Short on time? This page is the recap. For explanations, graphs and worked examples, use the full study guide.
Recap
- A weak acid has two forms: the acid form HA (protonated) and the base form A⁻ (deprotonated). Which one is present at the higher concentration is its protonation state.
- In a solution whose pH is fixed by other substances, compare the pH with the pK_a:
- pH < pK_a → HA predominates.
- pH = pK_a → [HA] = [A⁻].
- pH > pK_a → A⁻ predominates.
- For a weak base B, use the pK_a of BH⁺ (= 14.00 − pK_b at 25 °C). pH < pK_a(BH⁺) → BH⁺ predominates.
- An indicator is a weak acid, HIn, whose two forms have different colours. Its colour changes over roughly pK_a ± 1.
- Choose an indicator whose pK_a is close to the pH at the equivalence point, so the colour changes on the steep part of the curve.
Key relationships
| Relationship | Meaning | Use it to |
|---|---|---|
| [A⁻]/[HA] = K_a / [H₃O⁺] | rearranged K_a expression | see why pH and K_a set the ratio |
| [A⁻]/[HA] = 10^(pH − pK_a) | same thing in log form | size the ratio: 1 unit → 10, 2 units → 100 |
| pK_a + pK_b = 14.00 (25 °C) | conjugate pair | convert pK_b of a base to pK_a of its conjugate acid |
| Titration type | Equivalence pH | Example indicator |
|---|---|---|
| Strong acid + strong base | 7 | several work (long vertical section) |
| Weak acid + strong base | above 7 | phenolphthalein (8.3–10.0) |
| Weak base + strong acid | below 7 | methyl red (4.4–6.2) |
Assumptions
- Temperature is 25 °C, so K_w = 1.0 × 10⁻¹⁴ and pK_a + pK_b = 14.00.
- The indicator is present in a tiny amount and does not change the solution’s pH.
- Indicator colour ranges are approximate; they depend on the observer and on the solution.
Mistakes to avoid
- “Above pK_a = fully dissociated.” It only means A⁻ is the larger form.
- “pH = pK_a means neutral.” It means the two forms are equal.
- Comparing pH with pK_b. Convert to pK_a of the conjugate acid first.
- Always choosing an indicator for pH 7. Match the actual equivalence pH.
- Mixing up end point and equivalence point. A poor indicator separates them and gives a wrong titre.
Quick self-check
- HA has pK_a 8.0. Which form predominates at pH 6.0? (HA; [A⁻]/[HA] = 0.01)
- A base has pK_b 3.4. What is pK_a of its conjugate acid at 25 °C? (10.6)
- An acid’s pK_a is 5.0. At what pH is it 50% deprotonated? (pH 5.0)
- Which indicator suits a weak acid–strong base titration, methyl orange or phenolphthalein? (Phenolphthalein)
Next: practice questions.