1.22.10: Volume: Aqueous Binary Liquid Mixtures
For binary aqueous mixtures (at ambient pressure and fixed temperature) there are two interesting reference points.
- The molar volume of the pure liquid component 2, \(\mathrm{V}_{2}^{*}(\lambda)\).
In the latter case we imagine that each molecule of liquid 2 is surrounded by an infinite expanse of water. With gradual increase in \(\mathrm{x}_{2}\), so (on average) the molecules of liquid 2 move closer together.
Typically Aqueous Mixtures
For these systems \(\left[\mathrm{V}_{2}^{\infty}(\operatorname{mix})-\mathrm{V}_{2}^{*}(\lambda)\right]\) is negative. But this pattern is not unique to aqueous systems. The unique feature is the decrease in \(\left[\mathrm{V}_{2}(\operatorname{mix})-\mathrm{V}_{2}^{*}(\lambda)\right]\) with increase in \(\mathrm{x}_{2}\) at low \(\mathrm{x}_{2}\) [1]. In fact with increase in hydrophobicity of chemical substance 2, the decrease is more striking and the minimum in \(\left[\mathrm{V}_{2}(\operatorname{mix})-\mathrm{V}_{2}^{*}(\lambda)\right]\) occurs at lower \(\mathrm{x}_{2}\). At mole fractions beyond \(\mathrm{x}_{2}\left[\mathrm{~V}_{2}(\mathrm{mix})-\mathrm{V}_{2}^{*}(\lambda)\right]\) increases with increase in \(\mathrm{x}_{2}\). Many explanations have been offered for this complicated pattern. The following is one explanation.
The negative \(\left[\mathrm{V}_{2}^{\infty}(\operatorname{mix})-\mathrm{V}_{2}^{*}(\lambda)\right]\) is accounted for in terms of a liquid clathrate in which part of the hydrophobic group ‘occupies’ a guest site in the liquid water ‘lattice’. The decrease in \(\left[\mathrm{V}_{2}(\operatorname{mix})-\mathrm{V}_{2}^{*}(\lambda)\right]\) is accounted for in terms of an increasing tendency towards a liquid clathrate hydrate structure. With increase in \(\mathrm{x}_{2}\) there comes a point where there is insufficient water to construct the liquid clathrate host. Hence \(\left[\mathrm{V}_{2}(\operatorname{mix})-\mathrm{V}_{2}^{*}(\lambda)\right]\) increases [2,3].
Typically Non-Aqueous Systems
Although \(\left[\mathrm{V}_{2}^{\infty}(\operatorname{mix})-\mathrm{V}_{2}^{*}(\lambda)\right]\) is negative no minimum is observed in \(\left[\mathrm{V}_{2}(\operatorname{mix})-\mathrm{V}_{2}^{*}(\lambda)\right]\).
Footnotes
[1] See for example; fluoroalcohols(aq); C. H. Rochester and J. R. Symonds, J. Fluorine Chem.,1974, 4 ,141.
[2] F. Franks, Ann. N. Y. Acad. Sci.,1955, 125 ,277.
[3] For many binary aqueous mixtures the patterns in volume related properties often identify transition points at ‘structurally interesting compositions’; G. Roux, D. Roberts, G. Perron and J. E. Desnoyers, J. Solution Chem.,1980, 9 ,629.