Question

The molar solubility of Cd(OH)₂ is 1.84 × 10⁻⁵ M in water. The expected solubility of Cd(OH)₂ in a buffer solution of pH = 12 is :
(A) 6.23 × 10⁻¹¹ M (B) 1.84 × 10⁻⁹ M
(C) (2.49/1.84) × 10⁻⁹ M
(D) 2.49 × 10⁻¹⁰ M

Answer 1

Answer: d. 2.49 *10^-10.

see img for step by step explanation

Answer 2

The expected solubility of Cd(OH)₂ in a buffer solution of pH = 12 is equal to 2.49 × 10⁻¹⁰ M.

• One mole of Cd(OH)₂ dissociates to produce one mole of Cd²⁺ and two moles of OH⁻.
• If the molar solubility is S, then the Ksp of Cd(OH)₂ is equal to 4S³, hence Ksp is equal to 2.49 × 10⁻¹⁴ M³ and it remains constant.
• Let the expected solubility in a solution of pH = 12 be x, hence the concentration of Cd²⁺ is equal to x M and the concentration of OH⁻ is equal to (2x+10⁻²) M (since the buffer produces 10⁻² M of OH⁻).
• Ksp = [Cd²⁺].[OH⁻]² = x(2x+10⁻²)² ≈ 10⁻⁴.x (ignoring terms with higher powers of x).
• Hence, x = Ksp.10⁴ = 2.49 × 10⁻¹⁰ M.