Equilibrium between bulk and interfacial phases

Since the interfacial phase is in addition to the two bulk phases, the criteria (3.3.8) for phase equilibrium should be applicable if there are no external force fields. Therefore 

The molecules of any species i present in the bulk of a liquid phase experience a net force if they are at the surface of this phase (i.e. at the interface of two contiguous phases, liquid-liquid or liquid-air). This force creates a tendency for the bulk phase surface to contract and is termed the interfacial tension (unit, dyne/cm), where the superscripts refer to the two bulk phases 1 and 2. 

The coefficient in brackets on the left-hand side may be interpreted as follows. Since species 1 is the solute and s is the solvent, / ,(xii/xji) is the number of moles of solute 1 per unit area of the interface if the solvent and solute are present in the r-phase in the same ratio as in bulk phase 1. The coefficient in brackets in (3.3.38), if positive, indicates the excess number of moles of solute 1 per unit interfacial area at the interface due to a deviation in behavior from the bulk phase. Denote this explicitly by rewriting (3.3.38) as 

Incorporating such a departure in a total differential of the internal energy of the surface phase, and using Euler s theorem on homogeneous functions, the following relation can be shown to be valid for the surface phase (Guggenheim, 1967)  

Here F is called the surface excess of species i. Note that when i = s, F = 0, i.e. the surface excess of the solvent is zero. For surface active solutes, (dy /d,iiif) = (flji/Rr) (dy /dflji) is negative since y decreases with increasing solute concentration thus Ff is positive. For electrolytic solutes (e.g. salts) in an aqueous solution at an air-water interface, F could be negative since the electrolytic solute prefers the environment of the water molecules in the bulk compared to that of the air-water interface, raising the value of y over that of pure water. 

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