Chemical Equilibrium and Critical Phenomena: Solubility of Indium Oxide in Isobutyric Acid + Water Near the Consolute Point

We have determined the solubility, s, of indium oxide 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 vs 1/ T, the measurements of solubility lie on a straight line for values of the absolute temperature, T, which are sufficiently in excess of the critical solution temperature, T c . The sign of the slope, (∂ ln s /∂(1/ T )), indicates that the enthalpy of dissolution 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 enthalpy of solution is endothermic, the sign of the divergence should be negative. Both of these predictions are confirmed by the experimental data.