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

Abstract

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 degrees 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, ( partial differential ln s/ partial differential(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 ( partial differential ln s/ partial differential(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.

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

“…As T approaches T c , however, the critical behavior of (∂s/∂ T ) P, G=0 forces (∂ ln s/∂(1/T )) P, G=0 to depart from its expected constant value. At temperatures inside the critical region, (∂ ln s/∂(1/T )) P, G=0 goes to positive infinity, if the dissolution is exothermic, and it goes to negative infinity if the dissolution is endothermic [11]. We shall demonstrate that the latter prediction applies in the case of the dissolution of iron(III) oxide or cobalt(II,III) oxide in isobutyric acid + water at temperatures that lie along the critical isopleth.…”

“…1 are sufficiently dilute as to make their activity coefficients unity, and that the water and isobutyric acid are in sufficient excess as to make their respective activities independent of the solubility of the metal. Under these conditions, the solubility data can be fitted to the van't Hoff law in the form [11],…”

“…In Fig. 2 For temperatures inside the critical region, the slope of the van't Hoff plot can be calculated using the equation [11],…”

“…An example is (∂s/∂ T ) e , where the subscript, e, refers to chemical equilibrium [10,11]. There are two distinguishable cases: (1) When the experimental conditions are such that the fixed thermodynamic variables consist of fields and two or more densities, the derivative of a density with respect to a field is expected to be a smooth function of the temperature as T approaches the critical temperature, T c .…”

“…1 involves both components of the solvent, the mixture contains no inert components. In the absence of inert components, the thermodynamic derivative, (∂s/∂ T ) e , can be identified with (∂s/∂ T ) P, G=0 , where G = 0 is the criterion for dissolution equilibrium [10,11]. Since no densities are held fixed, (∂s/∂ T ) P, G=0 is expected to approach infinity strongly as T approaches T c [11].…”