Relative Solubility Example Problem

Ranking Solubility from Solubility Products

Relative solubility calculations let you predict how much of a solute will dissolve into a solution.
Relative solubility calculations let you predict how much of a solute will dissolve into a solution. GIPhotoStock / Getty Images

Solubility is a measure of how much of a compound dissolves in a specified volume of solvent. Relative solubility is a comparison of which compound is more soluble than another. One reason you might want to compare the solubility of compounds is so you can predict the formation of a precipitate or identify its composition. Relative solubility may also be used to separate components of a mixture. This example problem demonstrates how to determine the relative solubility of ionic compounds in an water.

Relative Solubility Problem

AgCl has a Ksp of 1.5 x 10-10.

Ag2CrO4 has a Ksp of 9.0 x 10-12.

Which compound is more soluble?

Solution:

AgCl dissociates by the reaction:

AgCl (s) ↔ Ag+ (aq) + Cl- (aq)

Each mole of AgCl that dissolves produces 1 mole of Ag and 1 mole of Cl.

solubility = s = [Ag+] = [Cl-]

Ksp = [Ag+][Cl-]
Ksp = s·s
s2 = Ksp = 1.5 x 10-10
s = 1.2 x 10-5 M

Ag2CrO4 dissociates by the reaction:

Ag2CrO4 (s) ↔ 2 Ag+ (aq) + CrO42- (aq)

For each mole of Ag2CrO4 dissolved, 2 moles of silver (Ag) and 1 mole of chromate (CrO42-) ions are formed.

[Ag+] = 2[CrO42-]

s = [CrO42-]
2s = [Ag+]

Ksp = [Ag+]2[CrO42-]
Ksp = (2s)2·s
Ksp = 4s3
4s3 = 9.0 x 10-12
s3 = 2.25 x 10-12
s = 1.3 x 10-4

Answer:

The solubility of Ag2CrO4 is greater than the solubility of AgCl. In other words, silver chloride is more soluble in water than silver chromate.