Chemical Equilibrium and Critical Phenomena: The Solubilities of Iron(III) Oxide and Cobalt(II,III) Oxide in Isobutyric Acid + Water Near the Consolute Point

Abstract

The solubilities of iron(III) oxide, formula Fe 2 O 3 , and cobalt(II,III) oxide, formula Co 3 O 4 , have been determined in the liquid mixture, isobutyric acid + water, along the critical isopleth at temperatures above the upper critical solution temperature near 299 K. When plotted in van't Hoff form with ln s versus 1/T , the measurements of solubility, s, lie on a straight line for values of the temperature, T , in kelvin, which are sufficiently in excess of the critical solution temperature, T c . The sign of the slope, (∂ ln s/∂(1/T )), indicates that in the case of both oxides, the dissolution reaction is endothermic. When the temperature is within 1 K of T c , however, the slope departs from its constant value and appears to diverge toward negative infinity. The principle of critical-point universality predicts that a divergence in (∂ ln s/∂(1/T )) is to be expected for T near T c in those cases where the stoichiometry of the dissolution reaction involves both components of the solvent; moreover, the Gibbs-Helmholtz equation predicts that, if the heat of solution is endothermic, the sign of the divergence should be negative. Both of these predictions are confirmed by the solubilities of Fe 2 O 3 and Co 3 O 4 measured as a function of temperature along the critical isopleth of isobutyric acid + water.

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

“…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 …”

“… 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 . …”

“…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.…”

Kinetics of two redox reactions in 2‐butoxyethanol and water near its critical point of solution

“…The dynamic property, such as mutual diffusion coefficient, exhibits vanishing as the temperature approaches to critical temperature . The chemical reaction rate exhibits interesting critical behaviors in the liquid–liquid critical binary solutions resulting from critical fluctuation …”

“…Snyder and Eckert measured the rate of the Dieles–Alder reaction of isoprene with maleic anhydride in critical binary solutions (binhexane/nitrobenzene, hexane/nitroethane) and found that the reactions accelerated 30–40% near the critical point. Baird et al . investigated the rates of various reactions in different critical binary solutions.…”