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Chemistry: Ionic Compounds: Relationship between Solubility and Solubility Product Constant

Relationship between Solubility and Solubility Product Constant

The Solubility Product Constant for a Substance is Related to Its Solubility

Illustration: Relationship between Solubility and Solubility Product Constant

1. Salt of AB type: Examples are AgCl, CaSO4. In such cases the solubility equilibrium can be represented as, AB (s) A+ (aq) + B- (aq) and Ksp = [A+ ] [B– ]

  • If the solubility of salt is β€˜s’ mol dm-3 then the concentrations of the cations and the anions would be β€˜s’ mol dm-3 each.
  • Substituting the values in the expression of Ksp we get,
  • Ksp = [ β€˜s’ mol dm-3] Γ— [ β€˜s’ mol dm-3] = s2 mol2dm-6

2. Salt of AB2 type: Example CaF2. In such cases the solubility equilibrium can be represented as - AB2 (s) A2 + (aq) + 2B- (aq) and Ksp = [A2 + ] (aq) [B– ]2

  • If the solubility of salt is β€˜s’ mol dmβˆ’ 3 then the concentration of the cations and the anions would be β€˜s’ mol dmβˆ’ 3 and β€˜2 s’ mol dmβˆ’ 3, respectively.
  • Substituting the values in the expression of Ksp we get, Ksp = [ β€˜s’ mol dmβˆ’ 3] Γ— [ β€˜2 s’ mol dmβˆ’ 3]2 = 4 s3 mol3 dmβˆ’ 9

3. Salt of A2B type: Example Ag2CrO4. In such cases the solubility equilibrium can be represented as A2B (s) 2 A+ (aq) + B2- (aq) , Ksp = [A+ ]2 [B2-]

If the solubility of salt is β€˜s’ mol dmβˆ’ 3 then the concentrations of the cations and the anions would be β€˜2 s’ mol dmβˆ’ 3 and β€˜s’ mol dmβˆ’ 3, respectively. Substituting the values in the expression of Ksp we get, Ksp = [ β€˜2 s’ mol dmβˆ’ 3]2 Γ— [ β€˜s’ mol dmβˆ’ 3] = 4 s3 mol3 dmβˆ’ 9

4. Salt of A3B2 type: Example Ca3 (PO4)2. In such cases the solubility equilibrium can be represented as A3B2 (s) 3 A2 + (aq) + 2B3- (aq) and Ksp = [A2 + ]3 [B3-]2

  • If the solubility of salt is β€˜s’ mol dmβˆ’ 3 then the concentrations of the cations and the anions would be β€˜3 s’ mol dmβˆ’ 3 and β€˜2 s’ mol dmβˆ’ 3, respectively. Substituting the values in the expression of Ksp we get, Ksp = [ β€˜3 s’ mol dmβˆ’ 3]3 Γ— [ β€˜2 s’ mol dmβˆ’ 3]2 = 108 s5 mol5 dmβˆ’ 15
  • In general, for a salt with the formula AxBy and a solubility of s mol dmβˆ’ 3 the relationship between the solubility and Ksp can be given as Ksp = [Ay + ]x [Bx – ]y = (xs)x (ys)y = xx yy sx + y

Effect of Common Ion on Solubility Equilibria

According to Le chatelier՚s principle, the common ion will shift the equilibrium in backward direction which will reduce its solubility.