5.5.6 Solubility Product

• 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)

When the undissolved MgCl₂ salt gets 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 = [Mg²⁺ (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

• 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

Answer

Expressing K_sp of ionic compounds answers table