1.10.24: Gibbs Energies- Salt Solutions- Pitzer's Equations
- Page ID
- 385635
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)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.