osmotic coefficient data. The interaction parameters are often
strongly correlated, and different experiments may not always give concordant results.
It is therefore advisable to investigate how sensitive the calculated activity coefficients
are for variations in the Pitzer parameters. Example 1 demonstrates the use of the two
models for a simple protolytic equilibrium and also how sensitive the Pitzer model is
for the numerical values of the parameters.
Use of the Pitzer model in equilibrium analysis. Here we are faced with slightly different problems from those described above. Pitzer parameters for complexes can rarely
be determined from mean activity coefficients; they have to be deduced from the ionic
strength/ionic medium dependence of equilibrium constants. This requires a very large
experimental effort and very precise values of the equilibrium constants. Very few data
of this type are available. A simplifying factor for the Pitzer analysis is when the reactants/products are present in such a low concentration that the main ion-ion interactions are those between the medium ions themselves and between the medium ions
and the reactants/products.
Complex formation equilibria are in general described using concentration equilibrium constants; these are "true" thermodynamic quantities as long as concentrations and activities for reactants/products are proportional to one another in the ionic
medium used. Each ionic medium may thus be considered as a particular solvent. A
practical way to compare equilibrium constants obtained in different ionic media is
to use one reference medium, usually pure water. A simplified Pitzer model for the
Table 10.1. Quantitative
(fP-£/2l
rP)
relationship between the
Ion combination
Pitzer parameters {f0) and
{fl) and the SIT parameter
M+,X0.035
0.34 = 0.3
Erfor different ion combinaM 2 +, X- and M+, X20.150
1.56 = 1.6
tions
M 3 +, X- and M+, X 3 -
0.366
4.29 ",,4.3
M 4 +, X- and M+, X 4 -
0.754
8.89",,8.9