Chemical Equilibrium and Critical Phenomena:  The Solubilities of Manganese Dioxide and Aluminum Oxide in Isobutyric Acid + Water near Its Consolute Point

We have measured the solubilities of manganese dioxide and aluminum oxide in isobutyric acid + water along its critical isopleth at temperatures above the upper critical solution temperature at 26.2 °C. Both oxides are basic anhydrides that react with isobutyric acid to produce the metal isobutyrate and water. In both cases, the measured solubility values, s, were in the parts per million range. When the solubility data for either of these oxides were plotted in van't Hoff form with ln s vs 1/T, a straight line resulted for absolute temperatures, T, sufficiently in excess of the critical solution temperature, T c. The sign of the slope of the line indicated that manganese dioxide dissolved endothermically, while aluminum oxide dissolved exothermically. When the temperature was within 1 K of T c, however, the local van't Hoff slope, (∂ ln s/∂(1/T)), appeared to diverge toward negative infinity in the case of manganese dioxide, while it appeared to diverge toward positive infinity in the case of aluminum oxide. By applying the principle of critical point universality to the critical behavior of thermodynamic derivatives, we have shown that the existence of a divergence in (∂ ln s/∂(1/T)) as T approaches T c is to be expected when the dissolution reaction of the oxide involves both components of the solvent. Application of the Gibbs−Helmholtz equation showed that the sign of the divergence must be opposite to the sign of the heat of solution. The experimental solubility data sets for both manganese dioxide and aluminum oxide are in good agreement with these theoretical assertions.