Gibbs equation verification

Fig. in-12. Verification of the Gibbs equation by the radioactive trace method. Observed (o) and calculated (line) values for for aqueous sodium dodecyl sulfate solutions. (From Ref. 108.)... 

The general form of the Gibbs equation (dy = -X T d/x,) is fundamental to all adsorption processes. However, experimental verification of the equation derived for simple systems is of interest in view of the postulation which was made concerning the location of the boundary surface. 

Direct experimental verification of the Gibbs adsorption equation in aqueous solutions is difficult, because physical separation of the monomolecular layer at the water surface is required to compare the concentration differences between the surface layer and the bulk solution. Several attempts have been made on this subject from 1910 to the present day, and although an exact fit has never been obtained, the results show a good agreement with the theory. McBain and co-workers used a suitable microtome to cut off a thin layer of approximately 50-100 4m from the surface of phenol, p-toluidine etc. solutions and verified the Gibbs equation within experimental error in 1932. Later, isotopically labeled solute molecules were employed for this purpose. Beta-emitter molecules, such as 3H, 14C and 35S have also been used and the radioactivity close to the surface measured. Since electrons only travel a short distance, the recorded radioactivity comes from the interface or very near the interface. 

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

Statistical Mechanical Verification of the Gibbs Adsorption Equation... 

This paper is devoted to the verification of the quality of experimental data regarding the solubility of sparingly soluble solids, such as drugs, environmentally important substances, etc. in mixed solvents. A thermodynamic consistency test based on the Gibbs-Duhem equation for ternary mixtures is suggested. This test has the form of an equation, which connects the solubilities of the solid, and the activity coefficients of the constituents of the solute-free mixed solvent in two mixed solvents of close compositions. 

The first verification of the fundamental equations of Gibbs and Lippmann was based on surface tension (surface energy) measurements. The investigation of solid electrodes with this method is restricted. In the following paragraph a description is given of some of the modem methods, which are used for investigation of the electrochemical double layer. 

There are many methods that have been used for experimental verification of the Gibbs adsorprion equation. McBain, using very thin films (0.05 mm) from surfactant solutions, measured the concentration of the interfacial phase. This and other methods have provided excellent agreement with the Gibbs adsorprion equation (Shaw, 1992). 

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