magnitudes decrease by a factor 28 when going from 12 to 18 C atoms. (As a
parameter to characterize the surface activity, the surfactant concentration
at whichGreaches a given proportion [say, 1/2] of its maximum value can
also be taken.)
It may finally be noted that the surface free energy is no longer equal
to the surface tension if the latter is altered by the presence of a surfactant. A
full explanation is intricate, but it has to do with the decrease in mixing
entropy (translational and conformational) of the solution upon depletion
of surfactant due to its adsorption. For surfactants like globular proteins,
the difference is generally small, since the high molar mass of the protein
limits the change in translational mixing entropy, and the change in
conformational entropy of the solution will also be small.
Question
Consider a saturated aqueous solution of Na-stearate (C18). 10%pure oil is added to
it and the mixture is emulsified so that droplets of average sized 32 ¼ 1 mm are
assumed to be formed. What proportion of the surfactant would then become
adsorbed onto the oil droplets? Make the same calculation for Na-myristate (C14) at
a concentration that equals its CMC. Assume Figure 10.6 to be valid.
Answer
From the figure, the solubility of Na-stearate is slightly below 100.5or about
0.3 mol?m^3. The specific oil surface area would equal 6/d 32 ¼ 6? 106 m^2 per m^3 of
oil. For 1 m^3 of water, the areaAthen is 6? 105 m^2. At the solubility limit,G&
9 mmol?m^2 , and A?Gwould amount to about 5.4 mol?m^3. However, this
corresponds to 18 times the amount of Na-stearate present, which is clearly
impossible. It is even unlikely that an emulsion can be made.
Doing the same calculation for Na-myristate, we would obtain 3.20 mol?m^3
for the CMC and 3.48 mol?m^3 forA?G, which is above the CMC, though not
greatly so. What now will happen is thatGwill be smaller than its plateau value, so
that the concentration left in solution (CMCA?G) will produce precisely thatG
value according to Figure 10.6b. This value is about 4.4mmol?m^2. (Check this
calculation.)
10.2.2 Adsorption Isotherms
Adsorption isotherms provide important knowledge, for instance, if the
amount of surfactant needed to make an emulsion has to be established, as