Ion exchange at the critical point of solution

Savoy, J.D.; Baird, James K.; Lang, Joshua R

doi:10.1016/j.chroma.2016.01.029

Cited by 5 publications

(6 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The coordinates of this point define the critical solution temperature, T c o , and the critical composition, X c o . If the coexistence curve is concave up, then T c o is a lower critical solution temperature (LCST), whereas if it is concave down, then T c o is an upper critical solution temperature (UCST) …”

Section: Introductionmentioning

confidence: 99%

“…If the coexistence curve is concave up, then T c o is a lower critical solution temperature (LCST), whereas if it is concave down, then T c o is an upper critical solution temperature (UCST). 1 More than 1000 pairs of liquids are known to exhibit this kind of behavior. 2 If a small amount of a third component is added to such a binary liquid mixture, the critical temperature T c o is shifted to a new value, T c , which can be either higher or lower than T c o , depending upon the nature and concentration of the third component.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

et al. 2018

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2018

View full text Add to dashboard Cite

show abstract

“…If the phase boundary curve is concave up, T c o is a lower critical solution temperature (LCST), and two liquid phases coexist at temperatures, T > T c o . If the boundary curve is concave down, T c o is an upper critical solution temperature (UCST), and two liquid phases coexist at temperatures T < T c o …”

Section: Theorymentioning

confidence: 99%

“…o is an upper critical solution temperature (UCST), and two liquid phases coexist at temperatures T < T c o . 21…”

Section: Introductionmentioning

confidence: 99%

Phase Rule and the Universality of Critical Phenomena in Chemically Reacting Liquid Mixtures

et al. 2019

View full text Add to dashboard Cite

Critical effects have been reported in the case of chemical equilibria, in which the solvent is a binary liquid mixture having a critical point of solution. At atmospheric pressure and for temperatures near the critical point, the critical effect manifests itself as a divergence in the temperature derivative of the extent of reaction. For a critical mixture of isobutyric acid + water (IBA/H2O) serving as the solvent, we report experimental results for three complex equilibria involving (i) parallel dissolution of aluminum oxide and manganese dioxide (involves 8 species); (ii) parallel dissolution of aluminum oxide and copper(I) oxide (involves 10 species); and (iii) dissolution of barium chromate (involves 9 species). In each case, we observe a divergence in the slope of the van’t Hoff plot of the extent of reaction in the critical region. By phase rule analysis of these and all other existing data, we find that the chemical equilibrium critical effect occurs in coincidence with three thermodynamic intensive variables being fixed, where two of these are the temperature and the pressure. The slope of the van’t Hoff plot in the critical region is observed to diverge toward negative infinity when the reaction is endothermic and toward positive infinity when it is exothermic. These two features are a characteristic of both homogeneous and heterogeneous equilibria and have been observed at both upper and lower critical solution temperatures. Taken together, these observations support the applicability of the universality concept to chemical equilibrium critical phenomena in binary liquid mixtures.

show abstract

“…If the extremum is a minimum, the temperature at the critical point is a lower critical solution temperature (LCST). 2…”

Section: Introductionmentioning

confidence: 99%

Theory of First Order Chemical Kinetics at the Critical Point of Solution

Baird

Lang

2017

J. Phys. Chem. A

View full text Add to dashboard Cite

Liquid mixtures, which have a phase diagram exhibiting a miscibility gap ending in a critical point of solution, have been used as solvents for chemical reactions. The reaction rate in the forward direction has often been observed to slow down as a function of temperature in the critical region. Theories based upon the Gibbs free energy of reaction as the driving force for chemical change have been invoked to explain this behavior. With the assumption that the reaction is proceeding under relaxation conditions, these theories expand the free energy in a Taylor series about the position of equilibrium. Since the free energy is zero at equilibrium, the leading term in the Taylor series is proportional to the first derivative of the free energy with respect to the extent of reaction. To analyze the critical behavior of this derivative, the theories exploit the principle of critical point isomorphism, which is thought to govern all critical phenomena. They find that the derivative goes to zero in the critical region, which accounts for the slowing down observed in the reaction rate. As has been pointed out, however, most experimental rate investigations have been carried out under irreversible conditions as opposed to relaxation conditions [Shen et al. J. Phys. Chem. A 2015, 119, 8784-8791]. Below, we consider a reaction governed by first order kinetics and invoke transition state theory to take into account the irreversible conditions. We express the apparent activation energy in terms of thermodynamic derivatives evaluated under standard conditions as well as the pseudoequilibrium conditions associated with the reactant and the activated complex. We show that these derivatives approach infinity in the critical region. The apparent activation energy follows this behavior, and its divergence accounts for the slowing down of the reaction rate.

show abstract

Ion exchange at the critical point of solution

Cited by 5 publications

References 21 publications

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

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

Phase Rule and the Universality of Critical Phenomena in Chemically Reacting Liquid Mixtures

Theory of First Order Chemical Kinetics at the Critical Point of Solution

Contact Info

Product

Resources

About