Solution Equilibria
High-Yield Summary
- Net ionic equation is built in 3 steps: molecular equation → total ionic equation (split strong electrolytes into ions) → remove spectator ions.
- Ksp (solubility product constant) describes equilibrium for a sparingly soluble salt AₘBₙ: Ksp = [Aⁿ⁺]ᵐ[Bᵐ⁻]ⁿ, solids excluded.
- Ksp belongs to a family with Keq (general), Ka/Kb (acid/base), and Kf (complex ion formation constant) — larger Kf means more stable complex.
- Ion product (IP) uses actual current ion concentrations in the Ksp expression; compare IP to Ksp: IP<Ksp unsaturated, IP=Ksp saturated, IP>Ksp supersaturated/precipitate forms.
- Common ion effect: solubility decreases when a constituent ion is already present in solution — a direct result of Le Chatelier's principle.
Key Terms
- Net ionic equation
- Reaction equation showing only species that actually participate, after removing spectator ions.
- Spectator ion
- An ion that appears unchanged on both sides of a reaction equation — doesn't actually participate.
- Ksp
- Solubility product constant — equilibrium constant for dissolution of a sparingly soluble salt.
- Kf
- Formation constant — equilibrium constant for formation of a complex ion from a metal ion and ligands.
- Ion product (IP)
- Same expression as Ksp but using actual current ion concentrations, regardless of equilibrium; the Q of Ksp.
- Common ion effect
- Solubility of a compound decreases when one of its own constituent ions is already present in solution.
Writing a Net Ionic Equation
- 1Molecular equation — write all reactants/products in neutral, undissociated form. Ex: AgNO₃(aq) + NaCl(aq) → AgCl(s) + NaNO₃(aq)
- 2Total ionic equation — split every strong electrolyte into its dissociated ions (keep insoluble/weak species undissociated). Ex: Ag⁺+NO₃⁻+Na⁺+Cl⁻ → AgCl(s)+Na⁺+NO₃⁻
- 3Net ionic equation — cancel spectator ions appearing unchanged on both sides. Ex: Ag⁺(aq) + Cl⁻(aq) → AgCl(s)
Solubility Product Constant
Ksp = [Aⁿ⁺]ᵐ[Bᵐ⁻]ⁿ (for AₘBₙ(s) ⇌ mAⁿ⁺(aq) + nBᵐ⁻(aq))
- m, n = stoichiometric coefficients of the dissociation
- Solids are never included — only dissolved ion concentrations.
- Worked example: AgCl, Ksp=1.8×10⁻¹⁰ → molar solubility s: s²=1.8×10⁻¹⁰ → s≈1.3×10⁻⁵ M.
IP vs. Ksp — Saturation State
| Comparison | Solution state |
|---|---|
| IP < Ksp | Unsaturated — more solute can still dissolve. |
| IP = Ksp | Saturated — at equilibrium. |
| IP > Ksp | Supersaturated — precipitation occurs. |
Must-Know Points
- Ksp describes a salt dissolving into ions; Kf describes those ions coming BACK TOGETHER into a complex ion — don't confuse the direction.
- Common ion effect example: adding Mg²⁺ (e.g., from MgCl₂) to a Mg₃(PO₄)₂ solution pushes equilibrium left (Le Chatelier), decreasing Mg₃(PO₄)₂'s solubility.
- AgCl's molar solubility drops from 1.3×10⁻⁵ M in pure water to 1.8×10⁻⁹ M in 0.10 M NaCl — roughly 7,000× less soluble, from the common ion effect.
Common MCAT Trap
- Mixing two solutions dilutes each before you calculate IP — halve concentrations (or scale by the volume ratio) before plugging into the IP expression, don't use the original stock concentrations.
- When a common ion is added in large excess, approximate [ion] ≈ the added concentration (the salt's own tiny contribution is negligible) — don't solve the full quadratic unnecessarily.
- Ksp only applies to sparingly SOLUBLE salts at equilibrium — it's meaningless (and not written) for freely soluble compounds like NaCl.
Quick Recall
What are the three steps to write a net ionic equation?
IP > Ksp for a mixture. What happens?
Why does adding excess NH₃ to AgCl increase its apparent solubility, even though Ksp is fixed?