Gibbs s adsorption equation

The decrease in interfacial tension is related to the amount of extractant adsorbed at the interface through the Gibb s adsorption equation (46). The molecular areas of the extractant at the interface can thus be directly obtained from this equation. As an example, an area of 104 8 A2 is obtained for the. V,.V -dimc(hyl dibu-tyltetradecylmalonamide (DMDBTDMA) at the dodecane/water interface (4, 34). For classical surfactants, it should be noted that a nearly constant area per molecule with the addition of salt strongly suggests that anions and cations are adsorbed and extracted as pairs (47). Thus, the variation of the area per molecule with added salt can provide information on the mechanism of extraction. 

The formal similarity between Gibbs s adsorption equation and the Gibbs-... 

They find, first, that the expansion X is related to the amount adsorbed and the pressure in a manner very similar to the surface pressure in Gibbs s adsorption equation, Chap. Ill, eq. (7.5)... 

Gibbs s adsorption equation. Guggenheim,2 developing some considerations put forward by Verschaffelt, has worked out the thermodynamics of surfaces, using a conception of the surface layer which is much more easily visualized physically than that used by Gibbs. Gibbs s surface excess is a very difficult quantity to interpret physically, as it is... 

Gibbs s adsorption equation, 196 equation for work of formation of drop, 371 thermodynamic model, 353 Gilbaut s compressibility formula, 68 glass, 1 cleaning, 281 closing pores in, 282 flow of, 1... 

The method of mixed electrolytes first presented in two fundamental papers by Hurwitz [11] and Dutldewicz and Parsons [12] was an important contribution to the methods of evaluation of specific adsorption. In Ref. [11], Gibbs s adsorption equation has been derived in a general form for the case of mixed solutions of strong electrolytes at constant molal ionic strength. 

Gibbs s adsorption equation was tested by W. C. McC. Lewis, F. W. Donnan and J. T. Barker, and (in a more satisfactory way) by J. W. McBain and C. W. Humphries and McBain and R. C. Swain,who confirmed it for an air-solution interface. Zawidzki found that the concentration of saponin in the foam of a solution was 1 26 to 1 33 times that in the bulk of the solution there can be no doubt that the concentration is actually greater in the surface layer of a solution than in the interior. Ramsden observed the formation of a solid film on the surface of some solutions and suspensions, and Metcalf the formation of a skin of peptone on a water surface. These phenomena are connected with Gibbs s theory. 

Usually Ax measurements are coupled with measurements of the surface excess T of adsorbate which causes the change of X T data are derived from surface tension measurements by means of Gibb s adsorption equation. The derivative 9(A)09r, or the integral slope AX/AF, then gives a measure of the average surface potential change per molecule of adsorbate in the... 

Thus the experimentally determined relationship between the specific volume of n-hexane film on the Teflon surface and zeta potential value was used to determine the film pressure II from the empirical equation similar to Gibb s adsorption equation, where in place of the vapor pressure zeta potential was introduced, yielding ... 

The method of deduction also applies when B is a liquid, or a solid, and (6) therefore holds for these cases. The equation (6) is called Gibbs s Adsorption Formula it was deduced independently by J. J. Thomson W (1888). The present deduction is due to Milner <12> (1907). 

Gas, cells, 464, 477, 511 characteristic equation, 131, 239 constant, 133, 134 density, 133 entropy, 149 equilibrium, 324, 353, 355, 497 free energy, 151 ideal, 135, 139, 145 inert, 326 kinetic theory 515 mixtures, 263, 325 molecular weight, 157 potential, 151 temperature, 140 velocity of sound in, 146 Generalised co-ordinates, 107 Gibbs s adsorption formula, 436 criteria of equilibrium and stability, 93, 101 dissociation formula, 340, 499 Helmholtz equation, 456, 460, 476 Kono-walow rule, 384, 416 model, 240 paradox, 274 phase rule, 169, 388 theorem, 220. Graetz vapour-pressure equation, 191... 

Gibbs s adsorption theorem (Chap. HI, eq. (7)) shows that the solubility of the substance in a surface film, in equilibrium with the interior, should increase according to the 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. 

Warburg (Wted. Ann. XLi. 1, 1890) observed that the surface tension of the interface between mercury and dilute acid docixiascs as the amount of the corresponding mercury salt present in the solution increases. He therefore concluded that the salt is positively adsorbed in accordance with Gibbs adsorption equation. The adsorption by mercury of its salts from aqueous solution has been directly observed by McLewis jPA /s. Ghem. Lxxvil. 129,... 

Ikeda,S. (1977) On the Gibbs adsorption equation for electrolyte solutions. Bull. Chem. Soc. Japan, 50(6), 1403-08. 

The variation of concentration of neutral components k also yields an equation similar in form to Gibbs s ordinary adsorption equation. If there is only one neutral component besides water, and if the solution is dilute, the adsorption of water can be neglected and (19) becomes... 

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. 

Here, Ms and Ms,ads are the electrochemical potentials of S in the bulk solution and in the adsorbed state. Let us apply the Gibbs adsorption equation to the interphase between a pure metal M and an aqueous solution containing molecular and ionic species denoted by the subscript j, in addition to water w and the species S. Choosing the neutral metal atoms M and the electrons e in excess with respect to metal atoms as the constituents of the metal phase, we may formally write ... 

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