Solubility Product Calculations (CIE A Level Chemistry)

• Calculations involving the solubility product (K_sp) may include::
  • Calculating the solubility product of a compound from its solubility
  • Calculating the solubility of a compound from the solubility product

Worked example: Calculating the solubility product of a compound from its solubility

Answer

• Step 1: Write down the equilibrium equation

PbBr₂ (s) ⇌ Pb²⁺ (aq) + 2Br^- (aq)

• Step 2: Write down the equilibrium expression

K_sp = [Pb²⁺(aq)] [Br^- (aq)]²

• Step 3: Calculate the ion concentrations in the solution

[PbBr₂(s)] = 1.39 x 10^-3 mol dm^-3

The ratio of PbBr₂ to Pb²⁺ is 1:1

[Pb²⁺(aq)] = [PbBr₂(s)] = 1.39 x 10^-3 mol dm^-3

The ratio of PbBr₂ to Br^- is 1:2

[Br^-(aq)] = 2 x [PbBr₂(s)] = 2 x 1.39 x 10^-3 mol dm^-3

= 2.78 x 10^-3 mol dm^-3

• Step 4: Substitute the values into the expression to find the solubility product

K_sp = (1.39 x 10^-3) x (2.78 x 10^-3)²

= 1.07 x 10^-8

• Step 6:  Determine the correct units of K_sp

K_sp = (mol dm^-3) x (mol dm^-3)²

= mol³ dm^-9

The solubility product is therefore 1.07 x 10^-8 mol³ dm^-9

Worked example: Calculating the solubility of a compound from its solubility product

Answer

• Step 1: Write down the equilibrium equation

CuO (s) ⇌ Cu²⁺ (aq) + O^2- (aq)

• Step 2: Write down the equilibrium expression

K_sp = [Cu²⁺ (aq)] [O^2- (aq)]

• Step 3: Simplify the equilibrium expression

The ratio of Cu²⁺ to O^2- is 1:1

[Cu²⁺(aq)] = [O^2-(aq)] so the expression can be simplified to:

K_sp = [Cu²⁺ (aq)]²

• Step 4: Substitute the value of K_sp into the expression to find the concentration

5.9 x 10^-36 = [Cu²⁺ (aq)]²

= 2.4 x 10^-18 mol dm^-3

Since [CuO(s)] = [Cu²⁺ (aq)] the solubility of copper oxide is 2.4 x 10^-18 mol dm^-3