Critical-point universality in adsorption: The effect of charcoal on a mixture of isobutyric acid and water near the consolute point

Abstract

The mixture of isobutyric acid and water has a consolute point at a temperature of 25.75 °C and mole fraction 0.1148 isobutyric acid. When charcoal is added to this mixture, the concentration of isobutyric acid is reduced by adsorption. We have measured the action of charcoal on solutions of isobutyric acid and water as a function of isobutyric acid mole fraction at temperatures of 25.85 and 32.50 °C. At the higher temperature, the specific adsorption density (y(2)(α)/m) satisfies the Freundlich equation (y(2)(α)/m)=KX(2)(1/n), where y(2)(α) is the mass of isobutyric acid adsorbed, m is the mass of charcoal, X(2) is the equilibrium mole fraction of isobutyric acid, n is the Freundlich index, and K=K(T) is an amplitude that depends upon the temperature T. At 25.85 °C, a critical endpoint is located at an isobutyric acid mole fraction X(2)(ce)=0.09. When compared with the Freundlich equation at this temperature, a plot of the specific adsorption density as a function of X(2) in the vicinity of the critical-endpoint composition assumes a shape which is reminiscent of the derivative of a Dirac delta function. Using critical-point scaling theory, we show that this divergent pattern is consistent with the principle of critical point universality.

Monte Carlo Study of a Liquid-Liquid Phase Transition Using a Modified Gibbs Ensemble

“…At about 0.8 K the two isotopes separate spontaneously into a nearly pure He 3 phase and a He 4 phase with a small amount of He 3 dissolved in it. A well-known binary liquid system with a room temperature critical point is that of isobutyric acid and water [4]. In this work we have considered the CS 2 -methanol system.…”

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

“…[38][39][40][41][42] The influence of the third component as an impurity on IBW has been of continuing interest and fundamental practical importance. Several studies have been attempted on the critical mixture of IBW in the presence of various impurities, including ionic salts, 26,[43][44][45][46][47][48] polymers, 27,[49][50][51][52] ionic liquid, 53 oxides, 24,25,54,55 charcoal, 56 acetone 57 and silica gel. 58 To the best of our knowledge, very little is known about influence of protein 27 on the critical mixture of IBW.…”