38 Kinetic properties
mass material to which the membrane is permeable can virtually be
eliminated.
The usefulness of osmotic pressure measurements is, nevertheless,
limited to a relative molecular mass range of about 104 -10^6. Below
104 , permeability of the membrane to the molecules under considera-
tion might prove to be troublesome; and above 106 , 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 7 c + 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
been treated thermodynamically^137 '^138 , 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