PHYSICAL CHEMISTRY IN BRIEF

CHAP. 14: DISPERSION SYSTEMS [CONTENTS] 463

The osmotic pressure is given by a relation analogous to that for molecular solutions (7.11).
If the system contains a low-molecular electrolyte KA, in addition to a high-molecular elec-
trolyte KR whose anion R−does not pass through the membrane, a different equilibrium is
established in the system. It is influenced by the activity of the electric charges of ions, and
it is known as theDonnan equilibrium. The equilibrium is conditioned by equal activity of
the electrolyte KA in both subsystems (denoted by the subscripts I and II)

(aK+aA−)I= (aK+aA−)II. (14.8)

Example

A subsystem I contains a polymerous electrolyte NaR of the concentrationc 1 = 0. 1 mmol dm−^3 ,

and an NaCl electrolyte of the concentrationc 2 = 1mmol dm−^3. Another subsystem, II, of the

same volume, separated from the first one by a membrane, contains pure water. Assuming unit

activity coefficients and complete dissociation, determine the equilibrium concentration of NaCl

in the second subsystem.

Solution

We usexto denote the amount of substance of the Na+and Cl−ions which pass through the

membrane to the second subsystem. For the first subsystem we thus have

(aNa+aCl−)I≈(cNa+cCl−)I= (c 1 +c 2 −x) (c 2 −x),

for the second subsystem we write

(aNa+aCl−)II≈(cNa+cCl−)II=x×x.

If we set both activities of the electrolytes equal, we obtain

x=

c 2 (c 2 +c 1 )

c 1 + 2c 2

=

1 × 10 −^3 (1× 10 −^3 + 1× 10 −^4 )

1 × 10 −^4 + 2× 10 −^3

= 0. 524 mmol dm−^3.

If there is only the strong high-molecular electrolyte KR on one side of the membrane,
which is actually present in the form of the K+and R−ions, the K+ions also pass to the
other subsystem. In order to preserve electroneutrality of both subsystems, the OH−ions by