Relating solubility and ion concentrations in saturated solutions of ionic solids
We have developed relationships showing how solubility is related to change in concentration of the ions as a result of dissolving.
It is important to realize that solubility is directly related to equilibrium concentration of only those ions present in solution exclusively due to the dissolving reaction. Compare dissolving PbCl2 in water with dissolving PbCl2 in 0.1 mol L-1 NaCl.
In both cases:
PbCl2(s)
Pb2+(aq) + 2Cl–(aq)
Ks = [Pb2+][Cl–]2
Solution 1: In water:
The initial concentrations of Pb2+ and Cl– are zero, the equilibrium concentrations of both ions are related directly to solubility through the stoicheiometry of the dissolving reaction.
Solution 2: In 0.1 mol L-1 NaCl:
Pb2+ arises exclusively from the dissolving reaction and is related to solubility as shown above. In contrast, the equilibrium concentration of Cl– includes Cl– initially present in the solution and is not a direct measure of solubility.
s(PbCl2) which is equal to the concentration of Pb2+ is lower than for water because the concentration of Cl– is higher and Ks(PbCl2) is constant.
It is important to realize that solubility is directly related to equilibrium concentration of only those ions present in solution exclusively due to the dissolving reaction. Compare dissolving PbCl2 in water with dissolving PbCl2 in 0.1 mol L-1 NaCl.
In both cases:
PbCl2(s)
Pb2+(aq) + 2Cl–(aq)Ks = [Pb2+][Cl–]2
| s(PbCl2) | = | change in [Pb2+] | = | change in [Cl–] |
| 1 | 2 |
Solution 1: In water:
The initial concentrations of Pb2+ and Cl– are zero, the equilibrium concentrations of both ions are related directly to solubility through the stoicheiometry of the dissolving reaction.
| In water | [Pb2+] | [Cl–] |
| initial | 0 | 0 |
| change | +s | +2s |
| equilibrium | s | 2s |
Solution 2: In 0.1 mol L-1 NaCl:
Pb2+ arises exclusively from the dissolving reaction and is related to solubility as shown above. In contrast, the equilibrium concentration of Cl– includes Cl– initially present in the solution and is not a direct measure of solubility.
s(PbCl2) which is equal to the concentration of Pb2+ is lower than for water because the concentration of Cl– is higher and Ks(PbCl2) is constant.
| In 0.1 mol L-1 NaCl | [Pb2+] | [Cl–] |
| initial | 0 | 0.1 |
| change | +s | +2s |
| equilibrium | s | 0.1 + 2s |