Phase rule method for applying the principle of critical point universality to chemically reacting open systems

We have measured the solubility of barium peroxide in the liquid mixture, isobutyric acid + water, in the single phase region along the critical isopleth at temperatures just above the critical solution temperature at 299 K. When the concentration, s, of Ba2 + is plotted in van't Hoff form with ln s vs. 1/T, where T is the Kelvin temperature, a straight line having negative slope is obtained for values of the temperature which are sufficiently in excess of the critical temperature Tc. Because the liquid phase is in equilibrium with a non-critical solid phase consisting of BaO2, the liquid constitutes an open system. A phase rule analysis taking this into account shows that one mole fraction describing the liquid phase can be fixed. Under such conditions, the principle of critical point universality predicts that the magnitude of the slope of the van't Hoff plot, (∂ ln s/∂(1/T)), should become infinite as T → Tc. Moreover, according to the Gibbs-Helmholtz equation, the sign of (∂ ln s/∂(1/T)) in the critical region should be negative. In agreement with both of these predictions, we find that when T is within 1.9 K of Tc, (∂ ln s/∂(1/T)) approaches negative infinity.