Handbook of Solvents - George Wypych - ChemTech - Ventech!

5.5 The phenomenological theory of solvent effects 289
Figure 5.5.3. Surface tension of 2-propanol-water mixtures.
The smooth line is drawn with eq. 5.5.26. (Reproduced
with permission from the Journal of Solution
Chemistry. reference 14.)
of surface tension in mixed solvent systems, air playing the role of the solute. Figures 5.5.3
and 5.5.4 show examples of these curve-fits. 14
When K2 = 0, eq [5.5.26] gives the 1-step model, eq. [5.5.27], where γ′ = γ −γ
⎡ Kx 1 2
γ = γ + γ′
1 ⎢
⎣x
+ K x
1 1 2
⎤
⎥
⎦
2 1 .
[5.5.27]
We had earlier 15 published an equation describing the dependence of surface tension
on composition, and a comparison of the two approaches has been given; 14 here we will restrict
attention to eqs. [5.5.26] and [5.5.27].
Suppose we set K 1 = 2 and K 2 = 1/2 in eq. [5.5.26]. This special condition converts eq.
[5.5.26] to
γ = γ x + γ x [5.5.28]
1 1 2 2
Figure 5.5.4. Surface tension of glycerol-water mixtures.
The smooth line is drawn with eq. 5.5.26. (Reproduced
with permission from the Journal of Solution
Chemistry. reference 14.)
which corresponds to ideal behavior; the surface tension is a linear function of x2. The restriction
K1 =2,K2= 1/2 is, however, a unique member of a less limited special case in
which K1 =4K2. This important condition (except when it happens to occur fortuitously)
implies the existence of two identical and independent binding sites. 16 Inserting K2 =K1/4 into eq. [5.5.26] yields, upon simplification, eq. [5.5.29], where γ′ = γ −γ
2 1 .