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 A^{n} is a conjugate base of an acid with equilibria
etc.
Although the salt dissociates to form M^{n+} and A^{n}, the A^{n} is basic and `grabs' protons from water. Acidic forms of the A^{n} 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 M^{n+} dissolved, one mole of A^{n} is initially formed. The A^{n}, in turn, is distributed among all acid forms.
From the a_{n} definition we know that the fraction of acid as A^{n} is
Substitution of this into the K_{sp} equation gives a simple result
As a concrete example, consider the molar solubility of calcium carbonate at pH 6. Calcium carbonate dissociates by
The K_{sp} =6.0x10^{9}. Carbonate will be distributed as CO_{3}^{2}, HCO_{3}^{}, and H_{2}CO_{3}
where K_{a1} = 4.45x10^{7} and K_{a2} = 4.69x10^{11}. The a expressions are
To find the molar solubility we use the table to find the amounts of solution phase species.
CaCO_{3} (s) > 
Ca^{2+} (aq) 
CO_{3}^{2} (aq) 

initial  solid 
0 
0 
change   x 
+ x 
+ x 
final  solid 
x 
x 
For each x mole of CaCO_{3} that dissolves, x mole of Ca^{2+} and x mole of CO_{3}^{2} are formed. The CO_{3}^{2} will be distributed in the different acid forms. But we know F_{A} and the concentrations of the various forms are still related to F_{A} through the a
The K_{sp} equation is cast in the form
Using the values from the table
where x is equal to [Ca^{2+}], F_{A}, and is the molar solubility of CaCO_{3}. To find the molar solubility we first determine a_{2}. At pH 6, [H_{3}O^{+}]=10^{6} and a_{2}=1.44x10^{5}. The molar solubility is
Molar solubilities at other pH's are given in the Table below. Notice that CaCO_{3} 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  pa_{2}  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 CaCO_{3} as a function of pH
This page was created by Professor Stephen Bialkowski, Utah State University.
August 03, 2004