Diverging Thermodynamic Derivatives Associated with Heterogeneous Chemical Equilibrium in a Binary Liquid Mixture with a Consolute Point

Hu, Biao; Baird, James K.; Alvarez, P. K.; Melton, K. C.; Barlow, Douglas A.; Richey, Randi D.

doi:10.1007/s10765-012-1376-9

Cited by 9 publications

(19 citation statements)

References 35 publications

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“…The dissolution of metal oxides by acid/base reaction in IBA/H 2 O produces mixtures having at least six chemical components. We will show that F = 3 in every case where a solubility critical effect has been reported. ,− Nonetheless, we should not neglect the fact that solubility critical effect can be anticipated even in the absence of reaction, as has recently been demonstrated in the case of the dissolution of excess phenolphthalein in a mixture of nitrobenzene + dodecane . This system consists of three components, and the phase rule calculation shows F = 3 …”

Section: Introductionsupporting

confidence: 51%

“… a Slope refers to the sign of the critical divergence in the van’t Hoff slope of the measured solubility. b See ref . c See ref . d PF refers to perfluoromethylcyclohexane. e See ref . f See ref . g See ref . h IBA refers to isobutyric acid. i See ref . j See ref . k See ref . l See ref . m See ref . n 2BE refers to 2-butoxyethanol. o The sign refers to the slope of the divergence as determined by the measured concentration of Mn 4+ and not Al 3+ . p The sign refers to the slope of the divergence as measured by the concentration of Al 3+ and not Cu + . q See ref . …”

Section: Discussionmentioning

confidence: 99%

“…The next case, C = 6, is encountered upon the dissolution of the individual metal oxides, copper(II) oxide, cobalt(II) oxide, nickel(II) oxide, tin(II) oxide, iron(III) oxide, aluminum oxide, manganese(IV) oxide, cerium(IV) oxide, and indium(VI) oxide in a critical mixture of IBA/H 2 O (UCST). The reaction scheme consists of eq and the generic metal oxide dissolution equation where the metal, M Z + , exhibits the oxidation state, Z +.…”

Section: Discussionmentioning

confidence: 99%

“…Upon substitution of C = 6, R = 2, ϕ = 2, and I = 1 into eq , we calculate F = 6 – 2 – 2 – 1 + 2 = 3. In all cases where the metal exhibits the single oxidation state, Z +, the corresponding oxide, M x O y (s), exhibits a critical solubility effect when reacting with IBA/H 2 O. ,− As the metals, M Z + , have included copper, cobalt, nickel, tin, iron, aluminum, manganese, cerium, and indium, the existence of the metal oxide solubility critical effect would seem to be independent of the position of the metal in the periodic table.…”

Section: Discussionmentioning

confidence: 99%

“…The reaction scheme for the simultaneous dissolution of aluminum oxide and copper(I) oxide in isobutyric acid + water begins with eqs and and then proceeds according to the following None of our previous solubility experiments ,− , have included a redox couple. The disproportionation of Cu + (aq) to form Cu 2+ (aq) and copper metal, as shown in eq , fills this gap.…”

Section: Methodsmentioning

confidence: 99%

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Phase Rule and the Universality of Critical Phenomena in Chemically Reacting Liquid Mixtures

et al. 2019

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Critical effects have been reported in the case of chemical equilibria, in which the solvent is a binary liquid mixture having a critical point of solution. At atmospheric pressure and for temperatures near the critical point, the critical effect manifests itself as a divergence in the temperature derivative of the extent of reaction. For a critical mixture of isobutyric acid + water (IBA/H2O) serving as the solvent, we report experimental results for three complex equilibria involving (i) parallel dissolution of aluminum oxide and manganese dioxide (involves 8 species); (ii) parallel dissolution of aluminum oxide and copper(I) oxide (involves 10 species); and (iii) dissolution of barium chromate (involves 9 species). In each case, we observe a divergence in the slope of the van’t Hoff plot of the extent of reaction in the critical region. By phase rule analysis of these and all other existing data, we find that the chemical equilibrium critical effect occurs in coincidence with three thermodynamic intensive variables being fixed, where two of these are the temperature and the pressure. The slope of the van’t Hoff plot in the critical region is observed to diverge toward negative infinity when the reaction is endothermic and toward positive infinity when it is exothermic. These two features are a characteristic of both homogeneous and heterogeneous equilibria and have been observed at both upper and lower critical solution temperatures. Taken together, these observations support the applicability of the universality concept to chemical equilibrium critical phenomena in binary liquid mixtures.

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