KEY2CHEM

Solubility Equilibrium

The dissolution of a ionic compound (or salt), such as $$\text{NaCl}$$, is a reversible process:

$$\require{mhchem}\ce{NaCl(s) <=> Na+(aq) + Cl^{-}(aq)}$$

Where the dissolving of the solid ionic compound is in equilibrium with the recrystallizing of the dissolved ions to re-form the solid. The equilibrium constant for this reaction is the solubility product constant, $$K_{sp}$$. The larger the $$K_{sp}$$ value, the more solid dissolves into its ions (meaning, the more soluble the salt is).

Example 1.

Which salt is predicted to have the lowest solubility in pure water? $$K_{sp}$$ values are provided.

A. $$\require{mhchem}\ce{BaF2}; K_{sp} = 1.8 \times 10^{-7}$$

B. $$\require{mhchem}\ce{MgF2}; K_{sp} = 7.4 \times 10^{-11}$$

C. $$\require{mhchem}\ce{SrF2}; K_{sp} = 2.5 \times 10^{-9}$$

Solution

B. $$\require{mhchem}\ce{MgF2}; K_{sp} = 7.4 \times 10^{-11}$$

The salt with the smallest solubility product constant ($$K_{sp}$$) has the lowest concentration of dissolved ions at equilibrium and the lowest solubility.

Example 2.

Place the following salts in order of increasing solubility in pure water. $$K_{sp}$$ values are provided.

$$\require{mhchem}\ce{PbCl2}; K_{sp} = 1.2 \times 10^{-5}$$

$$\require{mhchem}\ce{PbBr2}; K_{sp} = 6.6 \times 10^{-6}$$

$$\require{mhchem}\ce{PbI2}; K_{sp} = 8.5 \times 10^{-9}$$

A. $$\require{mhchem}\ce{PbCl2} < \require{mhchem}\ce{PbBr2} < \require{mhchem}\ce{PbI2}$$

B. $$\require{mhchem}\ce{PbI2} < \require{mhchem}\ce{PbBr2} < \require{mhchem}\ce{PbCl2}$$

C. $$\require{mhchem}\ce{PbBr2} < \require{mhchem}\ce{PbCl2} < \require{mhchem}\ce{PbI2}$$

Solution

B. $$\require{mhchem}\ce{PbI2} < \require{mhchem}\ce{PbBr2} < \require{mhchem}\ce{PbCl2}$$

The salt with the smallest solubility product constant ($$K_{sp}$$) has the lowest concentration of dissolved ions at equilibrium and the lowest solubility. The salt with the largest $$K_{sp}$$ value has the highest concentration of dissolved ions at equilibrium and the greatest solubility.

Example 3.

Which salt is most soluble in pure water? $$K_{sp}$$ values are provided.

A. $$\require{mhchem}\ce{NaCl}; K_{sp} = 36$$

B. $$\require{mhchem}\ce{AgCl}; K_{sp} = 1.8 \times 10^{-10}$$

C. $$\require{mhchem}\ce{CuCl}; K_{sp} = 1.7 \times 10^{-7}$$

Solution

A. $$\require{mhchem}\ce{NaCl}; K_{sp} = 36$$

The salt with the largest $$K_{sp}$$ value has the highest concentration of dissolved ions at equilibrium and the greatest solubility.