Page 47 - Introduction to Colloid and Surface Chemistry

38 Kinetic properties

mass material to which the membrane is permeable can virtually be
eliminated.
The usefulness of osmotic pressure measurements is, nevertheless,
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4
limited to a relative molecular mass range of about 10 -10 . Below
4
10 , permeability of the membrane to the molecules under considera-
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tion might prove to be troublesome; and above 10 , the osmotic pres-
sure will be too small to permit sufficiently accurate measurements.
Osmosis takes place when a solution and a solvent (or two
solutions of different concentrations) are separated from each other
by a semipermeable membrane - i.e. a membrane which is permeable
to the solvent but not to the solute. The tendency to equalise
chemical potentials (and, hence, concentrations) on either side of the
membrane results in a net diffusion of solvent across the membrane.
The counter-pressure necessary to balance this osmotic flow is termed
the osmotic pressure.
Osmosis can also take place in gels and constitutes an important
swelling mechanism.
The osmotic pressure II of a solution is described in general terms
by the so-called viral equation
( 1 2 }
U = cRT\ — + B 7c + B*c + . . . (2.21)
(M )
where c is the concentration of the solution (expressed as mass of
solute divided by volume of solution), M is the molar mass of the
solute, and # 2, #3, etc., are constants.
Therefore,

M = /?7Vlimn/c (2.22)
c-»0 X
Deviations from ideal behaviour are relatively small for solutions
of compact macromolecules such as proteins but can be quite
appreciable for solutions of linear polymers. Such deviations have
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been treated thermodynamically ' , mainly in terms of the
entropy change on mixing, which is considerably greater (especially
for linear polymers dissolved in good solvents) than the ideal entropy
change on mixing for a system obeying Raoult's law. This leads to
solvent activities which are smaller than ideal - i.e. an apparent
increase in the concentration and an actual increase in the osmotic
pressure of the polymer solution.
The resulting relative molecular mass refers to the composition of