Surfactants (Soaps and Detergents) and Physicochemical Properties - Surface and Colloid Chemistry: Principles and Applications - page 56

Interface Gas Phase

Solution

(a)

Solvent

Divinding Surface

Solute

Distance

(b)

FIGure 3.15 Liquid composition column in an ideal system (schematic).

In an exactly similar manner, the respective surface excess internal energy E x and
entropy S x can be defined by the following mathematical relationships (Chattoraj and
Birdi, 1984; Birdi, 1989):

E x = E t − E α − E β (3.13)

S x = S t − S α − S β (3.14)

Here, E t and S t are the total energy and entropy, respectively, of the system as a whole
for the actual liquid system. The energy and entropy terms for the α and β phases
are denoted by the respective superscripts. The excess (x) quantities thus refer to the
surface molecules in the adsorbed state.
The real and idealized systems are open so that following equation can be written:

dE t = T dS t −(p dV + p′ dV′ − γ dA) + μ 1 dn 1t +

μ 2 2 dn 2t + … + μ i dn i t (3.15)