1.10.32: Gibbs Energies- Liquid Mixtures- Typically Aqueous (TA)
For many binary aqueous liquid mixtures, the pattern shown by the molar excess thermodynamic parameters is \(\mathrm{G}_{\mathrm{m}}^{\mathrm{E}}>0\); \(\left|\mathrm{T} \, \mathrm{S}_{\mathrm{m}}^{\mathrm{E}}\right|>\left|\mathrm{H}_{\mathrm{m}}^{\mathrm{E}}\right|\). This pattern of excess molar properties defines TA mixtures. \({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\) is positive because the excess molar entropy of mixing is large in magnitude and negative in sign. In these terms mixing is dominated by the entropy change. The excess molar enthalpy of mixing is smaller in magnitude than either \({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\) or \(\mathrm{T} \, {\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\) but exothermic in water-rich mixtures.
The word ‘Typically’ in the description stems from observation that this pattern in thermodynamic variables is rarely shown by non-aqueous systems. At the time the classification was proposed [1], most binary aqueous liquid mixtures seemed to follow this pattern. Among the many examples of this class of system are aqueous mixtures formed by ethanol, 2-methyl propan-2-ol and cyclic ethers including tetrahydrofuran[2]. In water-rich mixtures, a large in magnitude but negative in sign \(\mathrm{T} \, {\mathrm{S}_{\mathrm{m}}}^{\mathrm{E}}\) produces a large (positive) \({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\). For mixtures rich in the apolar component m endothermic mixing produces a positive \({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\). The key point is that in m water-rich mixtures a positive \({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\) emerges from a negative \(\mathrm{T} \, {\mathrm{S}_{\mathrm{m}}}^{\mathrm{E}}\).
With reference to volumetric properties of these system, the partial molar volume \(\mathrm{V}(\mathrm{ROH})\) for monohydric alcohols can be extrapolated to infinite dilution; i.e. \(\operatorname{limit}\left(\mathrm{x}_{2} \rightarrow 0\right) \mathrm{V}(\mathrm{ROH})=\mathrm{V}(\mathrm{ROH} ; \mathrm{aq})^{\infty}\) where \(x_{2}\) is the mole fraction of alcohol. The difference, \(\left[\mathrm{V}(\mathrm{ROH} ; \mathrm{aq})^{\infty}-\mathrm{V}^{*}(\mathrm{ROH} ; \ell)\right]\) is negative. In fact this pattern is observed for both TA and Typical Non-aqueous binary aqueous mixtures. Examples where this pattern is observed included aqueous mixtures formed by DMSO, \(\mathrm{H}_{2}\mathrm{O}_{2}\) and \(\mathrm{CH}_{3}\mathrm{CN}\). Significantly \(\left[\mathrm{V}(\mathrm{ROH} ; \mathrm{aq})-\mathrm{V}^{*}(\mathrm{ROH} ; \ell)\right]\) is negative for TA mixtures, decreasing from \(\left[\mathrm{V}(\mathrm{ROH} ; \mathrm{aq})^{\infty}-\mathrm{V}^{*}(\mathrm{ROH} ; \ell)\right]\) with increase in mole fraction of \(\mathrm{ROH}\), accompanying by a tendency to immiscibility. The initial decrease in \(\left[\mathrm{V}(\mathrm{ROH} ; \mathrm{aq})-\mathrm{V}^{*}(\mathrm{ROH} ; \ell)\right]\) with increase in \(x_{2}\) is more dramatic the more hydrophobic the non-aqueous component; for 2-methyl propan-2-ol aqueous mixtures at \(298.2 \mathrm{~K}\) and ambient pressure, the minimum occurs at an alcohol mole fraction 0.04 (at \(298.2 \mathrm{~K}\)).
Many explanations have been offered for the complicated patters shown by the dependence of \(\left[\mathrm{V}(\mathrm{ROH} ; \mathrm{aq})-\mathrm{V}^{*}(\mathrm{ROH} ; \ell)\right]\) on mole fraction composition.
In one model, the negative \(\left[\mathrm{V}(\mathrm{ROH} ; \mathrm{aq})-\mathrm{V}^{*}(\mathrm{ROH} ; \ell)\right]\) at low mole fractions of \(\mathrm{ROH}\) is accounted for in terms of a liquid clathrate in which part of the hydrophobic R-group ‘occupies’ a guest site in the water lattice. The decrease in \(\left[\mathrm{V}(\mathrm{ROH} ; \mathrm{aq})-\mathrm{V}^{*}(\mathrm{ROH} ; \ell)\right]\) is accounted for in terms of an increasing tendency towards a clathrate structure. But with increase in \(x_{2}\) there comes a point where there is insufficient water to construct a liquid clathrate water host. Hence \(\left[\mathrm{V}(\mathrm{ROH} ; \mathrm{aq})-\mathrm{V}^{*}(\mathrm{ROH} ; \ell)\right]\) increases.
An important characteristic of TA mixtures is a tendency towards and in some cases actual decrease in liquid miscibility with increase in temperature. At ambient \(\mathrm{T}\) and \(\mathrm{p}\), the mixture 2-methyl propan-2-ol + water is miscible (but only just!) in all molar proportions. The corresponding mixtures prepared using butan-1-ol and butan-2-ol are partially miscible. TA systems are therefore often characterised by a Lower Critical Solution Temperature LCST. In fact nearly all examples quoted in the literature of systems having an LCST involve water as one component; e.g. \(\mathrm{LCST} = 322 \mathrm{~K}\) for 2-butoxyethanol + water [3]. This tendency to partial miscibility is often signalled by the properties of the completely miscible systems.
Returning to the patterns shown by relative partial molar volumes, \(\left[\mathrm{V}(\mathrm{ROH} ; \mathrm{aq})-\mathrm{V}^{*}(\mathrm{ROH} ; \ell)\right]\), a stage is reached whereby with increase in mole fraction of the non-aqueous component, this property increases after a minimum. Other properties of the mixtures also change dramatically including a marked increase in \(\left(\alpha_{a} / v^{2}\right)\) where \(\alpha_{\mathrm{a}}\) is the amplitude attenuation constant and \(ν\) is the frequency of the sound wave in the MHz range; e.g. \(70 \mathrm{~MHz}\). Actually the pattern is complicated. Over the range of mixture mole fractions \(x_{2}\) where \(\left[\mathrm{V}(\mathrm{ROH} ; \mathrm{aq})-\mathrm{V}^{*}(\mathrm{ROH} ; \ell)\right]\) decreases with increase in \(x_{2}\), the ratio \(\left(\alpha_{a} / v^{2}\right)\) hardly changes although the speed of sound increases. At a mole fraction \(x_{2}\) characteristic of the temperature and the non-aqueous component, \(\left(\alpha_{a} / v^{2}\right)\) increases sharply, reaching a maximum where the mixture has a strong tendency to immiscibility. This interplay between in-phase and out-of-phase components of the complex isentropic compressibility when the mole fraction composition of the mixture is changed highlights the molecular complexity of these systems. By way of contrast the ratio \(\left(\alpha_{a} / v^{2}\right)\) for DMSO + water mixtures (a TNAN system) changes gradually when the mole fraction of DMSO is changed.
For TA mixtures where \(\left(\alpha_{a} / v^{2}\right)\) is a maximum [4], other evidence points to the fact these mixtures are micro-heterogeneous; cf. excess molar isobaric heat capacities. Phase separation of the mixture 2-methyl propan-2-ol is observed when butane gas is dissolved in the liquid mixture. The miscibility curve shows an LCST near \(282 \mathrm{~K}\) [5].
Footnotes
[1] F. Franks in Hydrogen-Bonded Solvent Systems, ed. A. K. Covington and P. Jones, Taylor and Francis, London,1968, pp.31-47.
[2] The following references refer to properties of TA binary liquid mixtures.
-
alcohol + water mixtures. Isobaric heat capacities.
- H. Ogawa and S. Murakami, Thermochim. Acta, 1986, 109 ,145.
- G. I. Makhatadze and P. L. Privalov, J. Solution Chem.,1989, 18 ,927.
- R. Arnaud, L. Avedikian and J.-P. Morel,J. Chim. Phys., 1972,45.
-
fluoroalkanol + water mixtures.
-
\({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\)
R. Jadot and M.Fralha,J. Chem.Eng. Data,1988,33,237.
J. Murto and A. Kiveninen, Suomen Kemist. Ser. B, 1967,40,258. -
Enthalpies
M. Denda, H. Touhara and K. Nakanishi, J. Chem. Thermodyn., 1987, 19 ,539.
A. Kivinen, J. Murto and A.Vhtala, Suomen Kemist.1967, 40 ,298. - Volumes; J. Murto, A. Kivinen, S. Kivimaa and R. Laakso, Suomen Kemist., Ser. B, 1967, 40 ,250.
-
\({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\)
-
amine + water mixtures
- \({\mathrm{X}_{\mathrm{m}}}^{\mathrm{E}}\) and miscibility; J. L. Copp and D. H. Everett, m Discuss. Faraday Soc.,1953, 15 ,174.
- Et3N + water; miscibility; A. Bellemans, J.Chem.Phys.,1953, 21 , 368.
-
THF + water
-
\({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\)
J. Matous, J. P. Novak, J. Sobr and J. Pick, Collect. Czech. Chem.Commun.,1972, 37 ,2653.
C. Treiner, J.-F. Bocquet and M. Chemla, J. Chim..Phys., 1973, 70 , 72. -
\({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\) for \(\mathrm{THF} + \mathrm{~D}_{2}\mathrm{O}\);
J. Lejcek, J. Matous, J. P. Novak and J. Pick, J. Chem. Thermodyn., 1975, 7 ,927. -
Vapour composition;
W. Hayduk, H. Laudie and O. H. Smith, J. Chem.Eng Data,1973, 18 ,373. -
\({\mathrm{H}_{\mathrm{m}}}^{\mathrm{E}}\)
H. Nakayama and K. Shinoda, J. Chem. Thermodyn., 1971, 3 ,401. -
Activity of water
K. L. Pinder, J. Chem. Eng. Data, 1973, 18 ,275. -
Thermal expansivities
O. Kiyohara, P. J. D’Arcy and G. C. Benson, Can. J. Chem., 1978, 56 ,2803. -
\({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\) and \({\mathrm{V}_{\mathrm{m}}}^{\mathrm{E}}\).
Signer, H. Arm and H. Daeniker, Helvetica Chimica Acta, 1969, 52 , 2347. -
2-Methyl propan-2-ol + water
In the chemical literature, 2-methyl propan-2-ol is often called t-butanol but as Prof. David J. G. Ives often pointed out, there is no organic compound, t-butane. -
\({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\) and \({\mathrm{H}_{\mathrm{m}}}^{\mathrm{E}}\)
Y. Koga, W. W. Y. Siu and T. Y. H. Wong, J. Phys. Chem., 1990, 94 ,7700. -
Enthalpies
Y. Koga, Can. J.Chem.,1986, 64 ,206;1988, 66 ,1187,3171. -
Volumes
A. Hvidt, R. Moss and G. Nielsen, Acta Chem. Scand.,Sect. B, 1978, B32 , 274.
M. Sakurai, Bull. Chem. Soc. Jpn.,1987, 160 ,1. -
\(\mathrm{C}_{\mathrm{p}}\) and \(\mathrm{V}\)
B. de Visser, G. Perron, and J. E. Desnoyers, Can J. Chem.,1977, 55 ,856. -
X-ray scattering
K. Nishikawa, Y. Kodera and T. Iijima, J. Phys. Chem., 1987, 91 ,3694. -
Sound velocity
H. Endo and O. Nomoto,Bull. Chem. Soc. Jpn., 1973, 46 , 3004. -
Isentropic compressibilities;
J. Lara and J. E. Desnoyers, J. Solution Chem., 1981, 10 ,465. - Propan-1-ol + water
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\({\mathrm{V}_{\mathrm{m}}}^{\mathrm{E}}\)
G. C. Benson and O. Kiyohara, J. Solution Chem.,1980, 9 ,791.
M. I. Davis, Thermochim. Acta, 1990, 157 ,295.
C. De Visser, G. Perron and J. E. Desnoyers, Can. J.Chem.,1977, 55 ,856. -
Propanone + water \({\mathrm{X}_{\mathrm{m}}}^{\mathrm{E}}\) references;
M. J. Blandamer, N. J. Blundell, J. Burgess, H. J. Cowles and I. M. Horn, J. Chem. Soc. Faraday Trans.,1990, 86 ,283. -
Methyl vinyl ketone + water
LCST = \(301 \mathrm{~K}\); UCST = \(356 \mathrm{~K}\); J. Vojtko and M.Cihova, J. Chem. Eng. Data, 1972, 17 ,337.
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\({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\)
[3] F. Elizalde, J Gracia and M. Costas, J Phys.Chem.,1988, 93 ,3565.
[4] M. J Blandamer and D. Waddington, Adv. Mol. Relax.Processes,1970, 2 ,1.
[5] R. W. Cargill and D. E. MacPhee, J. Chem. Soc. Faraday Trans.1, 1989, 85 , 2665; an excellent observation!
[5] \({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\); M. J. Blandamer, J. Burgess, A. Cooney, H. J. Cowles, I. M. Horn, K. M. Martin, K.W. Morcom and P. Warrick, J. Chem. Soc. Faraday Trans., 1990, 86 , 2209.