Plotting a pH Curve with a pH Meter

An indicator tells you when a titration is finished. A pH meter tells you the whole story. By recording the pH after each addition of alkali, you can plot a complete titration curve, find the equivalence point without any indicator, and read off the pKa of a weak acid directly from the graph.

This practical is a staple of advanced chemistry courses because it ties together titration technique, weak acid equilibria, buffers and data analysis.

Aim

To record the pH curve for the titration of ethanoic acid with sodium hydroxide, and use it to find:

1. the equivalence point (and so the acid concentration), and
2. the pKa of ethanoic acid.

Equipment and chemicals

• pH meter or data-logging pH probe, calibrated with pH 4.00 and 7.00 (and ideally 10.00) buffers
• Magnetic stirrer and stirrer bar (or careful manual swirling)
• 250 cm³ beaker
• 25.00 cm³ pipette and filler
• 50.00 cm³ burette, clamp and stand
• About 0.1 mol/dm³ ethanoic acid (the “unknown”)
• Standardised 0.100 mol/dm³ sodium hydroxide
• Distilled water and wash bottle
• Eye protection

Method

1. Calibrate the pH meter with at least two standard buffers. See how a pH meter works.
2. Pipette 25.00 cm³ of ethanoic acid into the beaker. Add a stirrer bar and enough distilled water (say 25 cm³) to cover the probe’s bulb and junction. The added water doesn’t change the number of moles of acid, so it doesn’t change the equivalence volume.
3. Clamp the pH probe so the bulb is submerged but clear of the stirrer bar.
4. Record the initial pH.
5. Add NaOH from the burette in 2.00 cm³ portions, stirring and recording the pH once the reading is steady after each addition.
6. As the pH starts to rise quickly (usually above about pH 6), switch to 0.50 cm³ additions, then 0.10 cm³ (or single drops) through the steep section.
7. Once past the steep section, return to larger additions (1–2 cm³) until you’ve added about 10 cm³ beyond the equivalence point.
8. Rinse the probe and return it to storage solution.

The key technique: small additions where the pH changes quickly, larger ones where it changes slowly. That puts your data points where the curve needs them.

Sample data

The data below are calculated for 25.00 cm³ of 0.100 mol/dm³ ethanoic acid (pKa 4.76) titrated with 0.100 mol/dm³ NaOH at 25 °C, ignoring the added water for simplicity. Real classroom data will be close to these but slightly scattered.

NaOH added (cm³)	pH
0.00	2.87
2.50	3.81
5.00	4.16
10.00	4.58
12.50	4.76
15.00	4.94
20.00	5.36
22.50	5.71
24.00	6.14
24.50	6.45
25.00	8.72
25.50	11.00
26.00	11.29
30.00	11.96
35.00	12.22

Analysis 1: plot the curve

Plot pH on the y-axis against volume of NaOH on the x-axis. Draw a smooth curve through the points, not straight lines between them.

You should see:

• a quick initial rise from 2.87
• a flat buffer region from roughly 5 to 20 cm³
• a near-vertical rise between about 24.5 and 25.5 cm³
• a levelling off above pH 11

The shape is typical of a weak acid–strong base titration. See titration curves.

Analysis 2: find the equivalence point

Method A: midpoint of the steep section. Draw two parallel tangents to the curve, one just before and one just after the steep section. Draw a third line halfway between them; where it crosses the curve is the equivalence point. For the sample data, it’s at about 25.0 cm³, pH about 8.7.

Method B: first derivative. Calculate the change in pH per cm³ between each pair of points:

ΔpH ÷ ΔV

and plot it against the average volume of each pair. The equivalence point is the peak of this graph. Between 24.50 and 25.00 cm³, ΔpH/ΔV = (8.72 − 6.45) ÷ 0.50 = 4.5; between 25.00 and 25.50, it’s (11.00 − 8.72) ÷ 0.50 = 4.6. The peak lies at about 25.0 cm³. Data loggers often calculate this automatically.

Concentration of the acid: n(NaOH) = 0.100 × 0.02500 = 2.500 × 10⁻³ mol = n(CH₃COOH) c(CH₃COOH) = 2.500 × 10⁻³ ÷ 0.02500 = 0.100 mol/dm³

Analysis 3: find pKa

At the half-equivalence point, half the acid has been converted to its conjugate base, so [CH₃COOH] = [CH₃COO⁻] and, from the Henderson–Hasselbalch equation:

pH = pKa

Half of 25.0 cm³ is 12.5 cm³. Reading the curve at 12.5 cm³ gives pH 4.76, so pKa = 4.76 and Ka = 10⁻⁴·⁷⁶ = 1.7 × 10⁻⁵ mol/dm³.

This is one of the standard ways chemists measure pKa values experimentally.

Analysis 4: choose an indicator

Mark the pH ranges of common indicators on your graph as horizontal bands:

• Methyl orange (3.1–4.4) falls in the early part of the curve, well before equivalence. Unsuitable.
• Phenolphthalein (8.2–10.0) falls inside the steep section. Suitable.

This is a vivid visual way to see why indicator choice depends on the type of titration. See how to choose an indicator.

Extensions

1. Compare a strong acid. Repeat with 0.100 mol/dm³ HCl. The curve starts at pH 1, has no buffer region, and the steep section is centred on pH 7 and much taller.
2. Try a diprotic acid. Phosphoric acid or a carbonate solution shows two steep sections.
3. Identify an unknown acid. Determine the pKa of an unknown weak acid and compare with a data table.
4. Temperature effect. Repeat at a different temperature and see how pKa and the equivalence pH change.
5. Second derivative. Plot Δ(ΔpH/ΔV) ÷ ΔV; the equivalence point is where it crosses zero.

Evaluation

Sources of error

• Calibration drift: pH values may be slightly offset. Calibrate immediately before the experiment.
• Slow electrode response: reading too soon after an addition gives a value that’s still changing. Wait for stability, especially near equivalence.
• Too few points in the steep section: makes the equivalence point uncertain. Use 0.10 cm³ additions there.
• Temperature: pKa and the meter’s response depend on temperature. Record it.
• Carbon dioxide absorbed by NaOH changes its concentration. Standardise it just before use.

Why the half-equivalence method is robust

Because pH = pKa at half-equivalence regardless of concentration (for reasonable concentrations), small errors in the acid or base concentration don’t affect the pKa value much. That’s why it’s a favoured method for measuring pKa.

Safety

• Wear eye protection; 0.1 mol/dm³ NaOH irritates the eyes.
• Take care with the glass pH electrode bulb; it’s fragile.
• Keep electrical equipment (stirrers, loggers) away from spills.

Key takeaways

• A pH meter lets you record a full titration curve and find the equivalence point without an indicator.
• Use small additions in the steep section and larger ones elsewhere.
• Find the equivalence point from the steepest part of the curve or the peak of a first-derivative plot.
• At half-equivalence, pH = pKa, giving a direct measurement of the weak acid’s pKa.
• Marking indicator ranges on the curve shows why phenolphthalein suits weak acid–strong base titrations.