Short on time? This page is the recap. For explanations, figures and worked examples, use the full study guide.
Recap
- A titration curve plots pH (y-axis) against volume of titrant added (x-axis).
- The equivalence point is the middle of the steepest part of the curve, not the top.
- Strength changes the shape of the curve, not the volume needed: equal moles of a strong or weak monoprotic acid need equal moles of base.
- A weak acid curve starts at a higher pH than a strong acid of the same concentration, has a flat buffer region, and a basic equivalence point.
- A weak base curve is the mirror image: it starts high, falls through a buffer region and has an acidic equivalence point.
- A polyprotic acid shows one jump per proton (if each proton is acidic enough), with equal volumes between jumps.
Key relationships
| Relationship | When it applies | Use it to |
|---|---|---|
| n(titrant) = n(analyte) at equivalence | monoprotic acids and bases, strong or weak | find the analyte concentration |
| pH = pKa at V = ½ V(eq) | weak acid; for a weak base it gives pKa of BH⁺ | find Ka, or Kb via pKb = 14.00 − pKa |
| pH = pKa + log(n(A⁻) / n(HA)) | between start and equivalence | pH in the buffer region |
| [OH⁻] ≈ √(Kb × [A⁻]), Kb = Kw / Ka | weak acid at equivalence | basic equivalence pH |
| excess titrant ÷ total volume | after equivalence | pH from excess OH⁻ or H₃O⁺ |
| pH ≈ pKa₁ at ½ V(eq1); pH ≈ pKa₂ midway between V(eq1) and V(eq2) | diprotic acid | read each pKa |
Assumptions behind the numbers
- The titration reaction goes to completion: each mole of OH⁻ converts one mole of HA to A⁻.
- Temperature is 25 °C, so Kw = 1.0 × 10⁻¹⁴ and neutral pH is 7.00.
- At equivalence, A⁻ reacts so little with water that [A⁻] stays at its stoichiometric value.
- Volumes add: total volume = analyte volume + titrant volume.
Mistakes to avoid
- Assuming pH 7 at every equivalence point. Check what species remain.
- Forgetting the total volume. After mixing, divide by analyte + titrant volume.
- Halving the pH instead of the volume to find the half-equivalence point.
- Using the half-equivalence trick for a strong acid. It only works when a conjugate pair is present.
- Using the second equivalence volume of a diprotic acid with a 1:1 ratio. Use the first.
- Calculating every species on a polyprotic curve. Not required; reason about which species are major and which are minor.
Quick self-check
- 20.00 mL of a weak acid reaches equivalence with 16.00 mL of 0.125 M NaOH. Concentration of the acid? (0.100 M)
- The pH at 8.00 mL in that titration is 4.74. What is Ka? (1.8 × 10⁻⁵)
- Is the equivalence pH of NH₃ titrated with HCl above or below 7? (Below 7: NH₄⁺ is a weak acid.)
- A diprotic acid’s first equivalence point is at 12.0 mL. Where is the second? (24.0 mL)
Next: practice questions.