Solubility Product (Cambridge International A-Level Chemistry)

The Solubility Product, Ksp

• Solubility is defined as the number of grams or moles of compound needed to saturate 100 g of water, or it can also be defined in terms of 1 kg of water, at a given temperature

  • For example, sodium chloride (NaCl) is considered to be a soluble salt as a saturated solution contains 36 g of NaCl per 100 g of water
  • Lead chloride (PbCl₂) on the other hand is an insoluble salt as a saturated solution only contains 0.99 g of PbCl₂ per 100 g of water

Solubility product

• The solubility product(K_sp) is:

  • The product of the concentrations of each ion in a saturated solution of a relatively soluble salt
  • At 298 K
  • Raised to the power of their relative concentrations

C (s) ⇌ aA^x+(aq) + bB^y-(aq)

K_sp****= [A ^x+ (aq)]^a [B ^y- (aq)]^b

• When an undissolved ionic compound is in contact with a saturated solution of its ions, an equilibrium is established

• The ions move from the solid to the saturated solution at the same rate as they move from the solution to the solid

  • For example, the undissolved magnesium chloride (MgCl₂) is in equilibrium with a saturated solution of its ions

MgCl₂(s) ⇌ Mg²⁺(aq) + 2Cl^-(aq)

Ions in a saturated solution

When the undissolved magnesium chloride salt comes in contact with its ions in a saturated solution, an equilibrium between the salt and ions is established

• The solubility product for this equilibrium is:

K_sp= [Mg ²⁺ (aq)] [Cl - (aq)]²

• The K_sp is only useful for sparingly soluble salts
• The smaller the value of K_sp, the lower the solubility of the salt

Ksp Expressions

• The general equilibrium expression for the solubility product (K_sp) is:

C (s) ⇌ aA^x+(aq) + bB^y-(aq)

K_sp****= [A ^x+ (aq)]^a [B ^y- (aq)]^b

Worked Example Expressing K_sp of ionic compounds

• Give the equilibrium expressions, including units, for the solubility products of the following ionic compounds:

  1. Ca(OH)₂
  2. Fe₂O₃
  3. SnCO₃

Answer 1 - Ca(OH)₂:

• Step 1 - Write the balanced chemical equation:

Ca(OH)₂ (s) $\rightleftharpoons$ Ca²⁺ (aq) + 2OH^– (aq)

• Step 2 - Write the K_sp* *expression:

K_sp = [Ca²⁺ (aq)] [OH^– (aq)]²

• **Step 3 **- Deduce the units:

K_sp = [mol dm^-3] x [mol dm^-3]²

K_sp = [mol dm^-3]³

K_sp* *= mol³ dm^-9

Answer 2 - Fe₂O₃:

• Step 1 - Write the balanced chemical equation:

Fe₂O₃ (s) $\rightleftharpoons$ 2Fe³⁺ (aq) + 3O^2– (aq)

• Step 2 - Write the K_sp* *expression:

K_sp = [Fe³⁺ (aq)]² [O^2– (aq)]³

1. **Step 3 **- Deduce the units:

K_sp = [mol dm^-3]² x [mol dm^-3]³

K_sp = [mol dm^-3]⁵

K_sp* *= mol⁵ dm^-15

Answer 3 - SnCO₃:

• Step 1 - Write the balanced chemical equation:

SnCO₃ (s) $\rightleftharpoons$ Sn²⁺ (aq) + CO₃^2– (aq)

• Step 2 - Write the K_sp* *expression:

K_sp = [Sn²⁺ (aq)] [CO₃^2– (aq)]

• Step 3- Deduce the units:

K_sp = [mol dm^-3] x [mol dm^-3]

K_sp = [mol dm^-3]²

K_sp* *= mol² dm^-6