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 Fe2O3, and cobalt(II,III) oxide, formula Co3O4, 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, Tc. 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 1K of Tc, 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 Tc 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 Fe2O3 and Co3O4 measured as a function of temperature along the critical isopleth of isobutyric acid + water.