and this also holds for the Clions. Form 24 m 1 , the salt composition is
nearly the same in both compartments.
If a mixture of salts is present, the concentration ratio of all univalent
cations will be equal to that of Naþ, provided that the total concentration of
univalent cations is the same. This thus also applies to Hþ. Taking the upper
row of Table 6.2, where the ratio is 4.33, it follows that the pH would be
lower by log 4: 33 ¼ 0 :64 units in the compartment containing the polyelec-
trolyte. Such pH differences can indeed be measured. For a ratio of 2, the
pH difference would be log 2¼ 0 :30, etc. Increasing ionic strength thus leads
to smaller differences in salt composition and in pH. For a polybase, the pH
would be higher in the compartment with polymer. For coions, the
concentration ratio is the inverse of that for counterions.
It also follows that the osmotic pressure will be higher in the
compartment containing the polyelectrolyte, and water will be drawn in
until the osmotic pressure is equal on either side, provided that this would
not provoke a hydrostatic pressure difference. Accurate prediction of the
osmotic pressure is intricate, because of large nonideality, and we will only
consider the osmolality. As long as the volumes remain unchanged, a
difference in osmolality of
m 1
zþm 1 m 2
m 1 þ 2 m 2is produced. Some results are in Table 6.2. It is seen that the difference is far
larger than that due to the polymer only, which would have been
m 1 =z¼ 0 :01 mmolal in the present case. This implies that a simple
measurement of osmotic pressure to determine the molar mass of a polymer
would yield highly erroneous results for polyelectrolytes. Nevertheless,
reliable determinations can be made, but the theory is intricate, and
painstaking experimentation is needed.
Polyelectrolyte Conformation. Up till here, we have considered
two compartments separated by a semipermeable membrane. However, this
is not essential to the existence of the Donnan effect. In Figure 6.9
(especially 6.9c) a polyelectrolyte molecule is depicted with a volume around
it that contains an excess of counterions and that is depleted of coions.
Actually, there is no sharp boundary surface involved, since the difference in
concentration between counterions and coions gradually decreases with
distance from the polyelectrolyte molecule. This is reflected in the gradual
decrease in electric potential, as depicted in Figure 6.8. Since there are no