# Acid–Base Titration

Laplace’s Mini World · Plate 86 · Matter, Light & Sound · Matter

> Base of known strength goes in drop by drop until the indicator changes colour; the volume used on the burette tells how much acid the flask held.

- Interactive model: https://world.lapla.si/en/titration/
- Embed: https://world.lapla.si/embed/en/titration/
- 中文: https://world.lapla.si/zh/titration/
- Updated: 2026-11-03

## 01 A Titration on the Bench

The conical flask holds 25.00 mL of hydrochloric acid, measured in with a pipette; its strength is unknown. Above it a 50 mL burette holds sodium hydroxide solution of known strength, 0.100 mol/L. A few drops of indicator are in the flask, which stands on a white tile: a faint colour that the stand’s dark base would hide shows against it.

Opening the stopcock at the foot of the burette lets the base run into the flask, where it reacts with the acid: H⁺ + OH⁻ → H₂O. It goes in until the base has used up the acid exactly. The volume of base used, times its concentration, is the amount of acid the flask held.

The method is old. In the 18th century the strength of vinegar was judged by adding potassium carbonate a little at a time until it stopped bubbling. In 1824 Gay-⁠Lussac, assaying bleaching powder, already called his graduated tube a burette and stood the glass on a sheet of white paper; he reckoned the result good to one part in fifty. This bench has one thing more: a pH meter, its glass electrode in the flask, recording what the eye cannot see.

*25.00 mL hydrochloric acid · 0.100 mol/L sodium hydroxide · 50 mL burette · indicator · white tile · pH meter*

## 02 Reading the Burette

A burette reads 0 at the top and counts down the tube, with a line every 0.1 mL. One more figure is estimated between the lines, to 0.01 mL.

The surface of the liquid curves, lowest in the middle. The reading is taken at the bottom of the meniscus, with the eye level with it. An eye too high reads too little; too low, too much. As estimated here, an eye 3 cm too high at 30 cm reads about 0.05 mL short.

Each titration takes two readings, at the start and at the end; the volume used is the difference. After running liquid out, about 30 s is left for the film on the walls to drain before reading. A class A 50 mL burette is allowed an error of ±0.05 mL, about one drop.

*0 at the top · lines every 0.1 mL · read to 0.01 mL · at the bottom of the meniscus · class A ±0.05 mL*

## 03 Twenty-⁠Four Millilitres, Barely a Change

At the start the flask holds 0.100 mol/L hydrochloric acid at pH 1.00. As base goes in, the acid is used up bit by bit, yet the pH climbs slowly: at 24.00 mL, 96% of the acid is gone and the pH is only 2.69.

Each step of 1 in pH means the hydrogen ions fall to a tenth. From pH 1 to 2 takes 20.45 mL of base, from 2 to 3 only 4.05 mL, from 3 to 4 only 0.45 mL. The less acid is left, the larger the share one drop of base takes of it.

So a rough titration comes first, to find roughly where the end lies. On the next run the first part can go fast, the base running in a stream while the flask is swirled; within about 5 mL of the end it goes in smaller portions, and at last drop by drop.

*25.00 mL hydrochloric acid + sodium hydroxide, 0.100 mol/L · 0 mL pH 1.00 · 24.00 mL pH 2.69*

## 04 The Last Two Drops

A drop is about 0.03 to 0.05 mL; the page takes 0.05 mL. Two drops short, at 24.95 mL, the pH is 4.00. One more, at 25.00 mL, and base and acid are exactly equal: pH 7.00. One more, at 25.05 mL: pH 10.00.

Over 0.10 mL the pH leaps six units. A drop of base holds only 5.0 µmol of hydroxide and the flask held 2500 µmol of acid; but by now only the last few micromoles of acid are left, so one drop uses them up and the next is in excess.

This part of the curve is nearly vertical. Because it is so steep, the colour changes within a drop or two, and the end point can be read precisely.

*24.95 mL pH 4.00 · 25.00 mL pH 7.00 · 25.05 mL pH 10.00 · computed here for 25 °C*

## 05 Seen and Computed

The equivalence point is where the base exactly equals the acid, computed from the stoichiometry and never seen; the end point is the volume actually read, the drop at which the indicator changes or an instrument sees the jump. Here the equivalence point is 25.00 mL.

Phenolphthalein is colourless below pH 8.3 and pink by about 10. In this titration it starts to change at 25.001 mL and has finished by 25.050 mL, all within one drop after the equivalence point: end point and equivalence point all but coincide.

Near the end, each drop leaves a patch of pink where it lands, which fades as the flask is swirled, because there is still acid around it. The nearer the end, the longer the pink lasts. When a faint pink holds after swirling, for 10 to 30 s depending on the manual, the burette is read; left longer, the pink slowly fades again as carbon dioxide from the air dissolves.

*Equivalence point 25.00 mL (computed) · end point: the first pink that stays, 25.00 mL (seen)*

## 06 Acetic Acid Instead

The flask now holds 0.100 mol/L acetic acid, CH₃COOH, titrated with the same base. Acetic acid is weak, only about 1.3% ionised, so it starts at pH 2.87, higher than hydrochloric acid.

The base turns some of the acid into acetate, and with both acetic acid and acetate in the flask the solution is a buffer: the pH changes even more slowly. Half-⁠way, at 12.50 mL, the two are equal and the pH is 4.74, the pKa of acetic acid.

At the equivalence point the flask holds sodium acetate solution. Acetate is a weak base, so the pH is 8.72, not 7. Over the last two drops the pH leaps only 2.6 units, from 7.44 to 10.00. Past the equivalence point the two curves merge: the pH depends only on the excess sodium hydroxide.

*Acetic acid 0 mL pH 2.87 · 12.50 mL pH 4.74 = pKa · 25.00 mL pH 8.72 · buffer pH = pKa + log(\[A⁻\]/\[HA\])*

## 07 Changing on the Leap

An indicator is itself a weak acid whose acid and base forms differ in colour, and it changes over about pKa ± 1 (why phenolphthalein turns pink in a base is on the Ammonia Fountain plate). Methyl orange goes from red to yellow over pH 3.1⁠–⁠4.4, bromothymol blue from yellow to blue over 6.0⁠–⁠7.6, phenolphthalein from colourless to pink over 8.3⁠–⁠10.0.

For hydrochloric acid and sodium hydroxide the leap runs from pH 4 to 10, and all three change within half a millilitre of the equivalence point. Acetic acid is different: methyl orange starts to change at 0.4 mL and is done by 7.8 mL, 17 mL before the equivalence point; bromothymol blue drifts from 23.7 to 25.0 mL; only phenolphthalein falls on the leap.

The other way round, titrating hydrochloric acid with ammonia, the equivalence point is ammonium chloride solution at pH 5.28, slightly acidic. Methyl orange suits it; phenolphthalein does not start to turn pink until 27.8 mL, nearly 3 mL late.

*Methyl orange 3.1⁠–⁠4.4 · bromothymol blue 6.0⁠–⁠7.6 · phenolphthalein 8.3⁠–⁠10.0 · curves computed here for 25 °C*

## 08 The Curve the pH Meter Sees

At the foot of a pH meter’s glass electrode is a glass bulb about 50 µm thick. How many hydrogen ions the solution holds changes the voltage across it: at 25 °C, 59.16 mV for each unit of pH, which is RT·ln10/F.

The voltage carries other terms too, so the meter is first calibrated in buffers of known pH, often 4.01, 7.00 and 10.01. After that, a reading taken after each addition traces the whole titration curve.

The steepest point of the curve is the equivalence point. As computed here, at 0.100 mol/L the steepest points of all three titrations lie within a millionth of a millilitre of 25.00 mL. For a weak acid with a weak base, such as acetic acid with ammonia, the last two drops change the pH by only 0.16: no indicator gives a clear end point, and only the meter can.

*59.16 mV per pH unit at 25 °C · calibration buffers pH 4.01, 7.00, 10.01*

## 09 How Much Acid in Vinegar

The same method measures the acidity of vinegar. In the method of the International Organisation of Vine and Wine (OIV), 10 mL of vinegar goes into a 250 mL conical flask with water and a few drops of phenolphthalein, and is titrated with 0.5 mol/L sodium hydroxide to a pink that stays; the millilitres used, times 3, give the acid in grams per litre, counted as acetic acid. The acid in vinegar is mostly acetic acid, a weak acid, hence phenolphthalein.

A vinegar with 50 g of acetic acid per litre needs 16.65 mL of base. China’s national standard GB 2719-2018 asks for at least 3.5 g of total acid, as acetic acid, per 100 mL of vinegar, that is 35 g per litre, which would be 11.66 mL.

One drop too many, taken as 0.05 mL, adds 0.15 g per litre, 0.3% of 50 g. That is about the class A burette’s allowed error, so the same vinegar is titrated two or three times; the Royal Society of Chemistry averages results once they agree within 0.10 mL.

*OIV method: millilitres × 3 = g/L · 50 g/L → 16.65 mL · national minimum 35 g/L → 11.66 mL · one drop ≈ 0.3%*

## 10 Ten Things on the Bench

Burette, burette clamp, retort stand, conical flask, white tile, pH meter, glass electrode, sodium hydroxide, indicator, pipette. The precision rests on two class A pieces of glass: the 25 mL pipette measures the acid, to ±0.03 mL; the 50 mL burette the base, to ±0.05 mL.

*Burette · clamp · stand · conical flask · white tile · pH meter · glass electrode · sodium hydroxide · indicator · pipette*

## 11 Run a Titration

This is the page’s model, computed in the browser from the charge balance above, at 25 °C, with concentrations as activities. The end point is taken as the eye sees it: for phenolphthalein the first pink that stays, for methyl orange and bromothymol blue the colour half changed.

Each run sets the acid, the base, the indicator and the acid’s strength, then adds one drop at a time, or 1 mL at once, with the colour, the meter and the curve to read the end point from. The base is always 0.100 mol/L, the acid always 25.00 mL.

*The page’s model · Kw, Ka of acetic acid and Kb of ammonia from OpenStax · indicator ranges after the RSC and Clark 1922*

**Try this**: In the lab, choose acetic acid and methyl orange and add drops until the colour changes: at what volume is the end point? Try again with phenolphthalein. The acid in the flask needs 25.00 mL of base to be used up exactly.

## What the model leaves out

The bench is a model of a school or college titration, in the sizes of a DURAN 250 mL wide-⁠neck conical flask and a 50 mL class A burette; not a copy of any one rig. The curves are computed exactly from the charge balance at 25 °C, with concentrations taken as activities (0.1 mol/L hydrochloric acid really reads about pH 1.1, not 1.00), and no carbon dioxide from the air. The indicators’ colours are drawn: half changed at the middle of the range, the indicator’s own amount neglected. A drop is taken as 0.05 mL; the patch of colour where it lands, the swirl and how fast the patch fades are the page’s own model, there only to show the pink lasting longer near the end. A wide-⁠neck flask is used so the electrode fits; a titration by indicator alone usually has no electrode in the flask, and a pH-⁠meter titration is often done in a beaker with a magnetic stirrer.

## Easy to get wrong

The end point is not the equivalence point: the equivalence point is computed from the stoichiometry, the end point is the volume seen or measured, and with a well-⁠chosen indicator they differ by a drop or two. The pH at the equivalence point is not always 7: 7.00 for a strong acid with a strong base at 25 °C, 8.72 for acetic acid with sodium hydroxide, 5.28 for hydrochloric acid with ammonia; and at other temperatures neutral is not 7 either (6.31 at 80 °C). An indicator does not change at one pH but gradually, over about two pH units. Methyl orange on acetic acid is not late but early: it has finished before a third of the base is in. A pH meter measures a voltage and has to be calibrated with buffers; it reflects the activity of hydrogen ions, not quite their concentration.

## Common questions

### End point and equivalence point: what is the difference?

The equivalence point is where the base exactly equals the acid, computed from the stoichiometry and never seen; the end point is the volume actually read, the drop at which the indicator changes or an instrument sees the jump.

See: [05 Seen and Computed](https://world.lapla.si/en/titration/#endpoint)

### Why can one drop change the pH by several units near the end?

Over 0.10 mL the pH leaps six units.

See: [04 The Last Two Drops](https://world.lapla.si/en/titration/#jump)

### Why is the equivalence point above pH 7 for acetic acid?

At the equivalence point the flask holds sodium acetate solution.

See: [06 Acetic Acid Instead](https://world.lapla.si/en/titration/#weak)

### Why is methyl orange wrong for titrating acetic acid?

Acetic acid is different: methyl orange starts to change at 0.4 mL and is done by 7.8 mL, 17 mL before the equivalence point; bromothymol blue drifts from 23.7 to 25.0 mL; only phenolphthalein falls on the leap.

See: [07 Changing on the Leap](https://world.lapla.si/en/titration/#choose)

### Where is a burette read?

The reading is taken at the bottom of the meniscus, with the eye level with it.

See: [02 Reading the Burette](https://world.lapla.si/en/titration/#read)

## Sources

1. [OpenStax: Chemistry 2e, 4.5 (titration, the equivalence point and the end point; the strength of vinegar in the 18th century)](https://openstax.org/books/chemistry-2e/pages/4-5-quantitative-chemical-analysis)
2. [OpenStax: Chemistry 2e, 14.7 (titration curves, Table 14.2, Examples 14.21 and 14.22; indicators and how to choose one)](https://openstax.org/books/chemistry-2e/pages/14-7-acid-base-titrations)
3. [OpenStax: Chemistry 2e, 14.6 (buffers, the Henderson–Hasselbalch equation)](https://openstax.org/books/chemistry-2e/pages/14-6-buffers)
4. [OpenStax: Chemistry 2e, 14.4 (hydrolysis of salts: ammonium chloride solution is acidic)](https://openstax.org/books/chemistry-2e/pages/14-4-hydrolysis-of-salts)
5. [OpenStax: Chemistry 2e, 14.2 (pH and pOH; neutral is pH 7 only at 25 °C; the pH meter)](https://openstax.org/books/chemistry-2e/pages/14-2-ph-and-poh)
6. [OpenStax: Chemistry 2e, appendices H and I (Ka of acetic acid and Kb of ammonia, both 1.8 × 10⁻⁵)](https://openstax.org/books/chemistry-2e/pages/h-ionization-constants-of-weak-acids)
7. [David Harvey: Analytical Chemistry 2.1, 9.2 (equivalence and end points; the inflection point; indicators; finding the end point from the pH curve)](https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Analytical_Chemistry_2.1_by_David_Harvey/Analytical_Chemistry_2.1_(Harvey)/09%3A_Titrimetric_Methods/9.02%3A_AcidBase_Titrations)
8. [David Harvey: Analytical Chemistry 2.1, 11.2 (the glass electrode, the Nernst equation, calibrating with buffers)](https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Analytical_Chemistry_2.1_by_David_Harvey/Analytical_Chemistry_2.1_(Harvey)/11%3A_Electrochemical_Methods/11.02%3A_Potentiometric_Methods)
9. [Royal Society of Chemistry: Acid-⁠base indicators worksheet (methyl orange 3.1⁠–⁠4.4, phenolphthalein 8.3⁠–⁠10.0; which indicator for ammonia into hydrochloric acid, and for ethanoic acid with sodium hydroxide)](https://edu.rsc.org/download?ac=518622)
10. [W. M. Clark (1922): The Determination of Hydrogen Ions, 2nd ed. (Sørensen’s and Clark and Lubs’ indicator tables: bromothymol blue 6.0⁠–⁠7.6)](https://archive.org/details/determinationofh00clarrich)
11. [Thermo Scientific Orion: pH Calibration Procedure (pH 4.01, 7.00 and 10.01 buffers; slope 92⁠–⁠102%)](https://assets.thermofisher.com/TFS-Assets/CMD/Product-Bulletins/TN-ph-calibration-procedure-for-optimal-measurement-precision-T-PHCAL-EN.pdf)
12. [NIST: CODATA 2022 values (the molar gas constant R and the Faraday constant F)](https://physics.nist.gov/cgi-bin/cuu/Value?r)
13. [Royal Society of Chemistry: Titration method fact sheet (a rough titration first, smaller portions within 5 cm³ of the end point, concordant results within 0.10 cm³)](https://edu.rsc.org/download?ac=537507)
14. [Royal Society of Chemistry: Get to grips with titration poster (the white tile shows subtle colour changes; the conical flask is easy to swirl)](https://edu.rsc.org/infographics/mastering-titration-apparatus/4019251.article)
15. [Royal Australian Chemical Institute: A Guide to Titration (rinsing, swirling, local colour that reverts on mixing, an end point that holds for 10 s)](https://higherlogicdownload.s3.amazonaws.com/RACI/bc44ab80-cac0-4d72-b180-5539ea551222/UploadedImages/Education___Outreach/Titration_Competition/A_Guide_to_Titration.pdf)
16. [Middlebury College: Titration (a normal drop about 0.03 mL; viewed from above the reading appears lower; wait 30 s before reading)](https://sites.middlebury.edu/chem103lab/2016/09/02/bureting/)
17. [D. C. Harris: Experiments to Accompany Quantitative Chemical Analysis, 9th ed. (8 drops in about 0.4 mL; part drops; a pink that holds 15 s and slowly fades as carbon dioxide dissolves)](https://www.macmillanlearning.com/studentresources/college/chemistry/qca9e/experiments/qca9estudentexperimentsforwebsite29mar2015.pdf)
18. [BRAND: BLAUBRAND burettes, class A/AS (50 mL ±0.05 mL, graduated in 0.1 mL)](https://shop.brand.de/en/burettes-blaubrandr-class-as-boro-3-3-de-m-lateral-valve-cock-blue-schellbach-stripe-p385.html)
19. [BRAND: BLAUBRAND bulb pipettes, class AS (25 mL ±0.03 mL)](https://shop.brand.de/en/bulb-pipettes-blaubrandr-class-as-1-mark-blue-printed-scale-ar-glasr-de-m-p335.html)
20. [BRAND: Liquid meniscus explained (a concave meniscus read at its lowest point, the eye at its height)](https://www.brand.de/en/applications/volumetric-instruments/liquid-meniscus)
21. [DURAN Erlenmeyer flasks, size table (via Kou Hing Hong; 250 mL wide neck: 85 mm across, neck 50 mm, 140 mm high)](http://www.kouhing.com/duran-erlenmeyer-flask/)
22. [SCHOTT: DURAN Technical Data (borosilicate glass 3.3, refractive index 1.473)](https://media.schott.com/api/public/content/d43d3a52c79d4b10a2f358d9c097e77b)
23. [OIV: OIV-⁠MA-⁠VI-⁠01, total acidity of vinegars (10 mL vinegar, 0.5 mol/L sodium hydroxide, phenolphthalein; g/L = 3V)](https://www.oiv.int/standards/compendium-of-international-methods-of-analysis-for-vinegars/wine-vinegars/methods-of-analysis-for-vinegars)
24. [GB 2719-2018, National food safety standard: vinegar (total acid as acetic acid ≥ 3.5 g/100 mL)](https://www.fzmq.gov.cn/xjwz/zwgk/zfxxgkzdgz/spypaq/spaqbz/202109/P020210902403024539132.pdf)
25. [NIST Chemistry WebBook: acetic acid, molar mass](https://webbook.nist.gov/cgi/cbook.cgi?ID=C64197&Mask=0)
26. [Gay-⁠Lussac (1824): Instruction sur l’essai du chlorure de chaux, Annales de chimie et de physique 26 (the burette, the white paper, one part in fifty)](https://archive.org/details/s3id13207940)

## Data

The titration curves are computed here from the full charge balance at 25 °C, with Kw, Ka of acetic acid and Kb of ammonia from OpenStax Chemistry 2e (Flowers, Theopold, Langley, Robinson; Rice University, 2019; access for free at openstax.org), and checked against its Table 14.2 and Examples 14.21⁠–⁠14.22. Indicator ranges after the Royal Society of Chemistry’s Education in Chemistry worksheet, W. M. Clark, The Determination of Hydrogen Ions (1922; Sørensen’s and Clark and Lubs’ indicators) and D. Harvey, Analytical Chemistry 2.1 (DePauw University; LibreTexts). The glass electrode’s slope from the exact CODATA 2022 values of R and F (NIST); buffer values from a Thermo Scientific Orion calibration note. The bench and the procedure after the Royal Society of Chemistry’s practical pages and university laboratory manuals; burette and pipette tolerances, flask sizes and the vinegar method as quoted in docs/plates/titration/FACTS-⁠lab.md. The drop-⁠by-⁠drop run, the swirl and the colour where a drop lands are the page’s own model. The apparatus is this page’s model of a school or college bench, in the sizes of a DURAN 250 mL wide-⁠neck conical flask (85 mm across, 140 mm high, neck 50 mm) and a 50 mL class A burette; not a copy of any one rig. Material presets and the model kit as on the site’s other model plates (public/looks/CREDITS.md).

## Licence CC BY-NC 4.0

The text, pictures and models on this page are licensed CC BY-NC 4.0: free to use and adapt for teaching and other non-commercial purposes, with credit to world.lapla.si. Third-party material listed above keeps its own licence.

https://creativecommons.org/licenses/by-nc/4.0/deed.en

## Cite this plate

Laplace’s Mini World, Plate 86, “Acid–Base Titration”, https://world.lapla.si/en/titration/, CC BY-NC 4.0, updated 2026-11-03.