Influence of Polymer Molecular Weight and Concentration on Coexistence Curve of Isobutyric Acid + Water

Anomalous Solubility of an Inert Solid in a Binary Liquid Mixture with a Critical Point of Solution

We consider the dissolution of a chemically inert solid in a binary liquid mixture with a critical point of solution. When the mixture, acting as the solvent, has come to equilibrium with the solid, the state of the system is completely described by the temperature, pressure, and a concentration variable formed by dividing the molar amount of one solvent component by that of the other. Under conditions of fixed pressure, the principle of critical point isomorphism predicts that the slope of a van't Hoff plot of the solubility of the solid should diverge toward infinity as the temperature enters the critical region. The sign of the divergence is negative when the dissolution is endothermic, whereas it is positive when the dissolution is exothermic. In experiments where excess solid phenolphthalein dissolves in a binary mixture of nitrobenzene + dodecane, we have observed exothermic dissolution concurrently with a positive divergence of the van't Hoff slope. The data are insufficiently precise to compute an accurate numerical value for the exponent of the temperature power law expected to govern this divergence; nevertheless, on the basis of Widom scaling theory, we argue that the exponent should be equal to 0.326, which is identical to the value of the exponent that governs the temperature dependence of the shape of the liquid-liquid coexistence curve. Being entirely physical in nature, the anomalous solubility effect should be observable in the case of any chemically inert solid dissolving in any one of the more than 1000 liquid pairs known to have a critical point of solution.

Determination of liquid-liquid critical point composition using 90^{∘} laser light scattering

Despite over a century of characterization efforts, liquid-liquid critical point compositions are difficult to identify with good accuracy. Reported values vary up to 10% for even well-studied systems. Here, a technique is presented for high-precision determination of the critical composition of a partially miscible binary liquid system. Ninety-degree laser light-scattering intensities from single-phase samples are analyzed using an equation derived from nonclassical power laws and the pseudospinodal approximation. Results are reported for four liquid-liquid systems (aniline + hexane, isobutyric acid + water, methanol + cyclohexane, and methanol + carbon disulfide). Compared to other methods, the 90^{∘} light-scattering approach has a strong dependence on composition near the critical point, is less affected by temperature fluctuations, and is insensitive to the presence of trace impurities in the samples. Critical compositions found with 90^{∘} light scattering are precise to the parts-per-thousand level and show long-term reproducibility.

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.

A study of the conformational changes of β-lactoglobulin in the vicinity of critical point of binary mixed solvents

Most of the protein is entangled in the upper IB rich phase.

A chemical test of critical point isomorphism: reactive dissolution of ionic solids in isobutyric acid + water near the consolute point

Binary liquid mixtures having a consolute point can be used as solvents for chemical reactions. When excess cerium(IV) oxide is brought into equilibrium with a mixture of isobutyric acid + water, and the concentration of cerium in the liquid phase is plotted in van't Hoff form, a straight line results for temperatures sufficiently in excess of the critical solution temperature. Within 1 K of the critical temperature, however, the concentration becomes substantially suppressed, and the van't Hoff slope diverges toward negative infinity. According to the phase rule, one mole fraction can be fixed. Given this restriction, the temperature behavior of the data is in exact agreement with the predictions of both the principle of critical point isomorphism and the Gibbs-Helmholtz equation. In addition, we have determined the concentration of lead in the liquid phase when crystalline lead(II) sulfate reacts with potassium iodide in isobutyric acid + water. When plotted in van't Hoff form, the data lie on a straight line for all temperatures including the critical region. The phase rule indicates that two mole fractions can be fixed. With this restriction, the data are in exact agreement with the principle of critical point isomorphism.