1.10.29: Gibbs Energies- Binary Liquid Mixtures- Excess Thermodynamic Variables

The properties of binary mixtures are complicated. As a point of reference the excess molar properties of two non-aqueous binary liquid mixtures are often discussed. The mixtures are (A) trichloromethane + propanone, and (B) tetrachloromethane + methanol.

A snapshot of the thermodynamic properties of a given binary mixture (at fixed \(\mathrm{T}\) and \(\mathrm{p}\)) is provided by combined plots of \({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\), \({\mathrm{H}_{\mathrm{m}}}^{\mathrm{E}}\) and \(\mathrm{T} \, \mathrm{S}_{\mathrm{m}}^{\mathrm{E}}\) as a function of mixture composition [1-5]. In effect the starting point is the Gibbs energy leading to first, second, third and fourth derivatives [6]. At this stage we make some sweeping (and dangerous) generalizations. For most binary aqueous mixtures, \({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\) is a smooth function of water m mole fraction \(x_{1}\), with an extremum near \(x_{1} = 0.5\). Rarely for a given mixture does the sign of \({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\) change across the mole faction range m although this feature is not unknown; e.g. water + 1,1,1,3,3,3- hexafluropropan-2-ol mixtures at \(298.15 \mathrm{~K}\) [7] but contrast water + 2,2,2- trifluorethanol mixtures [8] where at \(298.2 \mathrm{~K} {\mathrm{~G}_{\mathrm{m}}}^{\mathrm{E}}\) is positive across the m whole mole fraction range. However a change in sign of \({\mathrm{H}_{\mathrm{m}}}^{\mathrm{E}}\) and \(\mathrm{T} \, {\mathrm{S}_{\mathrm{m}}}^{\mathrm{E}}\) and \({\mathrm{V}_{\mathrm{m}}}^{\mathrm{E}}\) with change in mole fraction composition is quite common.

For mixture A, \({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\) is negative indicating that \(\Delta_{\text{mix}}\mathrm{G}_{\mathrm{m}}\) is more negative than in the case of an ideal binary liquid mixture. In the case of Mixture A, the negative \({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\) is linked with a marked exothermic mixing; \({\mathrm{H}_{\mathrm{m}}}^{\mathrm{E}} < 0\). The latter is attributed to strong inter-component hydrogen bonding.

For both mixtures A and B the signs of \({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\) and \({\mathrm{H}_{\mathrm{m}}}^{\mathrm{E}}\) are the same. This feature is characteristic of binary non-aqueous liquid mixtures where in most instances, \(\left|\mathrm{H}_{\mathrm{m}}^{\mathrm{E}}\right|>\left|\mathrm{T} \, \mathrm{S}_{\mathrm{mm}}^{\mathrm{E}}\right|\). \({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\) and \({\mathrm{H}_{\mathrm{m}}}^{\mathrm{E}}\) are both positive for mixture B. Here the pattern is understood in terms of disruption of methanol-methanol hydrogen bonding ( i.e. intracomponent interaction) by the second component. Again we note that a positive \({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\) means that the tendency for \(\Delta_{\text{mix}}\mathrm{G}_{\mathrm{m}}\) to be negative (cf. ideal mixtures) is opposed.

Through a series of mixtures with increasing \({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\), a stage is reached where the magnitude of \({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\) is such that phase separation occurs [1]. For m many binary non-aqueous binary liquid mixtures the phase diagram for liquid miscibility has an upper critical solution temperature UCST. In other words only at high temperatures is the liquid mixture miscible in all proportions.

Often binary aqueous mixtures are used as solvents for the following reason. The solubilities of salts in water(l) are high because ‘water is a polar solvent’ but the solubilities of apolar solutes are low. However the solubilities of apolar substances in organic solvents (e.g. ethanol) are high. If the chemical reaction being studied involves both polar and apolar solutes, judicious choice of the composition of a binary aqueous mixture leads to a solvent where the solubilities of both polar and apolar solutes are high. Nevertheless the task of accounting for the properties of binary aqueous mixtures is awesome. For this reason the classification introduced by Franks [9] has considerable merit. A distinction is drawn between Typically Aqueous and Typically Non-Aqueous Binary Aqueous Mixtures, based on the the thermodynamic excess functions, \({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\), \({\mathrm{H}_{\mathrm{m}}}^{\mathrm{E}}\) and \(\mathrm{T} \, {\mathrm{S}_{\mathrm{m}}}^{\mathrm{E}}\).

Davis has explored how the properties of many binary aqueous mixtures can be subdivided on the basis of the ranges of mole fraction compositions [10].

Footnotes

[1] J. S. Rowlinson and F. L. Swinton, Liquids and Liquid Mixtures, Butterworths, London, 3rd. edn., 1982.

[2] K. N. Marsh, Annu. Rep. Prog. Chem., Sect. C, Phys. Chem.,1984, 81 , 209-245; Pure Appl. Chem.,1983,55,467.

[3] G. Scatchard. Chem. Rev.,1931,8,321.

[4] G. Scatchard, Chem. Rev.,1940, 44,7.

[5] With respect to compressibilities; G. Douheret, C. Moreau and A. Viallard, Fluid Phase Equilib., 1985, 22,289.

[6] Y. Koga, J.Phys.Chem.,1996,100,5172; Y. Koga, K. Nishikawa and P. Westh, J. Phys. Chem.A,2004,108,3873.

[7]

1. M. J. Blandamer, J. Burgess, A. Cooney, H. J. Cowles, I. M. Horn, K. J. Martin, K. W. Morcom and P. Warrick, J. Chem. Soc. Faraday Trans.,1990,86,2209.
2. A. Kivinen, J. Murto and A. Viit, Suomen Kemist.,Sect. B,1967,40,298.

[8] R. Jadot and M. Fraiha, J. Chem. Eng. Data, 1988, 33,237.

[9] F. Franks, in Hydrogen –Bonded Solvent Systems, ed. A. K. Covington and P. Jones, Taylor and Francis, London, 1968, pp.31-47.

[10]

1. M. I. Davis, Thermochim Acta, 1984,77,421; 1985,90,313; 1987,120,299.
2. M. I. Davis, M. C. Molina and G. Douheret.1988, 131, 153.
3. G. Douheret, A. Pal and M. I. Davis, J. Chem. Thermodyn., 1990, 22, 99.
4. G. Douheret, A. Pal, H. Hoiland, O. Anowi and M. I. Davis, J. Chem. Thermodyn., 1991, 23,569.
5. G. Douheret, A. H. Roux, M. I. Davis, M. E. Hernandez, H. Hoiland and E. Hogseth, J. Solution Chem.,1993,22,1041.
6. G. Douheret, C. Moreau and A. Viallard, Fluid Phase Equilib., 1985, 22, 277, 289.