Solubility product

Solubility Product (K_sp): Definition, Formula & Applications

What is Solubility Product?

The solubility product, denoted as K_sp, is an equilibrium constant that applies to the dissolution of a sparingly soluble salt in water. It represents the extent to which the salt dissociates into its ions in a saturated solution. A larger K_sp value indicates greater solubility of the compound.

Expression for K_sp

Let’s take a general salt, AB, which dissociates in the following manner:

    AB (s) ⇌ A⁺ (aq) + B⁻ (aq)
  

The solubility product expression is:

    Ksp = [A⁺][B⁻]
  

For a salt with a different stoichiometry, such as A₂B₃:

    A2B3 (s) ⇌ 2A3+ (aq) + 3B2− (aq)
    Ksp = [A3+]2 × [B2−]3
  

Example Calculation

For the salt AgCl, which dissolves as:

    AgCl (s) ⇌ Ag⁺ (aq) + Cl⁻ (aq)
  

Let the solubility of AgCl be s. Then:

    [Ag⁺] = s, [Cl⁻] = s
    Ksp = s²
  

If the given K_sp is 1.77 × 10⁻¹⁰, then:

    s = √(1.77 × 10−10) ≈ 1.33 × 10−5 mol/L
  

Factors Affecting K_sp

• Temperature: K_sp changes with temperature. Most salts dissolve more at higher temperatures.
• Common Ion Effect: When a common ion is present, it reduces the salt’s solubility by shifting the equilibrium position as per Le Chatelier’s principle.
• pH of the Solution: For salts with basic or acidic ions, pH can significantly alter solubility.

Applications of Solubility Product

• Assessing the possibility of precipitate formation in chemical reactions.
• Estimating the solubility of salts with limited solubility in water.
• Managing experimental parameters in qualitative analysis and gravimetric methods.
• Understanding environmental behavior, such as the movement of heavy metals in aquatic systems.