§ C-16 Solubility Product Kₛp, Golden Rain Precipitation (PbI₂↓) & Common-Ion Effect (Grade 9–11 · Solubility Product)
Crystallization of shimmering golden hexagonal PbI₂↓ platelets when Qₛp > Kₛp(T) and solubility suppression by excess I⁻ ions. Whenever the ionic product in solution exceeds the thermodynamic threshold Kₛp(T), glittering hexagonal crystals of PbI₂↓ nucleate from the clear liquid.
Theory Summary & Scientific Mechanism
In a saturated solution of a sparingly soluble salt such as lead(II) iodide PbI₂, a heterogeneous equilibrium exists between the solid crystal lattice and dissolved ions: PbI₂(s) ⇄ Pb²⁺(aq) + 2I⁻(aq). Its equilibrium constant is the solubility product: Kₛp = [Pb²⁺][I⁻]² (8.5× 10⁻⁹ at 25 ^°C).
Precipitation occurs whenever the reaction quotient (ionic product) exceeds Kₛp: Qₛp = [Pb²⁺][I⁻]² > Kₛp(T). Because Kₛp of PbI₂ increases steeply with temperature, heating dissolves the precipitate while slow cooling nucleates shimmering hexagonal golden platelets, the classic "Golden Rain" demonstration.
Adding a soluble salt containing a shared ion (such as KI) triggers the common-ion effect: by Le Chatelier’s principle, excess [I⁻] drives the equilibrium toward solid PbI₂↓, suppressing lead solubility from S₀ = sqrt[3]Kₛp/4 down to S = Kₛp/[I⁻]².
Everyday Analogy
In the famous "Golden Rain" experiment, a hot clear solution of PbI₂ nucleates thousands of glittering golden hexagonal platelets upon cooling because the ionic product Qₛp exceeds Kₛp(T)!
Interactive Question & Derivation
Under what condition does golden crystalline PbI₂↓ precipitate upon mixing Pb(NO₃)₂ and KI solutions, and how does adding excess KI affect PbI₂ solubility?
- A: Precipitation occurs when the ionic product exceeds the solubility product: Qₛp = [Pb²⁺][I⁻]² > Kₛp; excess common ion I⁻ shifts equilibrium toward the solid and sharply reduces PbI₂ solubility
- B: Precipitation occurs only when Qₛp < Kₛp, and adding KI increases PbI₂ solubility
- C: The solubility product Kₛp is independent of solution temperature
Study Hint: Precipitation occurs when Qₛp = [Pb²⁺][I⁻]² > Kₛp. Adding excess common ion I⁻ (KI) shifts equilibrium toward solid PbI₂↓ and sharply reduces solubility.
Proof & Explanation: In a saturated solution of sparingly soluble PbI₂(s) ⇄ Pb²⁺ + 2I⁻, the equilibrium constant is Kₛp = [Pb²⁺][I⁻]². When Qₛp > Kₛp, supersaturation drives crystallization of golden PbI₂ platelets. By Le Chatelier’s principle, adding common ion I⁻ suppresses lead solubility to S = Kₛp/[I⁻]².
Key Equations & 3D Simulation Parameters
Qₛp = [Pb²⁺][I⁻]², S₀ = sqrt[3](Kₛp)/(4), S_common = (Kₛp)/(([I⁻]₀ + C_KI)²)
- Initial lead cation concentration [Pb²⁺]₀: 0.001 … 0.015 mol/L (default: 0.005 mol/L)
- Initial iodide concentration [I⁻]₀: 0.002 … 0.025 mol/L (default: 0.01 mol/L)
- Solution temperature t (heating dissolves precipitate): 15 … 85 °C (default: 25 °C)
- Added common-ion salt KI (common-ion effect): 0 … 0.03 mol/L (default: 0 mol/L)