soaps and other small-molecule surfactants, which form micelles, i.e.,
roughly spherical aggregates in which the hydrophobic tails are in the
interior and the hydrophilic heads to the outside; see Figure 2.8a. Micelles
are often formed at a well-defined critical micellization concentration
(CMC), above which almost all additional molecules are incorporated into
micelles. This implies that properties that depend on the activity of the
solute, like osmotic pressure and surface tension, hardly alter above the
CMC, since the activity hardly increases anymore; see Figure 2.8b. The way
in which the activity coefficient alters is illustrated in Figure 2.7c.
Incidentally, the presence of micelles may greatly enhance the
apparent solubility of apolar components in an aqueous phase, since they
tend to be incorporated into the interior of the micelles up to a certain level.
The activity of such an apolar component remains of course very low, but it
FIGURE2.7 Hypothetical examples of nonideality of a solute (2) in aqueous
solutions. The activity coefficient is given asa 2 =x 2 versus the mole fractionx 2 :(a)
‘‘High concentration.’’ (b) Adsorption or binding. (c) Self-association, especially
micellization. (d) Electric shielding; the broken line is for a case where other salts are
present at constant concentration.