In this paper, the Gibbs−Duhem equation is extended to the partial molar surface thermodynamic properties of solutions. According to the surface Gibbs−Duhem equations, the sum of the mole fractions of the components in the surface region of a bulk solution multiplied by different partial molar surface quantities should equal zero if summation is taken by all components of the solution. There are four different partial molar surface quantities identified in this paper for which the surface Gibbs−Duhem equation is proven to be valid: (i) the reduced surface chemical potential, (ii) the surface chemical potential, (iii) the partial molar surface area, and (iv) the partial molar excess surface Gibbs energy = the product of partial molar surface area and the partial surface tension. The first one is known since Guggenheim (1940), but the other three are presented here for the first time. It is also demonstrated here how to apply the surface Gibbs−Duhem equations: (i) it is proven that the model equation applied by us recently for the reduced chemical potential [Adv Coll Interf Sci 2020, 283, 102212] obeys one of the surface Gibbs−Duhem equations, (ii) in contrary, it is proven that the model equation suggested by us recently for the partial molar surface area contradicts one of the surface Gibbs−Duhem equations; therefore, a new (and simpler) model equation for the partial molar surface areas of the components is suggested here that obeys the surface Gibbs−Duhem equation. It is also shown that the Butler equation obeys one of the surface Gibbs−Duhem equations. It is also concluded that surface composition in equilibrium should be one that ensures minimum surface tension.
Bulk, surface and interface thermodynamics of immiscible liquid alloys are considered within a unified theoretical framework. For bulk thermodynamic functions the exponential and the combined linear-exponential equations are discussed, obeying the 4th law of thermodynamics. Surface phase transition is discussed in details. For surface and interface thermodynamics the monolayer Butler equation is compared to the multilayer model. During further assessment of bulk thermodynamic data of immiscible liquid alloys their experimentally measured surface tension and interfacial energy should be also taken into account, coupled with the models presented here.
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