Short on time? This page is the recap. For explanations and worked examples, use the full study guide.
Recap
- Dissolving an ionic solid is reversible. In a saturated solution with solid present, dissolving and precipitating happen at equal rates, so the ion concentrations stay constant.
- The equilibrium constant for dissolving is the solubility-product constant, K_sp. It changes only with temperature.
- Molar solubility, s, is the moles of salt that dissolve per litre of saturated solution (mol L⁻¹). Multiply by the molar mass to get g L⁻¹.
- You can go from K_sp to s, or from a measured s (or one measured ion concentration) back to K_sp.
- K_sp > 1 matches a soluble salt (all Na⁺, K⁺, NH₄⁺ and NO₃⁻ salts). Sparingly soluble salts have K_sp much less than 1.
Key relationships
| Relationship | Meaning | Use it to |
|---|---|---|
| MₓAᵧ(s) ⇌ x Mᵃ⁺(aq) + y Aᵇ⁻(aq) | dissolving equation | find the coefficients |
| K_sp = [Mᵃ⁺]ˣ[Aᵇ⁻]ʸ | equilibrium ion concentrations | write the expression |
| [Mᵃ⁺] = xs, [Aᵇ⁻] = ys | from the formula | link ions to s |
| K_sp = s² (1:1), 4s³ (1:2 or 2:1), 27s⁴ (1:3), 108s⁵ (2:3 or 3:2) | built from (xs)ˣ(ys)ʸ | solve for s or K_sp |
| g L⁻¹ = s × M | M = molar mass | convert solubility units |
| Q vs K_sp (Topic 7.10) | Q > K_sp: precipitate forms | predict precipitation on mixing |
Assumptions
- The ions do not react further with water or with each other.
- Undissolved solid is present, so the solution is saturated.
- The temperature matches the one the K_sp was measured at.
Mistakes to avoid
- Forgetting the coefficient inside the bracket. For ZF₂, [F⁻] = 2s, not s.
- Forgetting the power. (2s)² = 4s², not 2s².
- Including the solid in the K_sp expression.
- Ranking by K_sp when ion ratios differ. Calculate s for each salt instead.
- Calling s the K_sp. s has a unit (mol L⁻¹); K_sp does not.
- Using one ion concentration as s when the ratio is not 1:1. If [Ag⁺] = 2.0 × 10⁻⁴ M for Ag₂X, then s = 1.0 × 10⁻⁴ M.
- Forgetting dilution when two solutions are mixed before you calculate Q.
Quick self-check
- A 1:1 salt MX has K_sp = 4.0 × 10⁻¹⁰. What is its molar solubility? (2.0 × 10⁻⁵ mol L⁻¹)
- A 1:2 salt MX₂ has molar solubility 1.0 × 10⁻³ mol L⁻¹. What is its K_sp? (4s³ = 4.0 × 10⁻⁹)
- A 2:1 salt M₂X has K_sp = 4.0 × 10⁻¹². What is its molar solubility? (∛(1.0 × 10⁻¹²) = 1.0 × 10⁻⁴ mol L⁻¹)
- Which of these two is more soluble: salt 1 (1:1, K_sp = 4.0 × 10⁻¹⁰) or salt 3 (2:1, K_sp = 4.0 × 10⁻¹²)? (Salt 3: s = 1.0 × 10⁻⁴ M against 2.0 × 10⁻⁵ M, despite the smaller K_sp)
Next: practice questions.