IB DP Chemistry Reactivity 3.1: Proton transfer: Kw, Ka, Kb, buffers and titration curves – Revision Notes

For full explanations and longer worked examples, read the proton transfer study guide first.

These notes boil down understandings Reactivity 3.1.9 to 3.1.17 of IB DP Chemistry, using the numbering of the Diploma Programme Chemistry guide (the edition published in February 2023, used for exams since 2025). Each understanding here is additional higher level (AHL) content, which makes these notes HL only. Use them for any session from 2025 onwards.

When you have revised, try the proton transfer practice questions. Track progress with the DP Chemistry checklist, find other units on the DP Chemistry hub, and use our free diagnostic quizzes to spot weak areas. The older Reactivity 3 revision notes summarise the whole theme.

Unless stated, every value below is at 298 K, where Kw = 1.00 × 10⁻¹⁴.

Key definitions

• pOH: −log₁₀[OH⁻].
• Ka: the equilibrium constant for HA(aq) ⇌ H⁺(aq) + A⁻(aq). It measures how far a weak acid ionises.
• Kb: the equilibrium constant for B(aq) + H₂O(l) ⇌ BH⁺(aq) + OH⁻(aq).
• pKa, pKb: −log₁₀Ka and −log₁₀Kb.
• Salt hydrolysis: reaction of an ion from a weak parent acid or base with water, which shifts the pH away from 7.
• Equivalence point: the stage at which acid and base have reacted in the mole ratio of the equation.
• End point: the stage at which an indicator changes colour.
• Indicator: a weak acid, HInd, whose two conjugate forms differ in colour.
• Buffer: a solution whose pH hardly shifts when a little acid or alkali is added.

Formulas

Quantity	Relationship
pOH	pOH = −log₁₀[OH⁻]; [OH⁻] = 10^(−pOH)
Water	Kw = [H⁺][OH⁻]; pH + pOH = 14.00 at 298 K
Weak acid	Ka = [H⁺][A⁻] / [HA]
Weak base	Kb = [BH⁺][OH⁻] / [B]
Conjugate pair	Ka × Kb = Kw; pKa + pKb = 14.00 at 298 K
Weak acid pH (approx.)	[H⁺] = √(Ka × c)
Weak base pH (approx.)	[OH⁻] = √(Kb × c)
Half-equivalence	pH = pKa (weak acid titrated); pOH = pKb (weak base titrated)
Acidic buffer	[H⁺] = Ka × [HA] / [A⁻]; pH = pKa + log₁₀([A⁻]/[HA])
Basic buffer	pOH = pKb + log₁₀([BH⁺]/[B])
Indicator	end point pH ≈ pKa(HInd)

Reactivity 3.1.9 pOH in four moves

Any one of [H⁺], [OH⁻], pH or pOH gives you the other three:

1. Concentration to “p” value: take −log₁₀.
2. “p” value to concentration: raise 10 to the minus that value.
3. Switch between pH and pOH: subtract from 14.00.

Reminder: 0.0150 mol dm⁻³ KOH has pOH = 1.82 and pH = 12.18.

Reactivity 3.1.10 and 3.1.11 Ka, Kb and conjugate pairs

• Bigger K or smaller pK means stronger. Compare acids by pKa, bases by pKb.
• Ka × Kb = Kw comes from multiplying the two expressions: [HA] and [A⁻] cancel, leaving [H⁺][OH⁻].
• A weak acid has a weak conjugate base, and the two strengths trade off. A very weak acid has a noticeably basic conjugate.

Method: pH of a weak acid (no quadratic needed)

1. Write Ka = [H⁺]² / c, assuming [H⁺] = [A⁻] and [HA] ≈ c.
2. Rearrange: [H⁺] = √(Ka × c).
3. pH = −log₁₀[H⁺].
4. For a weak base, do the same with Kb to get [OH⁻], then pOH, then pH.

Reminder: an acid with pKa 4.87 at 0.0800 mol dm⁻³ has [H⁺] = √(10^(−4.87) × 0.0800), so pH = 2.98.

Reactivity 3.1.12 Salt solutions

Split the salt into its ions and ask which parent each came from.

Parent acid	Parent base	Example salt	Solution
strong	strong	NaNO₃	neutral
strong	weak	NH₄Br	acidic: NH₄⁺ + H₂O ⇌ NH₃ + H₃O⁺
weak	strong	potassium ethanoate	basic: CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻
weak	weak	ammonium methanoate	compare Ka(cation) with Kb(anion)

Carbonate and hydrogencarbonate both accept a proton from water, making solutions basic: CO₃²⁻ + H₂O ⇌ HCO₃⁻ + OH⁻ (clearly basic) and HCO₃⁻ + H₂O ⇌ H₂CO₃ + OH⁻ (weakly basic, because its Kb outweighs its Ka).

Reactivity 3.1.13 The four pH curves

Acid in flask, base added	Start	Vertical section	Equivalence pH	Half-equivalence
strong / strong	about 1	long	7	no buffer region
weak / strong	about 3	on the alkaline side	above 7	pH = pKa
strong / weak	about 1	on the acidic side	below 7	–
weak / weak	about 3	none sharp	near 7 if Ka ≈ Kb	–

If a weak base sits in the flask and strong acid is added, the curve runs downhill and pOH = pKb at half-equivalence. The flat buffer region before equivalence is where both conjugates are present.

Reactivity 3.1.14 and 3.1.15 Indicators

HInd(aq) ⇌ H⁺(aq) + Ind⁻(aq). More H⁺ pushes left (HInd colour). Less H⁺ pushes right (Ind⁻ colour). The change happens near pH = pKa(HInd).

Method: choosing an indicator

1. Identify the salt formed and decide whether it is acidic, neutral or basic.
2. Estimate the equivalence pH from that.
3. Pick an indicator whose range sits inside the vertical section around that pH.
4. If the curve has no vertical section (weak with weak), say no indicator is suitable.

Universal indicator is a blend of indicators with gradual colour change over a wide range. It estimates pH; it does not give a sharp end point.

Reactivity 3.1.16 and 3.1.17 Buffers

Type	Made from	Removes added H⁺	Removes added OH⁻
Acidic	weak acid + its salt	A⁻ + H⁺ → HA	HA + OH⁻ → A⁻ + H₂O
Basic	weak base + its salt	B + H⁺ → BH⁺	BH⁺ + OH⁻ → B + H₂O

Method: buffer pH

1. Find [HA] and [A⁻] (or moles, if both are in one volume). If strong base was added to weak acid, subtract it first: A⁻ formed = OH⁻ added.
2. Substitute into [H⁺] = Ka × [HA] / [A⁻], or the log form.
3. Equal concentrations give pH = pKa.

Dilution leaves the ratio, and so the pH, nearly unchanged. It does lower the buffer’s capacity.

Must-know distinctions

• Strong vs concentrated: strength is extent of ionisation (Ka); concentration is amount per dm³.
• End point vs equivalence point: one is seen, the other is calculated. A good indicator makes them coincide.
• pH = pKa vs pOH = pKb: use the first for a weak acid titration, the second for a weak base titration.
• Weak acid alone vs buffer: √(Ka × c) only for the acid alone; with added A⁻, use the ratio.
• Ka of HA vs Kb of A⁻: multiply to give Kw; do not confuse them.

Quick self-test

1. Find the pH of a solution with [OH⁻] = 6.0 × 10⁻⁴ mol dm⁻³.
2. A solution has pH 2.85. Find [OH⁻].
3. Base X has pKb 3.36 and base Y has Kb 1.8 × 10⁻⁵. Which is stronger?
4. HCN has pKa 9.21. Find Kb for CN⁻.
5. Find the pH of 0.0500 mol dm⁻³ propanoic acid, Ka = 1.3 × 10⁻⁵.
6. Write the equation showing why sodium carbonate solution is basic.
7. At half-equivalence in a weak acid titration the pH is 4.38. Find Ka.
8. An indicator has pKa 5.1. Which titration type does it suit?
9. Find the pH of a buffer containing 0.400 mol dm⁻³ butanoic acid and 0.100 mol dm⁻³ sodium butanoate (pKa 4.82).
10. That buffer is diluted with an equal volume of water. What happens to its pH?
11. Explain why hydrochloric acid mixed with sodium chloride is not a buffer.

Answers

1. pOH = 3.22, so pH = 10.78.
2. pOH = 11.15, so [OH⁻] = 7.1 × 10⁻¹² mol dm⁻³.
3. pKb(Y) = 4.74, so X is stronger (lower pKb).
4. pKb = 14.00 − 9.21 = 4.79, so Kb = 1.6 × 10⁻⁵.
5. [H⁺] = √(1.3 × 10⁻⁵ × 0.0500) = 8.1 × 10⁻⁴, pH = 3.09.
6. CO₃²⁻(aq) + H₂O(l) ⇌ HCO₃⁻(aq) + OH⁻(aq).
7. pKa = 4.38, so Ka = 4.2 × 10⁻⁵.
8. A strong acid with a weak base, whose equivalence pH is below 7.
9. pH = 4.82 + log₁₀(0.100 ÷ 0.400) = 4.22.
10. Almost no change; the ratio stays 1 : 4.
11. Cl⁻ does not accept protons, so nothing removes added H⁺ (no weak acid/conjugate pair).

Where marks are usually lost

• Giving pH when the question asks for pOH, or the other way round.
• Including [H₂O] in a Kb expression.
• Using pH + pOH = 14.00 for data at a temperature other than 298 K.
• Applying √(Ka × c) to a buffer or to a mixture after partial neutralisation.
• Forgetting to subtract added OH⁻ from the weak acid before finding the buffer ratio.
• Writing hydrolysis equations for Na⁺ or Cl⁻, which do not hydrolyse.
• Treating the equivalence point as pH 7 for every titration.
• Picking an indicator by its colours instead of its range.
• Saying dilution changes buffer pH significantly; it lowers capacity, not pH.

Official syllabus

These notes are based on the Diploma Programme Chemistry guide (International Baccalaureate Organization), first assessment 2025, published February 2023, sub-topic Reactivity 3.1, understandings 3.1.9 to 3.1.17 (additional higher level).