Equilibria Involving Sparingly Soluble Salts — Ksp, Common Ion Effect Explained

For a sparingly soluble salt MₐXᵦ dissolving in water: MₐXᵦ(s) ⇌ aM^(b+)(aq) + bX^(a-)(aq)

The solubility product expression: Ksp = [M^(b+)]ᵃ × [X^(a-)]ᵇ

(The solid MₐXᵦ is not included in the expression as its activity = 1)

Examples:

1. AgCl(s) ⇌ Ag⁺ + Cl⁻ Ksp = [Ag⁺][Cl⁻] = 1.8 × 10⁻¹⁰ at 25°C

2. BaSO₄(s) ⇌ Ba²⁺ + SO₄²⁻ Ksp = [Ba²⁺][SO₄²⁻] = 1.1 × 10⁻¹⁰

3. Ca₃(PO₄)₂(s) ⇌ 3Ca²⁺ + 2PO₄³⁻ Ksp = [Ca²⁺]³[PO₄³⁻]²

4. Ag₂CrO₄(s) ⇌ 2Ag⁺ + CrO₄²⁻ Ksp = [Ag⁺]²[CrO₄²⁻]

Let s = molar solubility (moles of salt dissolving per litre of solution)

For AB type (1:1 salt like AgCl): [Ag⁺] = s, [Cl⁻] = s Ksp = s × s = s² s = √Ksp For AgCl: s = √(1.8 × 10⁻¹⁰) = 1.34 × 10⁻⁵ mol/L

For AB₂ type (like PbCl₂: Pb²⁺ + 2Cl⁻): [Pb²⁺] = s, [Cl⁻] = 2s Ksp = s × (2s)² = 4s³ s = (Ksp/4)^(1/3)

For A₂B type (like Ag₂CrO₄: 2Ag⁺ + CrO₄²⁻): [Ag⁺] = 2s, [CrO₄²⁻] = s Ksp = (2s)² × s = 4s³ s = (Ksp/4)^(1/3)

For A₂B₃ type (like Bi₂S₃: 2Bi³⁺ + 3S²⁻): [Bi³⁺] = 2s, [S²⁻] = 3s Ksp = (2s)²(3s)³ = 108s⁵

The common ion effect states that the solubility of a sparingly soluble salt is reduced when a soluble salt sharing a common ion is added to the solution.

Example: Solubility of AgCl in presence of 0.1 M AgNO₃ (common ion = Ag⁺): Ksp(AgCl) = [Ag⁺][Cl⁻] = 1.8 × 10⁻¹⁰ Let s = molar solubility of AgCl in 0.1 M AgNO₃ [Ag⁺] = 0.1 + s ≈ 0.1 (since s << 0.1) [Cl⁻] = s 1.8 × 10⁻¹⁰ = 0.1 × s s = 1.8 × 10⁻⁹ mol/L

Compare: in pure water, s = 1.34 × 10⁻⁵ mol/L Solubility is reduced by a factor of ~7500!

Applications of common ion effect:

• Qualitative analysis (selective precipitation of ions)
• Reducing contamination in gravimetric analysis
• Controlling precipitation in industrial processes

The ionic product (IP) or reaction quotient Q is defined the same way as Ksp but using actual concentrations (not equilibrium concentrations):

IP = [M^(b+)]ᵃ × [X^(a-)]ᵇ (using actual concentrations)

Comparison with Ksp:

1. IP < Ksp: Solution is unsaturated → no precipitation; more salt can dissolve
2. IP = Ksp: Solution is saturated → at equilibrium; no net change
3. IP > Ksp: Solution is supersaturated → precipitation occurs until IP drops to Ksp

Example: Will a precipitate form when 100 mL of 0.001 M BaCl₂ is mixed with 100 mL of 0.0004 M Na₂SO₄? Ksp(BaSO₄) = 1.1 × 10⁻¹⁰ After mixing: [Ba²⁺] = 0.001/2 = 5 × 10⁻⁴ M; [SO₄²⁻] = 0.0004/2 = 2 × 10⁻⁴ M IP = (5 × 10⁻⁴)(2 × 10⁻⁴) = 1 × 10⁻⁷ Since IP (1 × 10⁻⁷) > Ksp (1.1 × 10⁻¹⁰), BaSO₄ precipitates.

Selective precipitation separates a mixture of ions by adjusting conditions to precipitate one ion while keeping others in solution:

Example: A solution contains Ag⁺ and Pb²⁺. Adding dilute Cl⁻:

• Ksp(AgCl) = 1.8 × 10⁻¹⁰
• Ksp(PbCl₂) = 1.6 × 10⁻⁵ AgCl precipitates first (lower Ksp). Pb²⁺ remains in solution.

Applications:

1. Qualitative inorganic analysis (systematic salt analysis uses selective precipitation)
2. Water treatment — removal of fluoride, phosphate, heavy metals
3. Pharmaceutical manufacturing — crystallisation and purification
4. Formation of kidney stones (CaC₂O₄, calcium oxalate) — Ksp exceeded in urine
5. Formation of stalactites/stalagmites — CaCO₃ precipitation from Ca(HCO₃)₂ solution
6. Antacids — Mg(OH)₂ used (low Ksp, precipitates in stomach to neutralise acid)