Effect of Diverse Ions on Solubility

James Richard Fromm

The common ion effect, illustrated in the examples of the previous section, is the effect on solubility observed when an ion common to a slightly soluble salt is present in solution from some other source. Addition of a common ion will always operate directly through the solubility product expression to decrease the solubility. The common ion effect is large, to the point of decreasing the molar solubility by several orders of magnitude, and can never be neglected. Addition of an ion which is not common to the slightly soluble salt is also observed to decrease the solubility, but this diverse ion effect is much smaller and can usually be neglected. We shall consider it briefly here because it is a useful introduction to the difference between activity and concentration of solutes in water.

Deviation of Solute Activity from Concentration

The table below gives the mean activity coefficients for certain salts in aqueous solutions at 25oC. This table is necessary for quantitative understanding of the material of this section.

Table: Mean Activity Coefficients of Aqueous Salts at 25oC
Concentration Coefficient Coefficient Coefficient Coefficient
(mol/kg H2O) KCl (1:1) H2SO4 (2:1) CaCl2 (1:2) ZnSO4 (2:2)
0.0001 0.989 --- 0.962 ---
0.0005 0.975 0.885 0.918 0.780
0.001 0.965 0.830 0.887 0.700
0.005 0.928 0.639 0.783 0.477
0.01 0.901 0.544 0.724 0.387
0.05 0.816 0.340 0.574 0.202
0.10 0.769 0.265 0.518 0.150
0.50 0.649 0.154 0.448 0.063
1.00 0.603 0.130 0.500 0.044
5.00 0.590 0.212 5.89 (0.07)
10.00 --- 0.553 43.0 ---

Addition of any soluble compound to a saturated aqueous solution of a slightly soluble gas or salt is found to cause a small change in the solubility of the gas or salt; this phenomenon is sometimes referred to as salting in or salting out a compound from solution. It is also referred to as the diverse ion effect. Similar effects are found for all of the other equilibrium constants which describe the behavior of ions in dilute aqueous solution. As long as the solution remains "dilute enough", the equilibrium constants are, within experimental error, actually constant, but with rising concentrations of solutes the values of the constants are constant no longer. This change is generally measurable in aqueous solutions whose concentrations are above 0.01 molar and becomes quite marked when concentrations are above 0.1 molar.

It is tempting to explain this behavior in terms of the concentrations of water molecules being diluted by solute, but that would be an oversimplified picture. What is actually happening is that the chemical activity of the solute ions is deviating from their molar concentration. One can get the solute becoming less active, which is the usual case, on the basis that the ions interfere with each other's motions and reactions. One can also get the solute becoming more active, if its activity was previously reduced by interactions with water molecules, and in aqueous solutions of very high concentration this is sometimes found.

Chemists have found it most convenient to deal with this phenomenon by introducing an activity coefficient, usually symbolized by the Greek letter gamma (here G), which is simply the ratio between concentration and activity: a(x) = G(x)c(x). In this expression, a(x) is the actual chemical activity of some species x, c(x) is the actual molar concentration of x, and G(x) is the activity coefficient of x. We thus retain the definitions of equilibrium constants in terms of chemical activities just as they have been used in other sections, but take into account the real, and often quite measurable, differences between concentrations and activities. The approximation of activity by molar concentration is the approximation that the activity coefficient of the solute species is exactly one.

Since both activities and molar concentrations are measurable, activity coefficients can be obtained from measurements. The activity coefficients for many soluble compounds are accurately known, and a selected group of them are given in the above Table. These activity coefficients are the means of the individual activity coefficients of the ions of the salt in its aqueous solution. When slightly soluble salts are dissolved in these solutions, the activity coefficients for the ions of the soluble salts can also be used for the slightly soluble ions because the ions of the soluble salts are present in so much greater concentration that they dominate the solution.

As the table shows, the values of all solute activity coefficients approach one as the solution becomes more dilute. For ions whose charge is greater than one, the deviation is larger for the same concentration of salt because the greater electrostatic forces of the multiply-charged ions have a greater effect both upon the structure of water and upon each other.

Example. We can compare the expected values of the molar solubility of AgCl in solutions of a simple salt such as NaNO3 as the concentration of NaNO3 increases from zero to 1.0 molar, given that the molar solubility product of AgCl is 1.76 x 10-10. Since activity and molar concentration are directly proportional to each other with the proportionality constant being the activity coefficient G,

Ksp = G(Ag+)c(Ag+)G(Cl-)c(Cl-) = 1.76 x 10-10 for the equilibrium

AgCl(c) larrow.GIF (55 bytes)rarrow.gif (63 bytes) Ag+(aq) + Cl-(aq).

The molar solubility is equal to the concentration of Ag+ which in turn is equal to the concentration of Cl-, so

c2(Ag+) = Ksp/G(Ag+)G(Cl-)

At a concentration of sodium nitrate of zero, the activity coefficients of the ions can be taken as one because the solution is very dilute, so c(Ag+) is 1.33 x 10-5. As the concentration of sodium nitrate increases, the activity coefficients change. The change in the activity coefficients depends both upon the type of salt added and its concentration, but only to a lesser extent upon just which salt it is, so the effect on activity of KCl and NaNO3 are very much the same. Moreover, the effect upon activity coefficients of all slightly soluble salts is also very much the same, and so the values for KCl can be used for any ions dissolved in an aqueous solution of any univalent salt.

At c(NaNO3) = 0.0001, then, c2(Ag+) = 1.76 x 10-10/(0.989)2

and the molar solubility of silver chloride is 1.34 x 10-5 mol/liter. (For solutions this dilute the molar and molal concentrations do not differ significantly.) Tabulation of the molar solubility as a function of sodium nitrate concentration gives:

c, mol/kg H2O Molar Solubility
(NaNO3) (AgCl)
0.0 1.33 x 10-5
0.0001 1.34 x 10-5
0.001 1.37 x 10-5
0.01 1.47 x 10-5
0.1 1.73 x 10-5
1.0 2.20 x 10-5

As the above example shows, the diverse ion effect is always much smaller than the common ion effect. Addition of 0.01 molar sodium nitrate increases the molar solubility from 0.013 mmol/dm3 to 0.015 mmol/litre while addition of 0.01 molar sodium chloride reduces the molar solubility to 0.000018 mmol/litre.

Except in the most concentrated aqueous solutions, those above 0.1 molar, the activity coefficients differ from unity enough to affect only reasonably precise work. In concentrated solutions, activity coefficients of solute ions deviate significantly from each other and use of individual ionic activity coefficients is often required. Moreover, molarity and molality are significantly different in concentrated aqueous solutions. These complications, which become significant only in concentrated solutions, are beyond our scope.

Copyright 1997 James R. Fromm