Coaching Centre
Titration curves and conductivity graphs
Reading pH titration curves for strong and weak acids and bases: initial pH, buffer region, half-equivalence point where pH = pKa, equivalence point pH and the steep jump; choosing an indicator; polyprotic curves such as sodium carbonate; and conductometric titrations, why their graphs have the shapes they do and when to use them.
Add 0.1 mL of sodium hydroxide to a flask of hydrochloric acid that is almost neutralised and the pH jumps from about 3.7 to 10.3. That's two drops changing the hydrogen ion concentration by a factor of four million. This near-vertical cliff is what makes titration so precise, and its exact position and height tell you what kind of acid and base you're dealing with.
pH titration curves
A titration curve plots the pH of the flask against the volume of titrant added. In the lab you record it with a pH probe and data logger, adding titrant in small portions (smaller near the equivalence point). Every curve has the same landmarks:
- Initial pH: low for a strong acid, higher for a weak acid at the same concentration.
- Buffer region (weak acids or weak bases only): a flat section where both the weak acid and its conjugate base are present, so the pH changes slowly.
- Half-equivalence point (weak acid or base only): half the acid has been converted to its conjugate base, so [HA] = [A⁻] and pH = p$K_a$.
- Equivalence point: the middle of the steep section. Its pH is set by the salt that has formed.
- Excess titrant: the curve levels off towards the pH of the titrant.
The four types
| Titration | Salt at equivalence | Equivalence pH (0.1 mol/L) | Steep section | Suitable indicator |
|---|---|---|---|---|
| strong acid + strong base (HCl + NaOH) | NaCl, neutral | 7.0 | long: about pH 3.5–10.5 | almost any: bromothymol blue, phenolphthalein or methyl orange |
| weak acid + strong base (CH₃COOH + NaOH) | CH₃COONa, basic | about 8.7 | shorter, high: about pH 7–10.5 | phenolphthalein |
| strong acid + weak base (HCl + NH₃) | NH₄Cl, acidic | about 5.3 | shorter, low: about pH 3.5–7 | methyl orange or methyl red |
| weak acid + weak base (CH₃COOH + NH₃) | CH₃COONH₄, near neutral | about 7 | none: the pH changes gradually | none is reliable; use a conductometric titration |
The equivalence pH comes straight from 6E. At the equivalence point of CH₃COOH + NaOH, the flask holds sodium ethanoate, and CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻ makes it basic. At the equivalence point of NH₃ + HCl the flask holds NH₄⁺, which makes it acidic.
The half-equivalence point and pKa
Halfway to the equivalence point of a weak acid with NaOH, exactly half the HA has become A⁻. Put [HA] = [A⁻] into the $K_a$ expression:
$$K_a = \frac{[\mathrm{H_3O^+}][\mathrm{A^-}]}{[\mathrm{HA}]} = [\mathrm{H_3O^+}] \quad\Rightarrow\quad \mathrm{pH} = \mathrm{p}K_a$$
So you can read $K_a$ for an unknown weak acid straight off its titration curve. For a weak base titrated with a strong acid, the pH at half-equivalence is the p$K_a$ of the conjugate acid (9.25 for NH₄⁺).
25.00 mL of an unknown monoprotic acid was titrated with 0.100 mol/L NaOH. The equivalence point was at 18.40 mL and pH 8.4. At 9.20 mL of NaOH the pH was 3.75. Identify the acid and find its concentration.
Choosing an indicator
The indicator must change colour on the steep part of the curve, so that the end point falls within a drop or two of the equivalence point. In practice, choose an indicator whose colour change range includes (or sits very close to) the equivalence pH. For a weak acid–strong base titration, methyl orange would change colour in the buffer region, many millilitres too early. For a weak acid with a weak base there is no steep section at all, so the colour would change gradually over several millilitres.
Which indicator, methyl orange (3.1–4.4) or phenolphthalein (8.3–10.0), should be used to titrate ammonia solution with hydrochloric acid? Justify your choice.
Polyprotic curves: sodium carbonate
A base that can accept two protons, such as CO₃²⁻, shows two equivalence points when titrated with HCl:
CO₃²⁻(aq) + H₃O⁺(aq) → HCO₃⁻(aq) + H₂O(l) (first equivalence, pH ≈ 8.3)
HCO₃⁻(aq) + H₃O⁺(aq) → H₂CO₃(aq) + H₂O(l) (second equivalence, pH ≈ 3.9)
The second jump is sharper, so standardising HCl with Na₂CO₃ uses methyl orange and the overall 1 : 2 ratio: Na₂CO₃ + 2HCl → 2NaCl + H₂O + CO₂. Boiling the flask just before the end point drives off CO₂ and sharpens it further.
Conductometric titrations
In a conductometric titration you follow the electrical conductivity of the flask instead of the pH. Conductivity depends on how many ions there are and how fast each kind moves. H₃O⁺ and OH⁻ conduct far better than any other ions (roughly 7 and 4 times better than Na⁺), because they can pass protons along chains of hydrogen-bonded water molecules instead of physically pushing through the water.
| Titration (base added to acid) | Before equivalence | After equivalence |
|---|---|---|
| HCl + NaOH | falls steeply: fast H₃O⁺ replaced by slower Na⁺ | rises steeply: excess Na⁺ and fast OH⁻ accumulate |
| CH₃COOH + NaOH | starts low (few ions), then rises gently as CH₃COO⁻ and Na⁺ form | rises more steeply: excess OH⁻ and Na⁺ |
| HCl + NH₃ | falls steeply: H₃O⁺ replaced by NH₄⁺ | almost flat: excess NH₃ is a weak base and adds very few ions |
| CH₃COOH + NH₃ | rises: CH₃COO⁻ and NH₄⁺ form | almost flat: excess NH₃ adds very few ions |
The equivalence point is found by drawing straight lines through the data on either side and finding where they cross. Points near the equivalence point aren't needed, which is an advantage. Conductometric titrations also work for coloured or cloudy solutions (where an indicator can't be seen), for very dilute solutions, and for weak acid–weak base titrations, which have no usable pH jump.
Explain the shape of the conductivity graph when 0.1 mol/L NaOH is added to 25 mL of 0.1 mol/L HCl.
- With CH₃COOH + NaOH, slide to 12.5 mL. What pH does the sim give, and why is it so close to the p$K_a$ of ethanoic acid (4.74)? Then slide to 25.0 mL: what is the equivalence pH?
- Choose HCl + NaOH and compare the pH at 24.9 mL and 25.1 mL. How many pH units does it jump in those 0.2 mL?
- Back on CH₃COOH + NaOH, select phenolphthalein, then bromothymol blue. How far from the equivalence point does each change colour, and which does the sim call suitable?
- Choose NH₃ + HCl. What is the pH at the equivalence point? Test phenolphthalein and methyl orange.
- Choose Na₂CO₃ + HCl and find the pH at both equivalence points (25 mL and 50 mL). What is the pH at 12.5 mL and 37.5 mL, and what do those numbers tell you?
- Watch the conductivity graph for HCl + NaOH, then CH₃COOH + NH₃. Which one could only be done by conductometric titration?
Test yourself
A titration curve starts at pH 2.9, has a flat region near pH 4.8 and an equivalence point at pH 8.7. The titration is
A high starting pH, a buffer region and a basic equivalence point all point to a weak acid titrated with a strong base.
In the titration of a weak acid HA with NaOH, the pH at half the equivalence volume is 5.20. $K_a$ for HA is
At half-equivalence pH = p$K_a$, so $K_a$ = 10⁻⁵·²⁰ = 6.3 × 10⁻⁶.
Why does conductivity fall when NaOH is added to HCl before the equivalence point?
Each H₃O⁺ removed is replaced by a Na⁺, so the ion count stays similar, but Na⁺ moves about seven times more slowly.
Which titration is best followed by measuring conductivity rather than with an indicator?
A weak acid with a weak base has no steep pH change at equivalence, but the conductivity graph still has a clear change in slope.
Which indicator is most suitable for titrating 0.1 mol/L NH₃ with 0.1 mol/L HCl?
The equivalence point is about pH 5.3, inside methyl red's range.
Label the features of the titration curve.
Sort the titrations by the pH at the equivalence point.
In the titration of a weak acid with a strong base, the flat section before the equivalence point is the region. At the half-equivalence point, pH equals . The equivalence point is basic because the conjugate of the weak acid reacts with water. The most suitable indicator is . In conductometric titrations, H₃O⁺ and OH⁻ are the most ions.
A student titrated 20.00 mL of 0.100 mol/L ethanoic acid with 0.100 mol/L sodium hydroxide, recording both pH and conductivity. (a) Sketch or describe the pH curve, giving approximate pH values at the start, the half-equivalence point and the equivalence point, and the volume at which equivalence occurs. (b) Explain the pH at the equivalence point with an equation. (c) Describe and explain the shape of the conductivity graph.
(a) The pH starts at about 2.9, rises quickly at first, then flattens into a buffer region. At 10.00 mL (half-equivalence) pH = p$K_a$ ≈ 4.7. Near 20.00 mL it rises steeply from about 7 to about 11, with the equivalence point at 20.00 mL and pH ≈ 8.7, then levels off towards about 12.5 as excess NaOH is added.
(b) At equivalence the flask contains sodium ethanoate. Na⁺ is a spectator, but the ethanoate ion is a weak base: CH₃COO⁻(aq) + H₂O(l) ⇌ CH₃COOH(aq) + OH⁻(aq). This produces OH⁻, so the pH is above 7.
(c) Conductivity starts low, because ethanoic acid is a weak acid and only about 1% ionised, so there are few ions. As NaOH is added, CH₃COOH + OH⁻ → CH₃COO⁻ + H₂O converts molecules into Na⁺ and CH₃COO⁻ ions, so conductivity rises gently and roughly linearly. After 20.00 mL, excess Na⁺ and highly mobile OH⁻ accumulate, so the conductivity rises more steeply. The equivalence point is where the two straight lines intersect.