Gibb’s equation

Thus, adding surfactants to minimize the oil-water and solid-water interfacial tensions causes removal to become spontaneous. On the other hand, a mere decrease in the surface tension of the water-air interface, as evidenced, say, by foam formation, is not a direct indication that the surfactant will function well as a detergent. The decrease in yow or ysw implies, through the Gibb s equation (see Section III-5) adsorption of detergent. 

On account of the very great difficulty of measuring the extremely small amounts of adsorbed substance at a liquid/gas or liquid/liquid interface, very few experiments are available for testing Gibbs s equation. Zawidski(13) (1900) pointed out that the concentration of the foam of a solution should be different from that of the latter in bulk, and Miss Benson (14> (1903) by the analysis of a solution of amyl alcohol in water found... 

Equation (8) is the most general form of Gibbs s equation ( 148), and goes over into the latter when Cj = const. 

In addition to temperature (which decreases y), the properties of interfaces are governed by the chemistry of the molecules present, their concentration and their orientation with respect to the interface. Solutes adsorbed at an interface which reduce interfacial tension are known as surface active agents or surfactants. Surfactants reduce interfacial tension by an amount given, under ideal conditions, by the Gibb s equation ... 

A further, and rather striking, verification of Gibbs s equation will... 

Structure of adsorbed films on dilute solutions. Gibbs s equations (7.1 to 7.7) permit the calculations of the area per molecule, if the surface tension is determined over a range of concentration of the solutions. The area per molecule is proportional to the slope of the curve relating the lowering of surface tension to the activity /2c2 (the vapour pressure of component 2 if the vapour obeys the simple gas laws). This assumes... 

The lateral adhesion is greater, the smaller a Bis the approximate limiting value to which the curves approach as F becomes very large. For the six carbon acid, B is 25, and the actual areas are at 5 dynes pressure, 59 sq. A. at 20 dynes, 33 sq. A. at 40, 28-6 sq. A. It should be mentioned that the activity coefficients of the acids were not determined, though a correction to the approximate Gibbs s equation (7.7) was made for the ionization of the adds. 

New technique for the experimental measurement of the amount adsorbed is described by McBain, G. F. Mills, and T. F. Ford.1 The surface is reduced to a small fraction of its original area, the adsorbed material being displaced into the interior, and its amount estimated interferometrically. The results with hydrocinnamic and dodecyl sulphonic acids confirm Gibbs s equation fairly well, but the method does not yet appear consistent enough to give more than the order of magnitude of the adsorption. 

Explicit values Jj. and can be found by comparing expression (1.63) with the expression for derived from the principal Gibbs s equation... 

Gibb s equation expresses the relationship of interfacial tension, concentration of surfactant and adsorbed amount of surfactant at the interface ... 

Although Braun made some use of the second law of thermodynamics, his applications of it were neither correct nor fruitful, and the first quantitative theory of the electromotive force of a cell was given independently, in different forms, by Gibbs and Helmholtz. Apart from external work Gibbs s equation is ... 

From the Gibb s equation given above it follows that only the entropy term AAS (but not the enthalpy AAH ) is influenced by the temperature. Thus, the selectivity of an enzymatic reaction depends on the temperature as follows ... 

An analysis of the spreading forces for sodium on oxygen-tungsten was made by Bosworth 55). There is a relation between the spreading force F and the vapour pressure, p, obtained from Gibb s equation ... 

Eq. (4.19) leads to the following theoretical adsorption isotherm, using the Gibbs s equation,... 

---