Chemistry of Freshwaters - Principles of Environmental Chemistry - page 84

where the solubility product,
K SP ¼ Ca 2 þ Cl f 2 ¼ g Ca 2 þ g Cl ½ Ca 2 þ ½ Cl 2

We define the mean ion activity coecient as the geometric mean of
the single-ion activity coecients
g CaCl 2 ¼ð g Ca 2 þ g Cl g Cl Þ 1 = 3

The mean ion activity coecient values can be obtained from experi-
ments where the effect of electrolyte concentration on the K SP value
for a salt is determined. The mean values are then compared with
those for KCl under the same solution conditions. The single-ion
activity coecient for Ca 21 can then be computed if an assumption is
made about the individual values for K 1 and Cl . These ions have the
same magnitude of charge and similar electronic configuration, ionic
radii, and ionic mobilities. On the basis of these properties, the
MacInnes convention (1919) states that
g K 1 ¼ g Cl ¼ g KCl

In general: g cation ¼ð g cationCl x 1 Þ x =ð g KCl Þ x 1

Thus g CaCl 2 ¼ð g Ca 2 þ g Cl Þ 1 = 3 ¼ð g Ca 2 þ g 2 KCl Þ 1 = 3

and g Ca 2 þ ¼ð g CaCl 2 Þ 3 =ð g KCl Þ 2

For I ¼ 0.1 mol l 1 : g Ca 2 þ ¼ð 0 : 518 Þ 3 =ð 0 : 770 Þ 2 ¼ 0 : 234

(Mean salt data from Robinson and Stokes. 9 )

Although other methods using such experimental data have been
documented, 14 theoretical and/or empirical considerations have led to
various expressions involving a dependence on ionic strength, I, which is
a major factor influencing the activity of solutes in aqueous solution.

3.2.1.2 Ionic Strength. Ionic strength, I, is a measure of the charge
density in solution and is defined as
I ¼ 0 : 5 X i ½ z i ð 3 : 2 Þ