## Equilibria with Calcium Carbonate

### Ksp, Solubility of Minerals

The solubility product constant is the equilibrium constant for the dissolution of the solid in water.

The Ksp value for different substances depends on both the chemical composition and the crystalline form. A few examples for common minerals at 25 deg C is below.

 compound formula Ksp Aluminium hydroxide Al(OH)3 3 x 10-34 Aluminium phosphate AlPO4 9.84 x 10-21 Barium carbonate BaCO3 2.58 x 10-9 Calcium carbonate (calcite) CaCO3 3.36 x 10-9 Calcium carbonate (aragonite) CaCO3 6.0 x 10-9 Calcium hydroxide Ca(OH)2 5.02 x 10-6 Iron(II) carbonate FeCO3 3.13 x 10-11 Iron(II) sulfide FeS 8 x 10-19

### Calcium Carbonate and Water

Minerals containing calcium carbonate have different solubilities in water. Two types of carbonate minerals are listed in the table above. An average value for the Ksp of calcium carbonate is about 5 x 10-9.

Ksp = [Ca2+][CO32-] = 5 x 10-9

There must be net neutrality so the number of positive charges must equal the number of negative charges in solution.

2 [Ca2+] + [H+] = 2 [CO32-] + [HCO3-] + [HO-]

In any basic solution of calcium carbonate, the concentration of protons is much less than the concentration of calcium ions and the concentration of bicarbonate anions is greater than either carbonate or hydroxide anions, so:

2 [Ca2+] = [HCO3-]

### Effect of CaCO3 on pH

Let's review what we know so far.
1. Henry's Law tells us the concentration of dissolved CO2.
KH/pCO2 = [CO2] = 10-4.88

2. We can treat the dissolved CO2 as an acid.
Ka1 = [HCO3-][H+]/[CO2] = 10-6.37

3. Bicarbonate is also an acid.
Ka2 = [CO32-][H+]/[HCO3-] = 10-8.4

4. The concentration of calcium carbonate is governed by the solubility product constant of the mineral.
Ksp = [Ca2+][CO32-] = 10-8.3

Using the equations above, it is possible to calculate the concentration of any of the species in solution.

[CO2] = KH/pCO2

{[H+]}3 = [CO2]2(Ka1)2(Ka2)/2(Ksp)

[HCO3-] = [CO2](Ka1)/[H+] = 2 (Ksp)([H+]2)/(Ka1)(Ka2)[CO2]

[CO32-] = (Ka1)(Ka2)[CO2]/[H+]2

Professor Patricia Shapley, University of Illinois, 2010