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Lesson 5 · 30 min

Titration curves and indicators

Strong acids, weak acids, weak bases, and polyprotic acids each leave a fingerprint on the titration curve. Learn to read the jump, the half-equivalence point, and the equivalence point — and to pick the right indicator.

In this lesson

  • Recognize the curves of strong acids, weak acids, weak bases, and polyprotic acids
  • Distinguish the equivalence point from the indicator endpoint
  • Read pKa\mathrm{p}K_\mathrm{a} off the half-equivalence point
  • Choose a suitable indicator and compute an unknown concentration from titration data

Titration is one of the oldest and most precise methods in analytical chemistry. A 50 mL burette reads to ±0.02 mL — better than one part in a thousand — provided you know which drop to stop at. That drop hides where the titration curve is steepest.

Predict first

Titrate 25.0 mL of 0.10 M acetic acid with 0.10 M NaOH. What is the pH exactly at the equivalence point?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

One curve, four regions

When a strong base titrates a weak acid, the curve passes through:

  1. The start: only weak acid; pH set by KaK_\mathrm{a} and concentration (2.88 for 0.10 M acetic acid).
  2. The buffer region: added OHX−\ce{OH-} turns some HA into AX−\ce{A-}; the solution is a buffer and the curve is flat. At the half-equivalence point (half the base added) [HA]=[AX−][\ce{HA}] = [\ce{A-}], so pH = pKaK_\mathrm{a}.
  3. Equivalence: all acid has become conjugate base, and the pH shoots up over a tiny volume — the jump.
  4. Excess: surplus strong base sets the pH, which levels off toward that of the titrant.
caVa nb=cbVb na(at equivalence)c_\mathrm{a}V_\mathrm{a}\,n_\mathrm{b} = c_\mathrm{b}V_\mathrm{b}\,n_\mathrm{a}\qquad(\text{at equivalence})
For a monoprotic acid and a monobasic base na=nb=1n_\mathrm{a} = n_\mathrm{b} = 1, giving caVa=cbVbc_\mathrm{a}V_\mathrm{a} = c_\mathrm{b}V_\mathrm{b}.
ca,Vac_\mathrm{a}, V_\mathrm{a}
analyte concentration and volume
cb,Vbc_\mathrm{b}, V_\mathrm{b}
titrant concentration and volume to equivalence
nn
stoichiometric coefficients in the balanced equation
Virtual experiment · exact charge-balance solver

Acid–base titration bench

25.00 mL HCl\ce{HCl} 0.1000 M ← NaOH\ce{NaOH} 0.1000 M

05101520253035404550STIR501001502001.00pH25.0 °CCALREADMODE
Burette reading 0.00mL
pH 1.00
Colourcolourless
0 recorded

Titration curve: the points you recorded

Equivalence 1 0510152025303540Titrant volume V / mL02468101214pH

The endpoint is where the colour change persists. Switch to single drops as you approach it.

pH is re-solved from the exact charge balance after every drop (ideal solution, 25 °C). The flask colour comes from each indicator form’s absorption band via Beer–Lambert and CIE colorimetry. The flash of colour that appears and fades near the endpoint is the local, briefly higher pH where the drop lands, diluted as the stirrer mixes it. Particle proportions are quantitative; their positions are illustrative.
Switch experiments one by one: the strong acid has the longest jump (about pH 4–10); the weak acid starts higher with a shorter jump; sodium carbonate and phosphoric acid show more than one break. Change the indicator and see where its endpoint lands on the curve.

The endpoint is not the equivalence point

The equivalence point is a theoretical idea: exactly equal amounts of acid and base. The endpoint is an observation: the drop where the indicator changes and we stop. An indicator is itself a weak acid–base pair that changes over about pKIn±1\mathrm{p}K_\mathrm{In} \pm 1. Choosing an indicator means putting that range inside the jump — then endpoint and equivalence differ by less than a drop.

  • Weak acid + strong base (basic equivalence): phenolphthalein (8.2–10.0).
  • Weak base + strong acid (acidic equivalence, about 5.3): methyl red (4.4–6.2).
  • Strong acid + strong base: the jump is long; either works.

Worked example

An unknown concentration from the endpoint

25.00 mL of hydrochloric acid of unknown concentration is titrated with 0.1000 M NaOH; phenolphthalein turns permanently pink at 23.46 mL. Find the acid concentration.

Concept check

Which indicator suits titrating 0.10 M ammonia with 0.10 M HCl?

Try the calculation

Formic acid (pKa=3.75\mathrm{p}K_\mathrm{a} = 3.75) is titrated with NaOH. What is the pH at the half-equivalence point?

Key takeaways

  • Weak-acid curve: start → buffer region (pH = pKaK_\mathrm{a} at half-equivalence) → jump → excess.
  • Equivalence is the theoretical point of equal amounts; the endpoint is where the indicator changes.
  • Weak acids reach equivalence above pH 7 (use phenolphthalein), weak bases below 7 (use methyl red).
  • Compute unknowns with caVanb=cbVbnac_\mathrm{a}V_\mathrm{a} n_\mathrm{b} = c_\mathrm{b}V_\mathrm{b} n_\mathrm{a}; polyprotic acids show several breaks.
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Data and references

  1. D. C. Harris, Quantitative Chemical Analysis, 9th ed. (2016), Ch. 11 (acid–base titrations), Table 11-4 (indicators).
  2. D. A. Skoog, D. M. West, F. J. Holler, S. R. Crouch, Fundamentals of Analytical Chemistry, 9th ed. (2014), Ch. 14.