1.7.20: Compressions- Isothermal- Salt Solutions
In 1933 Gucker [1-3] reviewed attempts to measure the apparent isothermal molar compressions of salts in aqueous solution, these attempts dating back to the earliest reliable measurements by Rontgen and Schneider [4] in 1886 and 1887. Gucker showed [2] that for several aqueous salt solutions the apparent isothermal molar compression, \(\phi\left(\mathrm{K}_{\mathrm{T}_{\mathrm{j}}}\right)\) is a linear function of the square root of the salt concentration.
\[\phi\left(\mathrm{K}_{\mathrm{T}_{\mathrm{j}}}\right)=\phi\left(\mathrm{K}_{\mathrm{T}_{\mathrm{j}}}\right)^{\infty}+\mathrm{a} \, \mathrm{c}_{\mathrm{j}}^{1 / 2} \nonumber \]
This general equation holds for \(\mathrm{CaCl}_{2}(\mathrm{aq})\) at 60 Celsius. In general terms, \(\phi\left(\mathrm{K}_{\mathrm{T}_{\mathrm{j}}}\right)\) for salts is negative becoming less negative as the salt concentration increases. Gibson described an interesting approach which characterises salt solutions in terms of effective pressures, \(\mathrm{p}_{\mathrm{c}}\) exerted by the salt on the solvent [5]. This effective pressure is expressed as a linear function of the product of salt and solvent concentrations. The constant of proportionality is characteristic of the salt. Leyendekkers based an analysis using the Tammann-Tait-Gibson (TTG) model, on the assertion that solutes, salts and organic solutes, exert an excess pressure on water in aqueous solution [6,7]. The TTG approach described by Leyendekkers is intuitively attractive but the analysis is based on an extra - thermodynamic assumption [8]. Calculation of an excess pressure requires an estimate of the volume of solute molecules, \(\phi_{j}\) in solution. If this property is independent of solute molality \(\mathrm{m}_{j}\), the dependence of the volume of a solution (in \(1 \mathrm{~kg}\) of water) on solute molality is described by the dependence of the ‘partial molar volume' of water. The difference between \(\left[\mathrm{V}\left(\mathrm{aq} ; \mathrm{w}_{1}=1 \mathrm{~kg}\right)-\mathrm{m}_{\mathrm{j}} \, \phi(\mathrm{Vj})\right]\) and \(\mathrm{M}_{1}^{-1} \, \mathrm{V}_{1}^{*}(\ell)\) is understood in terms of an effective pressure on the solvent. The assumptions underlying this calculation are not trivial. Furthermore from a thermodynamic viewpoint, the pressure is the same in every volume element of a solution [8].
Footnotes
[1] F. T. Gucker, J. Am. Chem.Soc.,1933, 55 ,2709.
[2] F. T. Gucker, Chem.Rev.,1933, 13 ,111.
[3] F. T. Gucker, F. W. Lamb, G. A. Marsh and R. M. Haag, J.Am. Chem. Soc.,1950, 72 ,310.
[4] W. C. Rontgen and J. Schneider, Wied. Ann., 1886, 29 ,165;1887, 31 ,36.
[5] R. E. Gibson, J.Am.Chem.Soc.,1934, 56 ,4.;1935, 57 ,284.
[6] J. V. Leyendekkers, J. Chem. Soc. Faraday Trans.1,1981, 77 ,1529; 1982, 78 ,357; 1988, 84 , 397,1653.
[7] J. V. Leyendekkers, Aust. J. Chem.,1981, 34 ,1785.
[8] M. J. Blandamer, J. Burgess and A. Hakin, J. Chem. Soc. Faraday Trans.1,1986, 82 ,3681.