1.14.59: Salting-In and Salting-Out
A classic subject concerning the properties of salt solutions has centred for more than a century on the effects of an added salt on the solubility of an apolar (volatile) solute.
In terms of the Phase Rule, a given closed system contains two phases, gas and liquid. The liquid phase is an aqueous salt solution. A volatile chemical substance is distributed between the vapour and liquid phases. Hence the number of phases \(\mathrm{P}\) equals 2; the number of components \(\mathrm{C}\) equals 3; i.e. water + salt + volatile chemical substance. Hence the number of degrees of freedom \(\mathrm{F}\) equals 3. If therefore we define the temperature, pressure and concentration of salt in the aqueous salt solution, the thermodynamic equilibrium is completely defined.
Similarly if the closed system contains pure liquid \(j\) and an aqueous salt solution which also contains solute \(j\), the number of degrees of freedom is again 3. Then the equilibrium state is completely defined by specifying \(\mathrm{T}, \mathrm{~p}\) and the concentration (molality) of salt in solution. In this case the equilibrium at defined \(\mathrm{T}\) and \(\mathrm{p}\) is defined by Equation \ref{a}.
\[\mu_{\mathrm{j}}^{*}(\ell)=\mu_{\mathrm{j}}^{\mathrm{eq}}(\mathrm{aq})\label{a} \]
In the absence of salt, treating substance \(j\) as a solute in aqueous solution, Equation \ref{b} describes this equilibrium in terms of the equilibrium composition of the solution assuming ambient pressure is close to the standard pressure.
\[\mu_{\mathrm{j}}^{*}(\ell)=\mu_{\mathrm{j}}^{0}(\mathrm{aq})+\mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{m}_{\mathrm{j}} \, \gamma_{\mathrm{j}} / \mathrm{m}^{0}\right)_{\mathrm{aq}}^{\mathrm{cq}}\label{b} \]
A similar equilibrium is established but this time the aqueous solution contains a salt, molality \(\mathrm{m}_{\mathrm{s}}\). Equation \ref{b} takes the following form.
\[\mu_{\mathrm{j}}^{*}(\ell)=\mu_{\mathrm{j}}^{0}(\mathrm{aq})+\mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{m}_{\mathrm{j}} \, \gamma_{\mathrm{j}} / \mathrm{m}^{0}\right)_{\mathrm{s}}^{\mathrm{\alpha q}}\label{c} \]
The subscript on the last term in Equation \ref{c} indicates that the aqueous solution contains salt \(\mathrm{S}\) as well as apolar solute \(j\). According to equations \ref{b} and \ref{c}, the two solubilities of substance \(j\) are related.
\[\left(m_{j} \, \gamma_{j}\right)_{a q}^{e q}=\left(m_{j} \, \gamma_{j}\right)_{s}^{e q}\label{d} \]
Equation \ref{d} is thermodynamically correct. The change in solubility of chemical substance \(j\) on adding salt \(\mathrm{S}\), molality ms is compensated by a change in the activity coefficient of solute \(j\). The corresponding equation on the concentration scale has the form shown in Equation \ref{e}.
\[\left(c_{j} \, y_{j}\right)_{a q}^{e q}=\left(c_{j} \, y_{j}\right)_{s}^{e q}\label{e} \]
The latter is the usual form of the equation. The analysis is readily repeated for the case where the chemical substance \(j\) is a volatile gas.
At this stage a number of extra-thermodynamic assumptions are built into the analysis. To reduce the clutter of symbols we drop the designation ‘\(\mathrm{eq}\)’ taking this condition as implicit in all that follows. Further we assume that substance \(j\) is sparingly soluble so that in the aqueous solution \(j-j\) solute-solute interactions are unimportant. Therefore the properties of solute \(j\) are ideal; \(\left(\mathrm{y}_{\mathrm{j}}\right)_{\mathrm{aq}}=1\). Hence from Equation \ref{e},
\[\ln \left[\left(c_{j}\right)_{\mathrm{aq}} /\left(\mathrm{c}_{\mathrm{j}}\right)_{\mathrm{s}}\right]=\ln \left[\left(\mathrm{y}_{\mathrm{j}}\right)_{\mathrm{s}}\right]\label{f} \]
In these terms \(\left(\mathrm{y}_{j}\right)_{\mathrm{s}}\) is the activity coefficient of solute \(j\) in the aqueous salt solutions where the concentration of salt is represented by \(\mathrm{c}_{\mathrm{s}}\). For dilute salt solutions the assumption is made that \(\ln \left[\left(\mathrm{y}_{\mathrm{j}}\right)_{\mathrm{s}}\right]\) is a linear function of \(\mathrm{c}_{\mathrm{s}}\).
\[\ln \left[\left(\mathrm{y}_{\mathrm{j}}\right)_{\mathrm{s}}\right]=\mathrm{k} \, \mathrm{c}_{\mathrm{s}}\label{g} \]
Combination of equations \ref{f} and \ref{g} yields the following equation.
\[\ln \left[\left(c_{j}\right)_{a q} /\left(c_{j}\right)_{s}\right]=k \, c_{s}\label{h} \]
Equation \ref{h} is one form of the Setchenow equation in which constant \(\mathrm{k}\) (at fixed \(\mathrm{T}\) and \(\mathrm{p}\)) is characteristic of salt \(\mathrm{S}\) and solute \(j\). An alternative form starts by expressing \(\left(c_{j}\right)_{s}\) as \(\left(c_{j}\right)_{a q}-\delta c_{j}\) implying a reduction in the solubility of solute \(j\) when a salt is added; i.e. a salting-out.[2] Hence,
\[\delta \mathrm{c}_{\mathrm{j}} /\left(\mathrm{c}_{\mathrm{j}}\right)_{\mathrm{aq}}=\mathrm{k} \, \mathrm{c}_{\mathrm{s}}\label{i} \]
This Setchenow Equation requires that \(\delta \mathrm{c}_{\mathrm{j}} /\left(\mathrm{c}_{\mathrm{j}}\right)_{\mathrm{aq}}\) is a linear function of \(\mathrm{c}_{\mathrm{s}}\). A positive \(\mathrm{k}\) describes a salting-out; a negative \(\mathrm{k}\) describes a salting-in. The phenomenon by which solubilities of gases in aqueous solutions are changed by adding a salt attracts enormous interest, both from practical and theoretical standpoints [3,4]. Conway reviewed theoretical models which attempt to account quantitatively for the phenomenon [5]. Considerable attention has been given to theories based on the relationship between the impact of the non-polar solute on the dielectric properties of the solvent and hence the chemical potential of the salt in solution [6,7].
For the most part salting-out is the commonly observed pattern [8]. Nevertheless there are some interesting cases where apolar solutes are salted-in by tetra-alkylammonium salts; benzene[9,10] , methane[11] and helium[12] in \(\mathrm{Bu}_{4}\mathrm{N}^{+} \mathrm{~Br}^{-} (\mathrm{aq})\). It would appear that an added apolar solute is stabilized by interaction with the apolar alkyl groups of the cations [13].
Footnotes
[1] J.Setchenow, Z. Phys. Chem.,1889, 4 ,117.
[2]
\[\begin{aligned}
&\ln \left[\frac{\left(c_{j}\right)_{a q}}{\left(c_{j}\right)_{s}}\right]=\ln \left[\frac{\left(c_{j}\right)_{a q}}{\left(c_{j}\right)_{a q}-\delta c_{j}}\right]=-\ln \left[\frac{\left(c_{j}\right)_{\mathrm{aq}}-\delta c_{j}}{\left(c_{j}\right)_{\mathrm{aq}}}\right] \\
&\quad-\ln \left[1-\frac{\delta c_{j}}{\left(c_{j}\right)_{\mathrm{aq}}}\right] \equiv \frac{\delta c_{j}}{\left(c_{j}\right)_{\mathrm{aq}}}
\end{aligned} \nonumber \]
[3] F. A. Long and W. F. McDevit, Chem. Rev.,1952, 51 ,119.
[4] For a review of the definitions of units used in this subject area see H. L. Clever, J. Chem. Eng. Data, 1983, 28 ,340.
[5] B. E. Conway, Pure Appl. Chem.,1985, 57 ,263.
[6] P. Debye and J. MacAulay, Z. Phys. Chem.,1925, 26 ,22.
[7] B. E. Conway, J. E. Desnoyers and A. C. Smith, Philos. Trans. R. Soc.,A 1964, 256A , 389.
[8]
- \(\mathrm{N}_{2}\) and \(\mathrm{CH}_{4}\) in NaCl(aq); T. D. O’Sullivan and N. O. Smith, J. Phys. Chem., 1970, 70 , 1460.
- Phenolic salts in salt solutions; B. Das and R. Ghosh, J. Chem. Eng. Data, 1984, 29 ,137.
- Oxygen in salt solutions; W. Lang and R. Zander, Ind. Eng. Chem. Fundam., 1986, 25 ,775.
- Hg in NaCl(aq); D. N. Glew and D. A. Hames, Can.J.Chem.,1972, 50 ,3124.
- Aromatic hydrocarbons in salt solutions; I. Sanemaa, S. Arakawa,M. Araki and T. Deguchi, Bull. Chem. Soc. Jpn.,1984, 57 ,1539.
- n-Butane in NaCl(aq); P. A. Rice, R. P. Gale and A. J. Barduhn, J. Chem. Eng. Data, 1976, 21 ,204.
- Ar in MX(aq); L. Clever and C. J. Holland, J. Chem. Eng. Data, 1968, 13 ,411.
- Benzene in NaCl(aq); D.F. Keeley, M.A. Hoffpaulr and J. Meriwether, J. Chem. Eng. Data, 1988, 33 ,87.
- B. E. Conway, D. M. Novak and L. H. Laliberte, J. Solution Chem.,1974, 3 ,683; Ar in \(\mathrm{R}_{4}\mathrm{NX}(\mathrm{aq})\).
- R. Aveyard and R. Heselden, J. Chem. Soc. Faraday Trans. 1, 1974, 70 ,1953.
- Ar in benzene in \(\mathrm{R}_{4}\mathrm{NX}(\mathrm{aq})\); A. Ben-Naim, J. Phys. Chem.,1967, 71 ,1137.
- A. Ben-Naim and M. Egel-Thal, J. Phys. Chem.,1965, 69 ,3250; Ar in MX(aq).
- \(\mathrm{Et}_{3}\mathrm{N}\) in \(\mathrm{R}_{4}\mathrm{NCl}(\mathrm{aq})\); A. F. S. S. Mendonca, D. T. R. Formingo and I. M. S. Lampreia, J Solution Chem.,2002, 31 ,653.
- \(\mathrm{Et}_{3}\mathrm{N}\) in \(\mathrm{CaCl}_{2}(\mathrm{aq})\); A. F. S. S. Mendonca, D. T. R. Formingo and I. M. S. Lampreia, J Solution Chem.,2003, 32 ,1033.
[9] Benzene in \(\mathrm{R}_{4}\mathrm{N}^{+} \mathrm{~Br}^{-} (\mathrm{aq})\);J. E. Desnoyers, G. E. Pelletier and C. Jolicoeur, Can. J. Chem.,1965, 43 ,3232.
[10] Benzene in R4NBr(aq); H. E. Wirth and A. LoSurdo, J. Phys. Chem.,1968, 72 ,751.
[11] RH in \(\mathrm{R}_{4}\mathrm{NBr}(\mathrm{aq})\);W.-Y. Wen and J. H. Hung, J.Phys.Chem.,1970, 74 ,170.
[12] A. Feillolay and M. Lucas, J. Phys. Chem.,1972, 76 ,3068.
[13] C. Treiner and A. K. Chattopadhyay, J. Chem. Soc Faraday Trans. 1, 1983, 79 ,2915.