Undergraduate · 15 min

Precipitation and the solubility product

Mix lead(II) nitrate and potassium iodide solutions to observe yellow lead(II) iodide and relate precipitation to Q versus Ksp.

Goal

Predict whether PbI₂ precipitates by calculating Q = [Pb²⁺][I⁻]² and comparing it with Ksp = 9.8 × 10⁻⁹ at 25 °C.

Apparatus and reagents

Dilute lead nitrate and potassium iodide solutions; clean test tubes, droppers, goggles and a labelled heavy-metal waste container.

Procedure

Record the clear appearance of each dilute solution before mixing.
Add KI dropwise to Pb(NO₃)₂ while swirling gently; compare the observed yellow solid with the simulation.
For a mixture with [Pb²⁺] = 5.0 × 10⁻³ M and [I⁻] = 1.0 × 10⁻³ M, calculate Q and decide if the mixture is undersaturated.
Increase iodide concentration: determine when Q first exceeds Ksp and note that excess I⁻ can also suppress solubility through the common-ion effect.

What to observe

A yellow PbI₂ precipitate appears when Q > Ksp; a saturated solution is at equilibrium when Q = Ksp.
At the lower trial, Q = (5.0 × 10⁻³)(1.0 × 10⁻³)² = 5.0 × 10⁻⁹ < Ksp, so no precipitate is predicted. At [I⁻] = 2.0 × 10⁻³ M, Q = 2.0 × 10⁻⁸ > Ksp and solid forms.

Explanation

The ionic product for PbI₂ is Q = [Pb²⁺][I⁻]². Pure-water solubility is s = (Ksp/4)¹ᐟ³ ≈ 1.35 × 10⁻³ M at 25 °C. Precipitation begins when Q first exceeds Ksp; warming dissolves PbI₂ and slow cooling recrystallises it — the classic “golden rain”.

History of the experiment

Chemists had ranked salts by 'insolubility' for a century when Nernst's ionic solution theory and Ostwald's dilution work made precipitation a number, not a verdict. The solubility product — the ion-concentration product at saturation — came out of that 1890s thermodynamic school, and qualitative analysis schemes of the period, sorting cations group by group, ran entirely on

K_{sp}

logic. Today's environmental tests for lead or sulfate still do.

Chemists behind it

Walther Nernst Wilhelm Ostwald