Ion exchange at the critical point of solution

A mixture of isobutyric acid (IBA)+water has an upper critical point of solution at 26.7°C and an IBA concentration of 4.40M. We have determined the Langmuir isotherms for the hydroxide form of Amberlite IRN-78 resin in contact with mixtures of IBA+water at temperatures, 27.0, 29.0, 31.0 and 38.0°C, respectively. The Langmuir plot at 38.0°C forms a straight line. At the three lower temperatures, however, a peak in the Langmuir plot is observed for IBA concentrations in the vicinity of 4.40M. We regard this peak to be a critical effect not only because it is located close to 4.40M, but also because its height becomes more pronounced as the temperature of the isotherm approaches the critical temperature. For concentrations in the vicinity of the peak, the data indicate that the larger isobutyrate ion is rejected by the resin in favor of the smaller hydroxide ion. This reversal of the expected ion exchange reaction might be used to separate ions according to size. Using the Donnan theory of ion exchange equilibrium, we link the swelling pressure to the osmotic pressure. We show that the peak in the Langmuir plot is associated with a maximum in the "osmotic" energy. This maximum has its origin in the concentration derivative of the osmotic pressure, which goes to zero as the critical point is approached.