A solution contains Ca²⁺ and Pb²⁺ ions, both at a concentration of 0.010 M. You wish to separate the two ions from each other as completely as possible by precipitating one but not the other using aqueous Na₂SO₄ as the precipitating agent.

1. (a) Which will precipitate first as sodium sulfate is added, CaSO₄ or PbSO₄?
2. (b) What will be the concentration of the first ion that precipitates (Ca²⁺ or Pb²⁺) when the second, more soluble salt begins to precipitate?

Interpretation:

Predict which salt PbSO4 or CaSO4 precipitate first when aqueous Na2SO4 is added to the solution containing lead and calcium ions.

Concept introduction:

The solubility of a salt is defined as the maximum amount of salt that can be dissolved in definite amount of solvent. It is expressed in moles per liter or grams per liter. Solubility in terms of moles per liter is called molar solubility and is defined as the number of moles of solute (salt) dissolved in per liter of solution.

Solubility product constant Ksp is an equilibrium constant and is defined as the product of the equilibrium concentration of the ions of the salt raised to the power of their coefficients in the balanced chemical equation.

The expression for Ksp of a salt is given as,

AxBy(s)⇌xAy+(aq)+yB−x(aq)Ksp=[Ay+]x[B−x]y

When in the solution more than one insoluble salt having one common ion is present than the one which requires less amount of the common ion to exceed its solubility product value and precipitate will precipitate out first from the solution. This is known as preferential precipitation.

Given:

Refer to the Appendix J in the textbook for the value of Ksp.

Solubility product constant Ksp for PbSO4 is 2.5×10−8.

Solubility product constant Ksp for CaSO4 is 4.9×10−5.

The initial concentration of calcium ions present is 0.01 M.

The initial concentration of lead ions present is 0.01 M.

PbSO4 dissociates as follows in water,

  PbSO4(s)⇌Pb2+(aq)+SO42−(aq)

Ksp=[Pb2+][SO42−]

Rearrange for [SO42−] and substitute values.

[SO42−]=Ksp[Pb2+]=(2.5×10−8)(0.01)=2

Interpretation:

The concentration of first ion (Ca2+ or Pb2+ ) that is present in the solution when second salt just begins to precipitate is to be calculated.

Concept introduction:

Solubility product constant Ksp is an equilibrium constant and is defined as the product of the equilibrium concentration of the ions of the salt raised to the power of their coefficients in the balanced chemical equation.

The expression for Ksp of a salt is given as,

AxBy(s)⇌xAy+(aq)+yB−x(aq)Ksp=[Ay+]x[B−x]y