Use of Acid Distributions in Solubility Problems

For solutions with controlled pH, the counter ion solubility effects are easily accounted for in determining the solubility of a salt producing a conjugate base. Say we have a metal/conjugate base salt, MA, that ionizes (dissociates) in solution by

where An- is a conjugate base of an acid with equilibria

etc.

Although the salt dissociates to form Mn+ and An-, the An- is basic and `grabs' protons from water. Acidic forms of the An- anion do not form an insoluble salt complex.

The problem is not intractable. In fact, it is easy if the pH is known. To find the solution, we note that for each mole of Mn+ dissolved, one mole of An- is initially formed. The An-, in turn, is distributed among all acid forms.

From the an definition we know that the fraction of acid as An- is

Substitution of this into the Ksp equation gives a simple result

As a concrete example, consider the molar solubility of calcium carbonate at pH 6. Calcium carbonate dissociates by

The Ksp =6.0x10­9. Carbonate will be distributed as CO3, HCO3­, and H2CO3

where Ka1 = 4.45x10­7 and Ka2 = 4.69x10­11. The a expressions are

To find the molar solubility we use the table to find the amounts of solution phase species.

 CaCO3 (s) --> Ca2+ (aq) CO32- (aq) initial solid 0 0 change - x + x + x final solid x x

For each x mole of CaCO3 that dissolves, x mole of Ca2+ and x mole of CO32- are formed. The CO32- will be distributed in the different acid forms. But we know FA and the concentrations of the various forms are still related to FA through the a

The Ksp equation is cast in the form

Using the values from the table

where x is equal to [Ca2+], FA, and is the molar solubility of CaCO3. To find the molar solubility we first determine a2. At pH 6, [H3O+]=10­6 and a2=1.44x10­5. The molar solubility is

Molar solubilities at other pH's are given in the Table below. Notice that CaCO3 is soluble in acid solution but is insoluble in basic solution. This feature is used by Geologists to test for carbonate rock (calcite). Calcite `fizzes' when HCl is dropped on it but has no reaction with NaOH. Why does it `fizz?'

 pH pa2 molar solubility 2 12.68 170 4 8.68 1.70 6 4.84 0.020 8 2.34 0.0011 10 0.49 1.4x10-4 12 0.0092 7.8x10-5

solubility of CaCO3 as a function of pH