Thermodynamics of Binary Systems The Gibbs Equation

We now come to a very important topic, namely, the thermodynamic treatment of the variation of surface tension with composition. The treatment is due to Gibbs [35] (see Ref. 49 for an historical sketch) but has been amplified in a more conveniently readable way by Guggenheim and Adam [105]. 

As in Section III-2A, it is convenient to suppose the two bulk phases, a and /3, to be uniform up to an arbitrary dividing plane S, as illustrated in Fig. Ill-10. We restrict ourselves to plane surfaces so that C and C2 are zero, and the condition of equilibrium does not impose any particular location for S. As before, one computes the various extensive quantities on this basis and compares them with the values for the system as a whole. Any excess or deficiency is then attributed to the surface region. 

Taking the section shown in Fig. HI-10 to be of unit area in cross section, then, if the phases were uniform up to 5, the amount of the ith component present would be 

the distances x and a are relative to planes A and B located far enough from the surface region so that bulk phase properties prevail. The actual amount of component i present in the region between A and B will be 

For the case where the phase /3 is gaseous, cf may be neglected, and quantities ni-65 and III-66 become 

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