• 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