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 H2 Chemistry of Aqueous Solutions learning outcomes This hub covers the core acids/bases calculations and the solubility equilibria tools that appear in structured and data-based questions.
Before you start Beginner path: follow the Lessons (Recommended Order) from top to bottom.
Revision: Jump to: Quick Reference · What You Must Memorise · Common Exam Traps · Hub Quiz .
Prerequisites: skim the Prerequisites list first if you’re rusty.
Useful links: A Level portal · Exam Skills
What You’ll Learn
Use Kₐ K_b K_w
Explain buffers and choose indicators from titration curves.
Use Kₛₚ
Lessons (Recommended Order)
Ka, Kb, Kw, pKa, pKb What the constants mean and how they link.
pH Calculations (Strong and Weak) Strong/weak workflows plus approximation checks.
Buffer Solutions Buffer action and ratio-based pH calculations.
Titration Curves and Indicators Read curves and choose indicators correctly.
Ksp and Solubility Calculations Write Ksp, find solubility, predict precipitates.
Common Ion Effect and Complex Ions Explain solubility shifts in linked equilibria.
Quick Reference
What You Must Memorise
pH and pOH : pH = - log ₁₀[H⁺] pOH = - log ₁₀[OH⁻] mol dm⁻³ K_w K_w = [H⁺][OH⁻] pH + pOH = 14.00 [H⁺] = [OH⁻] Conjugate pair : KₐK_b = K_w pKₐ + pK_b = pK_w Weak acid/base approximation check : justify using x/c < 0.05 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 [HA] = [A⁻] Half-equivalence point (weak base + strong acid) : pOH = pK_b pH = pK_w-pK_b Kₛₚ only temperature changes Kₛₚ .Precipitation test : compare Qₛₚ Kₛₚ Common ion vs complex : common ion effect decreases solubility; complex formation increases solubility by lowering free metal-ion concentration (without “changing Kₛₚ 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 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 ³ mol dm⁻³
Mixing Kₐ K_b
Henderson–Hasselbalch: use moles after addition (not the original concentrations).
Writing the wrong Kₐ/K_b/Kₛₚ
Treating Kₛₚ Qₛₚ Kₛₚ
Saying “Kₛₚ
Hub Quiz and Check Your Understanding
Use practice in two passes: first without notes, then return to the lesson covering the idea you found difficult.
Aqueous Equilibria Hub Quiz Check Ka, Kb, Kw, pH, buffers, titration curves, Ksp and linked solubility equilibria.
H2 Aqueous Equilibria Knowledge Check Find the idea that needs more work, use the feedback, then try a fresh question independently.
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Why does 1.0 mol dm⁻³ ethanoic acid conduct electricity much less well than 1.0 mol dm⁻³ hydrochloric acid?
Ethanoic acid is only partially dissociated, so its solution contains far fewer ions. Ethanoic acid is more dilute than hydrochloric acid. Ethanoic acid molecules are larger, so they move more slowly and carry less current. Hydrogen chloride is ionic, whereas ethanoic acid is covalent. At 298 K, Ka of HCN is 4.9 × 10⁻¹⁰ mol dm⁻³ and Ka of HNO₂ is 4.5 × 10⁻⁴ mol dm⁻³. Which statement about 0.10 mol dm⁻³ solutions of each is correct?
HNO₂ is the stronger acid: its larger Ka means a greater extent of dissociation, a higher [H⁺] and a lower pH. HCN is the stronger acid, because a smaller Ka means it holds its proton less tightly. Both solutions have the same pH, because they have the same concentration. HNO₂ has the larger Ka, because its solution is more concentrated. Ka of NH₄⁺ is 5.6 × 10⁻¹⁰ mol dm⁻³ at 298 K and Kw = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K. What is the pH of 0.20 mol dm⁻³ aqueous ammonia?
What is the pH of 0.025 mol dm⁻³ barium hydroxide, Ba(OH)₂, at 298 K? Kw = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K.
0.10 mol dm⁻³ ethanoic acid is titrated with 0.10 mol dm⁻³ sodium hydroxide. Indicator ranges: methyl orange pH 3.1–4.4; phenolphthalein pH 8.3–10.0. Which choice is correct?
Phenolphthalein, because the ethanoate ion makes the equivalence point alkaline and the steep part of the curve lies above pH 7. Methyl orange, because the acid being titrated is ethanoic acid. Methyl orange, because the equivalence point is at pH 7. Either indicator, because the steep section runs from pH 3 to pH 11. A buffer contains aqueous ammonia and ammonium chloride. Which equation shows how it removes a small amount of added sodium hydroxide?
NH₄⁺ + OH⁻ → NH₃ + H₂O NH₃ + OH⁻ → NH₂⁻ + H₂O NH₃ + H⁺ → NH₄⁺ Cl⁻ + OH⁻ → ClOH⁻ River water brings small amounts of acid into the sea, yet seawater stays at about pH 8. Which explanation is correct?
Seawater contains CO₃²⁻ and HCO₃⁻; added H⁺ is removed by CO₃²⁻ + H⁺ → HCO₃⁻, so the pH changes very little. The dissolved sodium chloride neutralises the added acid. The sea is so large that added H⁺ ions are diluted to zero. Added H⁺ is removed by HCO₃⁻ + H⁺ → CO₃²⁻ + H₂. 50.0 cm³ of 0.20 mol dm⁻³ methanoic acid (pKa = 3.75) is mixed with 25.0 cm³ of 0.20 mol dm⁻³ sodium hydroxide. What is the pH of the mixture?
What are the expression and units of Ksp for silver chromate, Ag₂CrO₄?
Ksp = [Ag⁺]²[CrO₄²⁻]; mol³ dm⁻⁹ Ksp = [Ag⁺][CrO₄²⁻]; mol² dm⁻⁶ Ksp = [Ag⁺]²[CrO₄²⁻] / [Ag₂CrO₄]; mol² dm⁻⁶ Ksp = 2[Ag⁺][CrO₄²⁻]; mol² dm⁻⁶ Mg(OH)₂(s) ⇌ Mg²⁺(aq) + 2OH⁻(aq). Which added substance decreases the solubility of magnesium hydroxide?
Sodium hydroxide solution, because the common ion OH⁻ shifts the equilibrium to the left. Ammonium chloride solution. Hydrochloric acid. More water.
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Why does 1.0 mol dm⁻³ ethanoic acid conduct electricity much less well than 1.0 mol dm⁻³ hydrochloric acid?
Ethanoic acid is only partially dissociated, so its solution contains far fewer ions. Ethanoic acid is more dilute than hydrochloric acid. Ethanoic acid molecules are larger, so they move more slowly and carry less current. Hydrogen chloride is ionic, whereas ethanoic acid is covalent. At 298 K, Ka of HCN is 4.9 × 10⁻¹⁰ mol dm⁻³ and Ka of HNO₂ is 4.5 × 10⁻⁴ mol dm⁻³. Which statement about 0.10 mol dm⁻³ solutions of each is correct?
HNO₂ is the stronger acid: its larger Ka means a greater extent of dissociation, a higher [H⁺] and a lower pH. HCN is the stronger acid, because a smaller Ka means it holds its proton less tightly. Both solutions have the same pH, because they have the same concentration. HNO₂ has the larger Ka, because its solution is more concentrated. Ka of NH₄⁺ is 5.6 × 10⁻¹⁰ mol dm⁻³ at 298 K and Kw = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K. What is the pH of 0.20 mol dm⁻³ aqueous ammonia?
What is the pH of 0.025 mol dm⁻³ barium hydroxide, Ba(OH)₂, at 298 K? Kw = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K.
0.10 mol dm⁻³ ethanoic acid is titrated with 0.10 mol dm⁻³ sodium hydroxide. Indicator ranges: methyl orange pH 3.1–4.4; phenolphthalein pH 8.3–10.0. Which choice is correct?
Phenolphthalein, because the ethanoate ion makes the equivalence point alkaline and the steep part of the curve lies above pH 7. Methyl orange, because the acid being titrated is ethanoic acid. Methyl orange, because the equivalence point is at pH 7. Either indicator, because the steep section runs from pH 3 to pH 11. A buffer contains aqueous ammonia and ammonium chloride. Which equation shows how it removes a small amount of added sodium hydroxide?
NH₄⁺ + OH⁻ → NH₃ + H₂O NH₃ + OH⁻ → NH₂⁻ + H₂O NH₃ + H⁺ → NH₄⁺ Cl⁻ + OH⁻ → ClOH⁻ River water brings small amounts of acid into the sea, yet seawater stays at about pH 8. Which explanation is correct?
Seawater contains CO₃²⁻ and HCO₃⁻; added H⁺ is removed by CO₃²⁻ + H⁺ → HCO₃⁻, so the pH changes very little. The dissolved sodium chloride neutralises the added acid. The sea is so large that added H⁺ ions are diluted to zero. Added H⁺ is removed by HCO₃⁻ + H⁺ → CO₃²⁻ + H₂. 50.0 cm³ of 0.20 mol dm⁻³ methanoic acid (pKa = 3.75) is mixed with 25.0 cm³ of 0.20 mol dm⁻³ sodium hydroxide. What is the pH of the mixture?
What are the expression and units of Ksp for silver chromate, Ag₂CrO₄?
Ksp = [Ag⁺]²[CrO₄²⁻]; mol³ dm⁻⁹ Ksp = [Ag⁺][CrO₄²⁻]; mol² dm⁻⁶ Ksp = [Ag⁺]²[CrO₄²⁻] / [Ag₂CrO₄]; mol² dm⁻⁶ Ksp = 2[Ag⁺][CrO₄²⁻]; mol² dm⁻⁶ Mg(OH)₂(s) ⇌ Mg²⁺(aq) + 2OH⁻(aq). Which added substance decreases the solubility of magnesium hydroxide?
Sodium hydroxide solution, because the common ion OH⁻ shifts the equilibrium to the left. Ammonium chloride solution. Hydrochloric acid. More water.
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Separate 0.10 mol dm⁻³ solutions of hydrochloric acid and ethanoic acid are compared at 298 K. Which statement is correct?
Hydrochloric acid has the lower pH and reacts faster with magnesium, because HCl is fully dissociated and gives a higher [H⁺]. Both solutions have the same pH, because the acids have the same concentration. Ethanoic acid reacts faster, because each molecule contains four hydrogen atoms. Hydrochloric acid gives a larger total volume of hydrogen with excess magnesium. What is Kw, and what is its value at 298 K?
Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ Kw = [H⁺] + [OH⁻] = 2.0 × 10⁻⁷ mol dm⁻³ Kw = [H⁺][OH⁻] = 1.0 × 10⁻⁷ mol² dm⁻⁶ Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol dm⁻³ Propanoic acid has pKa = 4.88 at 298 K. What is the pH of 0.10 mol dm⁻³ propanoic acid?
10.0 cm³ of 0.50 mol dm⁻³ nitric acid is diluted with water to 250 cm³. What is the pH of the diluted solution?
0.10 mol dm⁻³ aqueous ammonia is titrated with 0.10 mol dm⁻³ hydrochloric acid. Indicator ranges: methyl orange pH 3.1–4.4; bromothymol blue pH 6.0–7.6; phenolphthalein pH 8.3–10.0. Which indicator is most suitable?
Methyl orange, because the equivalence point of a weak base–strong acid titration is acidic and the steep part of the curve lies in the acidic range. Phenolphthalein, because ammonia is a base. Bromothymol blue, because every titration has its equivalence point at pH 7. Any of them, because the pH changes sharply from about 3 to 11. A buffer contains ethanoic acid and sodium ethanoate. How does it resist a change in pH when a small amount of hydrochloric acid is added?
The large amount of CH₃COO⁻ removes the added H⁺: CH₃COO⁻ + H⁺ → CH₃COOH, so [H⁺] changes very little. CH₃COOH removes the added H⁺: CH₃COOH + H⁺ → CH₃COOH₂⁺. The added H⁺ is neutralised by OH⁻ ions from the water. The pH stays exactly constant, because Ka changes to compensate. Rising atmospheric carbon dioxide is causing ocean acidification. Which description of the chemistry is correct?
More CO₂ dissolves and forms H⁺ and HCO₃⁻; the H⁺ reacts with CO₃²⁻ to form HCO₃⁻, so CO₃²⁻ is used up and the pH of seawater slowly falls. Dissolved CO₂ reacts with OH⁻, so seawater becomes more alkaline. The CO₃²⁻/HCO₃⁻ buffer keeps the pH exactly constant however much CO₂ dissolves. Dissolved CO₂ forms extra CO₃²⁻ ions, which raise the pH. A buffer contains 0.20 mol dm⁻³ benzoic acid and 0.10 mol dm⁻³ sodium benzoate. The pKa of benzoic acid is 4.20. What is the pH of the buffer?
Ksp of calcium fluoride, CaF₂, is 3.9 × 10⁻¹¹ mol³ dm⁻⁹ at 298 K. What is its solubility in water?
2.1 × 10⁻⁴ mol dm⁻³ 6.2 × 10⁻⁶ mol dm⁻³ 3.4 × 10⁻⁴ mol dm⁻³ 4.4 × 10⁻⁶ mol dm⁻³ Which change increases the amount of solid silver chloride that dissolves in a given volume of solution?
Adding aqueous ammonia, which forms [Ag(NH₃)₂]⁺ and lowers the free [Ag⁺]. Adding sodium chloride solution. Adding silver nitrate solution. Adding more solid silver chloride.
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