Aqueous Equilibria
pH, Ka, Kb, buffers, solubility and titration curves.
Before you begin
pH, Ka, Kb, buffers, solubility and titration curves.
Learning goals
- Ka, Kb, Kw, pKa, pKb
- pH Calculations (Strong and Weak)
- Titration Curves and Indicators
- Buffer Solutions
- Ksp and Solubility Calculations
- Common Ion Effect and Complex Ions
Syllabus statements covered
- explain qualitatively the differences in behaviour between strong and weak acids and bases in terms of the extent of dissociation
- explain the terms pH; Ka; pKa; Kb; pKb; Kw and apply them in calculations, including the relationship Kw = KaKb
- calculate [H+(aq)] and pH values for strong acids, weak monobasic (monoprotic) acids, strong bases, and weak monoacidic bases [calculations involving weak acids/bases will not require solving of quadratic equations]
- explain how buffer solutions control pH
- describe and explain the uses of buffer solutions, including the role of CO32–/HCO3– in maintaining pH in oceans, and how the rapid increase in atmospheric carbon dioxide gas contributed to ocean acidification
- calculate the pH of buffer solutions, given appropriate data
- describe the changes in pH during acid-base titrations and explain these changes in terms of the strengths of the acids and bases
- explain the choice of suitable indicators for acid-base titrations, given appropriate data
- show understanding of, and apply, the concept of solubility product, Ksp
- calculate Ksp from concentrations and vice versa
- discuss the effects on the solubility of ionic salts by the following: — common ion effect
- discuss the effects on the solubility of ionic salts by the following: — formation of complex ion, as exemplified by the reactions of halide ions with aqueous silver ions followed by aqueous ammonia (see also Section 13)
Lessons
Work through them in order.
- Ka, Kb, Kw, pKa, pKbExplain what Ka, Kb, Kw, pKa and pKb mean and convert between them.
- pH Calculations (Strong and Weak)Calculate the pH of strong and weak acids and bases, and check any approximation.
- Titration Curves and IndicatorsRead acid–base titration curves and choose a suitable indicator.
- Buffer SolutionsExplain buffer action and calculate a buffer's pH from its acid–salt ratio.
- Ksp and Solubility CalculationsWrite Ksp expressions, calculate solubility and predict whether a precipitate forms.
- Common Ion Effect and Complex IonsExplain how a common ion or complex formation shifts a solubility equilibrium.
Practise and check
Recommended nextAqueous Equilibria topic check
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Topic reference
This topic covers acid–base and solubility equilibria in water. The lessons start with Ka, Kb and Kw, use them for pH, buffers and titration curves, then apply the same equilibrium reasoning to Ksp and solubility.
Be comfortable with:
- Acids and Bases (Theories): strong and weak, conjugate pairs.
- Solution Concentration and Dilution: n = cV and unit conversions.
- Titration Calculations: stoichiometry before equilibrium.
- Equilibrium Constants (Kc, Kp): writing K expressions and ICE tables.
Quick Reference
| If you need… | Use… | Check this |
|---|---|---|
| pH / pOH | pH = - log ₁₀[H⁺], pOH = - log ₁₀[OH⁻] | concentrations in mol dm⁻³ |
| mixing workflow | moles first → total volume → new concentrations | then apply Kₐ/K_b/K_w/Kₛₚ |
| log + rounding | log ₁₀ for pH (not ln) | pH typically to 2 d.p. (unless stated) |
| link [H⁺] and [OH⁻] | K_w = [H⁺][OH⁻] | at 25°C: K_w = 1.0 × 10⁻¹⁴, pK_w = 14.00 |
| conjugate pair link | KₐK_b = K_w and pKₐ + pK_b = pK_w | must be same temperature |
| weak acid / base quick estimate | [H⁺] ≈ square root of (Kₐ c) or [OH⁻] ≈ square root of (K_b c) | check x/c < 0.05 before using |
| buffer pH | pH = pKₐ + log ₁₀([A⁻]/[HA]) | adjust moles after addition first |
| precipitation check | compare Qₛₚ with Kₛₚ | use ion concentrations after mixing/dilution |
| solubility from Kₛₚ | write dissolution first, then solve for s | include stoichiometric powers (e.g. Kₛₚ = 4s³ for MX₂) |
What You Must Memorise
- pH and pOH: pH = - log ₁₀[H⁺] and pOH = - log ₁₀[OH⁻] (concentrations in mol dm⁻³).
- K_w link: K_w = [H⁺][OH⁻] and (at 25°C) pH + pOH = 14.00; neutral means [H⁺] = [OH⁻], not “pH 7 always”.
- Conjugate pair: KₐK_b = K_w and pKₐ + pK_b = pK_w (same temperature).
- Weak acid/base approximation check: justify using x/c < 0.05 (otherwise solve properly).
- Buffers: Henderson–Hasselbalch form and the “moles first after addition” habit (don’t use it when a component is nearly used up).
- Half-equivalence point (weak acid + strong base): pH = pKₐ (because [HA] = [A⁻]).
- Half-equivalence point (weak base + strong acid): pOH = pK_b (so pH = pK_w-pK_b at the same temperature).
- Kₛₚ expressions: omit the solid, use correct powers from coefficients; only temperature changes Kₛₚ.
- Precipitation test: compare Qₛₚ with Kₛₚ using ion concentrations after mixing/dilution.
- Common ion vs complex: common ion effect decreases solubility; complex formation increases solubility by lowering free metal-ion concentration (without “changing Kₛₚ” at fixed temperature).
Common Exam Traps
- Using initial concentration instead of equilibrium concentration (skipping an ICE table).
- Forgetting dilution after mixing solutions (final concentrations in total volume).
- Using pH + pOH = 14.00 without stating 25°C (or ignoring a given pK_w).
- Applying the weak acid/base approximation without checking x/c < 0.05.
- Using Henderson–Hasselbalch when one buffer component is almost used up.
- Mixing units (cm³ vs dm³) or forgetting mol dm⁻³ in final answers.
- Mixing Kₐ and K_b for salts: identify the conjugate acid/base first.
- Henderson–Hasselbalch: use moles after addition (not the original concentrations).
- Writing the wrong Kₐ/K_b/Kₛₚ expression (wrong species or missing powers).
- Treating Kₛₚ as a “solubility” directly instead of comparing Qₛₚ vs Kₛₚ.
- Saying “Kₛₚ changes” when a common ion/complex is added (it’s temperature-dependent only).