Predicting Precipitation: Qsp vs Ksp

Core Concept

Whether a solid forms depends on how the current ion product Qsp compares to the equilibrium constant Ksp. If Qsp < Ksp, the solution is unsaturated and can dissolve more; if Qsp = Ksp, it is saturated at equilibrium; if Qsp > Ksp, the solution is supersaturated and a precipitate forms until the product falls back to Ksp. This is Le Châtelier's principle applied to dissolution, and it is the basis for predicting — and even engineering — precipitation in the lab and in nature.

Key Ideas

• Qsp: the ion product computed from actual (non-equilibrium) concentrations.
• Ksp: the ion product at equilibrium (saturation).
• Qsp < Ksp: no precipitate; unsaturated (more solid can dissolve).
• Qsp = Ksp: saturated; at equilibrium.
• Qsp > Ksp: precipitate forms until Qsp = Ksp.
• Mixing calculations: after combining solutions, recompute each ion's concentration (dilution) before evaluating Qsp.
• Selective precipitation: add a reagent that pushes one ion's Qsp over Ksp while others remain below theirs.

Equations and Variables

• Qsp = [Mⁿ⁺]ˣ[Aᵐ⁻]ʸ (using current concentrations)
• Precipitation occurs when Qsp > Ksp
• Dilution after mixing: C_new = (C_original × V_original) / V_total
• Common-ion form: adding more of an ion raises Qsp toward (or past) Ksp.

How It Works

1. Write the dissolution equilibrium and the Ksp expression.
2. After mixing any solutions, first apply the dilution formula to get the new concentration of each ion in the total volume.
3. Compute Qsp with those concentrations (raised to the proper stoichiometric powers).
4. Compare Qsp to Ksp. If Qsp exceeds Ksp, the solution is supersaturated and solid precipitates; if not, no solid forms.
5. For selective precipitation, choose a reagent whose common ion pushes only the target ion's Qsp above its Ksp.

Worked Example

Will AgCl precipitate when 100.0 mL of 1.0 × 10⁻³ M AgNO₃ is mixed with 200.0 mL of 1.0 × 10⁻³ M NaCl? (Ksp of AgCl = 1.8 × 10⁻¹⁰.)

Total volume = 300.0 mL = 0.300 L.

[Ag⁺] = (1.0 × 10⁻³ M × 0.100 L) / 0.300 L = 3.3 × 10⁻⁴ M

[Cl⁻] = (1.0 × 10⁻³ M × 0.200 L) / 0.300 L = 6.7 × 10⁻⁴ M

Qsp = [Ag⁺][Cl⁻] = (3.3 × 10⁻⁴)(6.7 × 10⁻⁴) = 2.2 × 10⁻⁷

Since Qsp (2.2 × 10⁻⁷) > Ksp (1.8 × 10⁻¹⁰), AgCl will precipitate.

How it works

1. Write the dissolution equilibrium and the Ksp expression.
2. After mixing any solutions, first apply the dilution formula to get the new concentration of each ion in the total volume.
3. Compute Qsp with those concentrations (raised to the proper stoichiometric powers).
4. Compare Qsp to Ksp. If Qsp exceeds Ksp, the solution is supersaturated and solid precipitates; if not, no solid forms.
5. For selective precipitation, choose a reagent whose common ion pushes only the target ion's Qsp above its Ksp.

Common confusions

• "Any mixing of ions causes precipitation." — Only if Qsp exceeds Ksp; many dilute mixes stay unsaturated.
• "Forgetting to account for dilution." — Mixing changes volumes, so you must recompute each ion's concentration in the combined volume before Qsp.
• "Qsp and Ksp are interchangeable." — Ksp is a fixed constant at a given temperature; Qsp is whatever the solution currently has.
• "Qsp > Ksp means the solid dissolves." — It means the opposite: solid precipitates.
• "Common ion always causes precipitation." — It lowers solubility and raises Qsp, but precipitation occurs only if the result pushes Qsp past Ksp.

Quick review

• Qsp = current ion product; Ksp = equilibrium value.
• Qsp > Ksp → precipitate; = → saturated; < → unsaturated.
• Dilute each ion after mixing, then compute Qsp.
• Selective precipitation uses different Ksp values to separate ions.