Q2(b)(i). Interfacial tension between two immiscible liquids

1. Interfacial tension γ_(AB) is the work needed to create unit area of the A | B interface. Separating unit area of that interface creates unit area of each liquid–air surface, so the work of adhesion is W_(AB)=γ_A+γ_B-γ_(AB) (Dupré equation). A and B molecules attract each other, so W_(AB)>0 and γ_(AB)<γ_A+γ_B.
2. The liquid of lower surface tension, B, spreads over A. In the container each liquid soon saturates the other, and the surface of A is covered by a film of B. At this equilibrium the spreading coefficient of B on A, S=γ_A-γ_B-γ_(AB), falls to zero, which gives γ_(AB)=γ_A-γ_B
3. Example: with the pure-liquid values for water (72.75 mN m⁻¹) and benzene (28.88 mN m⁻¹) at 293 K the difference is 43.9 mN m⁻¹. This is an upper estimate: the rule uses the surface tensions of the mutually saturated layers, which are lower than those of the pure liquids. The rule is empirical and only approximate.
4. A closer estimate (Girifalco–Good, Fowkes) counts only the forces that act across the interface: γ_(AB)=γ_A+γ_B-2γ_A^dγ_B^d, where γ^d is the dispersion part of each surface tension. For water and a hydrocarbon only dispersion forces act across the boundary.

Reading the answer: γ_(AB) is always less than γ_A+γ_B, because the A–B attraction lowers it; it is close to γ_A-γ_B for mutually saturated liquids, where B no longer spreads on A. The more alike the two liquids, the stronger the A–B attraction and the smaller γ_(AB); for liquids that mix, the interface and its tension disappear. A low γ_(AB) is what an emulsifier produces when it collects at an oil–water interface.