Aqueous equilibria
Work through H2 Chemistry pH, Ka and Kb, titration curves, buffers and solubility equilibria, with lessons on calculations and chemical explanations.
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Before you begin
This topic applies equilibrium to ions in water. It starts with the constants Kₐ, Kb and Kw, uses them to calculate pH for strong and weak acids and bases, explains titration curves, indicators and buffers, then uses the solubility product, Kₛₚ, to predict precipitation and to explain how common ions and complex ions change solubility.
Be comfortable with: conjugate acid–base pairs, equilibrium constants, Le Chatelier’s principle, solution concentration, and logarithms to base 10.
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.
- Acid–base constants and conjugate pairsInterpret Ka and Kb, compare pK values and connect matching conjugate partners.
- Water ionisation, pH and neutralityConnect hydrogen and hydroxide concentrations and use the temperature-specific neutral pH.
- pH of strong acids and basesCount hydrogen or hydroxide ions after dilution, then calculate pH.
- pH of weak acids and basesBuild the equilibrium concentration relationship and test the small-dissociation approximation.
- Explain acid–base titration curvesExplain acid–base titration curves, equivalence pH and half-equivalence readings.
- Choose indicators from titration dataChoose an indicator by comparing its transition range with titration curve and volume–pH data.
- Buffer action and pH calculationsExplain buffer action, distinguish pH from capacity and calculate pH after neutralisation.
- Buffer uses and ocean acidificationExplain buffer uses and how dissolved carbon dioxide changes ocean pH and carbonate availability.
- Solubility products and molar solubilityWrite solubility-product expressions and calculate molar solubility from ion ratios.
- Predict precipitation after mixingCalculate trial ion concentrations after mixing and compare them with saturation.
- Common-ion effects on solubilityExplain a common-ion response and test the large-excess approximation.
- Complex ion formation and solubilityDistinguish free and total dissolved silver and explain silver-halide responses to ammonia.
Practise and check
Or choose
Topic reference
Quick reference
| Question evidence | First move | Essential check |
|---|---|---|
| a strong acid or strong base | [H⁺] or [OH⁻] from the formula and concentration | count the ions per formula unit; use the final volume |
| a weak acid or weak base | [H⁺] ≈ square root of Kₐc or [OH⁻] ≈ square root of Kbc | check that x is a small fraction of c |
| a hydroxide concentration | find pOH, then pH = pKw-pOH | pKw = 14.00 only at 25 °C |
| a conjugate pair | KₐKb = Kw, pKₐ + pKb = pKw | the acid and base must be a conjugate pair |
| a buffer | pH = pKₐ + log ₁₀([A⁻]/[HA]) | react any added acid or base first, in moles |
| a half-equivalence reading | pH = pKₐ for a weak acid | half the equivalence volume, not halfway up the pH axis |
| choosing an indicator | compare its range with the steep section of the curve | the whole range must lie inside the steep section |
| a sparingly soluble salt | write the dissolution equation, then Kₛₚ in terms of s | concentrations from coefficients, then the powers |
| two solutions mixed | ion concentrations in the total volume, then Q | precipitate only if Q > Kₛₚ |
| a common ion | s ≈ Kₛₚ/C | check that s is much smaller than C |
Core knowledge to remember
- A strong acid or base dissociates completely in water; a weak acid or base dissociates only partly.
- Kₐ = [H⁺][A⁻]/[HA] and Kb = [BH⁺][OH⁻]/[B]. A larger Kₐ, or a smaller pKₐ, means a stronger acid.
- Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ at 25 °C. A neutral solution has [H⁺] = [OH⁻], so its pH is pKw/2.
- pH = - log ₁₀[H⁺], pKₐ = - log ₁₀Kₐ, and KₐKb = Kw for a conjugate pair.
- At equivalence the pH is 7 for a strong acid and strong base, above 7 for a weak acid and strong base, and below 7 for a strong acid and weak base.
- A suitable indicator changes colour completely within the steep section of the titration curve.
- A buffer solution resists changes in pH when small amounts of acid or base are added. It contains a weak acid and its conjugate base, or a weak base and its conjugate acid, both in large amounts.
- The carbonate/hydrogencarbonate pair buffers seawater; dissolving more carbon dioxide uses up carbonate ions and lowers ocean pH.
- The solubility product, Kₛₚ, is the product of the ion concentrations in a saturated solution, each raised to the power of its coefficient. It depends only on temperature.
- A common ion lowers the solubility of a salt; forming a complex ion with one of its ions raises it.
Common mistakes
- Using initial concentrations where equilibrium concentrations are needed.
- Forgetting to use the total volume after mixing or diluting.
- Using pH + pOH = 14.00 at a temperature other than 25 °C.
- Using square root of Kₐc without checking that the acid is only slightly dissociated.
- Using the buffer equation before reacting the added acid or base, or after one member of the pair has been used up.
- Assuming every equivalence point is at pH 7.
- Writing a Kₛₚ expression without the coefficients as powers, or including the solid.
- Comparing Kₛₚ values of salts with different formula types to decide which is more soluble.
- Saying a common ion or a complex ion changes Kₛₚ. Only the solubility changes.