1.10.24: Gibbs Energies- Salt Solutions- Pitzer's Equations
The Debye-Huckel treatment of the properties of salt solutions is based on a linearization of the Botzmann Equation leading to an equation for the radial distribution function, \(\mathrm{g}_{i j} (\mathrm{r})\). If a further term is taken into the expansion, the equation for \(\mathrm{g}_{i j} (\mathrm{r})\) takes the following form [1].
\[g_{i j}(r)=1-q_{i j}+\left(q_{i j}^{2} / 2\right) \nonumber \]
When equation (a) was tested against the results of a careful Monte Carlo calculation the conclusion was drawn that the three-term equation is good approximation [2]. The result is a set of equations for both the practical osmotic coefficient \(\phi\) and mean ionic activity coefficient for the salt in a solution having ionic strength \(\mathrm{I}\) [3,4]. The theory has been extended to consider the properties of salt solutions at high \(\mathrm{T}\) and \(\mathrm{p}\) [5,6]. In fact key parameters in Pitzer equations covering extensive ranges of \(\mathrm{T}\) and \(\mathrm{p}\) have been extensively documented [7]. The Pitzer treatment has been extended to a consideration of the properties of mixed salt solutions [8].
Footnotes
[1] K. S. Pitzer, Acc. Chem.Res.,1977, 10 ,371.
[2] D. N. Card and J. P. Valleau, J. Chem. Phys.,1970, 52 ,6232.
[3] K. S. Pitzer, J.Phys.Chem.,1973, 77 ,268.
[4] Activity and Osmotic Coefficients for
- 1:1 salts: K. S. Pitzer and G. Mayorga, J.Phys.Chem.,1973, 77 ,2300.
- For 2:2 salts: K. S. Pitzer and G. Mayorga, J. Solution Chem., 1974, 3 ,539.
-
For 3:2 salts etc;
- K. S. Pitzer and L. V. Silvester, J.Phys.Chem.,1978, 82 ,1239.
- L. F. Silvester and K. S. Pitzer, J. Solution Chem.,1978, 7 ,327.
- K. S. Pitzer, J. R. Peterson and L. E. Silvester, J. Solution Chem.,1978, 7 ,45.
[5]
- R. C. Phutela, K. S. Pitzer and P. P. S. Saluja, J. Chem. Eng. Data, 1987, 32 ,76.
- H. F. Holmes and R. E. Mesmer, J. Phys.Chem.,1983, 87 ,1242.
[6] R. C. Phutela and K. S. Pitzer, J. Phys Chem.,1986, 90 ,895.
[7]
- J. Ananthaswamy and G. Atkinson, J. Chem. Eng. Data,1984, 29 ,81.
- R. P. Beyer and B. R. Staples, J. Solution Chem.,1986, 15 ,749.
- P. P. S. Salija, K. S. Pitzer and R. C. Phutela, Can J.Chem.,1986, 64 ,1328.
- R. T. Pabalan and K. S. Pitzer, J. Chem. Eng. Data, 1988, 33 ,354.
[8]
- R. C. Phutela and K. S. Pitzer, J. Solution Chem.,1986, 15 ,649.
- A. Kumar, J. Chem. Eng. Data,1987, 32 ,106.
- K. S. Pitzer and J. J. Kim, J. Am. Chem.Soc.,1974, 96 ,5701.
- K. S. Pitzer and J. M. Simonson, J. Phys.Chem,.,1986, 90 ,3005.
- C. J. Downes and K.S. Pitzer, J. Solution Chem.,1976, 5 ,389.
- J. C. Peiper and K. S. Pitzer, J.Chem.Thermodyn.,1982, 14 ,613.