Solubility and Solubility Product · Chemistry

Saturated solutions and the solubility product

In a saturated solution of a sparingly soluble salt, the solid is in dynamic equilibrium with its ions: AgCl(s) ⇌ Ag⁺(aq) + Cl⁻(aq). The equilibrium constant, which leaves out the solid, is the solubility product K_sp.

Salt	Dissolving	K_sp expression	K_sp at 25 °C
Silver chloride, AgCl	AgCl ⇌ Ag⁺ + Cl⁻	[Ag⁺][Cl⁻]	1.8 × 10⁻¹⁰ mol²/dm⁶
Barium sulphate, BaSO₄	BaSO₄ ⇌ Ba²⁺ + SO₄²⁻	[Ba²⁺][SO₄²⁻]	1.1 × 10⁻¹⁰
Calcium hydroxide, Ca(OH)₂	Ca(OH)₂ ⇌ Ca²⁺ + 2OH⁻	[Ca²⁺][OH⁻]²	5.5 × 10⁻⁶
Lead(II) iodide, PbI₂	PbI₂ ⇌ Pb²⁺ + 2I⁻	[Pb²⁺][I⁻]²	7.1 × 10⁻⁹

Worked exampleSolubility from Ksp

The K_sp of silver chloride is 1.8 × 10⁻¹⁰. Find the solubility in mol/dm³.

If s mol/dm³ dissolves, [Ag⁺] = [Cl⁻] = s.
K_sp = s².

Answer: The solubility of AgCl is about 1.3 × 10⁻⁵ mol/dm³.

Try itSolubility from the solubility product

Choose the type of salt (1 = AB, such as AgCl; 2 = AB₂, such as PbI₂) and its K_sp as a power of ten. Find the solubility s.

For AB₂, [A] = s and [B] = 2s, so K_sp = s(2s)² = 4s³.

Precipitation and the common ion effect

A precipitate forms if the ionic product (the same expression as K_sp using the concentrations at that moment) is greater than K_sp. No precipitate forms if it is less. The common ion effect: adding a soluble salt that shares an ion with a sparingly soluble salt reduces its solubility. Silver chloride is much less soluble in sodium chloride solution than in pure water.

Adding chloride ions from sodium chloride pushes the equilibrium to the left, so less AgCl dissolves.

Applications

Application	Idea
Water softening	Adding sodium carbonate precipitates Ca²⁺ as insoluble CaCO₃
Barium meal in X-rays	BaSO₄ is so insoluble that the toxic Ba²⁺ is not absorbed
Testing for chloride ions	Silver nitrate forms insoluble AgCl
Tooth enamel	Hydroxyapatite dissolves in acid, which is why sugar and acid cause decay; fluoride makes it less soluble
Removing heavy metals from waste water	Precipitation as hydroxides or sulphides

Check yourself Which expression is the solubility product of PbI₂?

Check yourself Adding NaCl to a saturated solution of AgCl will…

Check yourself Which condition causes precipitation?

Key terms

Solubility product: K_sp, the equilibrium constant for a sparingly soluble salt dissolving.
Ionic product: The product of the ion concentrations at a given moment.
Common ion effect: The reduction in solubility of a salt caused by a common ion from another source.
Sparingly soluble: Dissolving only very slightly.

Summary

K_sp is the product of the ion concentrations in a saturated solution.
AB: s = √K_sp; AB₂: s = (K_sp ÷ 4)^(1/3).
A precipitate forms when the ionic product exceeds K_sp.
A common ion decreases solubility.