Acid-base titrations — the technique — Chemistry

Before this

Moles from mass, volume and concentration
Stoichiometry — mole ratios
Acids and alkalis — pH and neutralisation · coming soon

This leads to

A concentration you cannot see

Here are two bottles of hydrochloric acid. Both are clear and colourless. One is twice as concentrated as the other. Which is which?

You cannot tell by looking. You cannot weigh the acid either, because it is dissolved in water and the water weighs far more than the acid. The number you need, the concentration in mol/dm³, is a count of particles that are invisible and mixed into a liquid.

Chemists solve this with a clever trick. They do not count the acid particles directly. They let them react, one by one in a known ratio, with particles of a solution whose concentration is already known. Then they measure how much of the known solution it took. That volume is the count, written in cm³. This is a titration.

The idea is simple. The difficulty lives in the measurement. A titration is only as good as the hands that do it, so this lecture is about technique: what each piece of equipment is for, how to see the exact moment to stop, and how to know your results can be trusted. The next lecture turns the measurements into a concentration.

The words and the equipment

Four words come first, because books and exams use them precisely.

The standard solution is the solution whose concentration is known accurately.
The analyte is the solution whose concentration you want to find.
The titre is the volume of solution delivered from the burette in one titration. It is a volume in cm³, not a solution.
An indicator is a dye whose colour depends on pH. It shows when the reaction is complete.

A burette, held vertically in a clamp, delivers the standard solution into a conical flask that holds the analyte and a few drops of indicator. The white tile makes a small colour change easy to see. (Which solution goes in the burette can be swapped; see Worked Example 3.)

Each piece of equipment has one job, and the job explains its shape.

Volumetric pipette (with a pipette filler, never by mouth): delivers one fixed volume, usually exactly 25.0 cm³, of the analyte into the flask. It is a long, narrow tube with a single mark. The narrow neck at the mark means a small error in where the liquid sits is only a tiny volume.
Burette: a long tube marked from 0.00 cm³ at the top to 50.00 cm³ near the tap. It measures a variable volume: how much you let out. You read it to the nearest 0.05 cm³.
Conical flask: its sloping sides let you swirl the mixture hard without spilling, so each drop mixes in at once.
White tile: placed under the flask, so a faint change of colour stands out.

Reading a burette

The surface of a watery solution in a narrow tube is curved: it dips in the middle. This curve is the meniscus. Read the scale at the bottom of the meniscus, with your eye level with it. If your eye is higher or lower, the mark you line up with shifts. That error is called parallax.

A close-up of a burette. The bottom of the meniscus is halfway between 24.3 and 24.4, so the reading is 24.35 cm³. Notice that the numbers increase downwards: a burette measures how much has run out.

Two habits follow from the 0.05 cm³ precision. First, every reading is written to two decimal places, ending in 0 or 5: 24.35, 0.00, 25.90. Writing "0" instead of "0.00" tells an examiner you did not read the burette carefully. Second, the titre is always a difference: final reading minus initial reading. You never need to start exactly at 0.00.

The moment to stop

As you add the standard solution, the reaction in the flask uses up the analyte. At one particular volume, the amounts of acid and base are exactly in the ratio of the balanced equation. Neither is left over. This is the moment you are hunting for.

Equivalence point and end point

The equivalence point is reached when the amount of standard solution added has reacted exactly with all of the analyte, in the ratio given by the balanced equation.

The end point is the point at which the indicator changes colour permanently. It is what you actually see, and a good indicator makes it fall at, or extremely close to, the equivalence point.

Notice the words "in the ratio given by the balanced equation". For hydrochloric acid and sodium hydroxide, the ratio is 1 : 1:

HCl(aq) + NaOH(aq) \to NaCl(aq) + H₂O(l)

But sulfuric acid, H₂SO₄, needs two NaOH for every H₂SO₄. At its equivalence point, the moles of acid and base are not equal. They are in the ratio 1 : 2. This is the mole ratio from the stoichiometry lecture, and the next lecture uses it every time.

Choosing an indicator

An indicator does not change colour at one exact pH. It changes over a small range. Two indicators cover most titrations at this level:

Indicator	Colour in acid	Colour in alkali	Changes between pH
Phenolphthalein	colourless	pink	8.2 and 10.0
Methyl orange	red	yellow (orange at the end point)	3.2 and 4.4

Near the equivalence point, the pH in the flask jumps suddenly. One drop can move it by several pH units. An indicator works if its colour-change range lies inside that jump.

Strong acid with strong base (hydrochloric acid with sodium hydroxide): the jump is large, from about pH 3 to about pH 10. Both indicators change inside it, so either works.
Weak acid with strong base (ethanoic acid, the acid in vinegar, with sodium hydroxide): the jump is higher up, in the alkaline region. Use phenolphthalein.
Strong acid with weak base (hydrochloric acid with ammonia): the jump is lower down, in the acidic region. Use methyl orange.
Weak acid with weak base: there is no sharp jump, so no simple indicator gives a clear end point. Chemists use a pH meter instead.

Why does a weak acid move the jump up, and a weak base move it down? The reason is that the salt formed is not neutral. A later lecture on indicators and titration curves explains this with graphs of pH. For now, one pattern is enough. The equivalence point lies on the side of the strong partner. A strong base makes it alkaline, so use phenolphthalein. A strong acid makes it acidic, so use methyl orange.

The method, one step at a time

Every step in the method exists to protect one number. Step through the method below and read the reason for each step before you go on.

Step through — a titration, and why each step is there

Press Next to add one step. Read the reason before you go on.

Each step of the method, and the reason it is there.

Rinse the pipette with a little of the analyte, then discard it. Water left inside would dilute the analyte, so the 25.0 cm³ would hold fewer moles than it should.
Fill the pipette with a filler until the bottom of the meniscus sits on the mark. Run it into the conical flask and touch the tip on the inside of the flask. The pipette is calibrated to deliver its volume this way. Do not blow out the last drop.
Add two or three drops of indicator. Enough to see the colour clearly. The indicator is itself a weak acid, so a large amount would use up a little of the solution.
Rinse the burette with a little of the standard solution, then fill it using a funnel. Remove the funnel. Water would dilute the standard. A funnel left in the top can drip in extra liquid during the titration.
Run a little solution through the tap until the jet below it is full, with no air bubble. Read the initial volume. An air bubble that escapes during the titration would be counted as liquid delivered.
Do a rough titration: add the solution quickly, swirling, until the colour changes. This finds roughly where the end point is, so you know where to slow down. It usually overshoots, so it is not used in the mean.
Repeat accurately: run in quickly to about 1 cm³ below the rough titre, then add drop by drop, swirling after each drop. One drop is about 0.05 cm³. Near the end point, one drop can change the colour.
Wash the inside walls of the flask with a little distilled water near the end. Drops stuck to the sides have not reacted yet. Water does not change the number of moles in the flask.
Stop at the first permanent colour change: the colour stays after swirling. A colour that appears where the drop lands and then fades means the equivalence point has not been reached.
Read the final volume, and repeat until the titres are concordant. One result could hide an error. Agreeing results show the method is precise.

Did you notice the pattern in the reasons? Every rinse protects the moles. Every reading habit protects the volume. That one idea answers almost every exam question about titration technique.

Stop and think

You rinse the burette with the standard solution, because water would dilute it. So should you also rinse the conical flask with the analyte?

Show the answer

No. The flask must contain exactly the moles of analyte that the pipette delivered, no more. Rinsing it with analyte would leave extra analyte behind, so the flask would hold more moles than you think, and the titre would be too large. Rinsing the flask with water is fine, and so is a flask that is still wet. Water adds volume but no moles of analyte, and the reaction depends only on the moles. The burette is different: its concentration matters, because you read a volume from it and convert that volume into moles.

Concordant results

A single titre is not enough. You repeat the accurate titration until two or more titres are concordant: they agree closely. Most schemes ask for titres within 0.10 cm³ of each other. (Some mark schemes accept a slightly wider spread, such as 0.20 cm³, when averaging. Use the rule your syllabus gives.) The mean titre is the average of the concordant titres only. The rough titre and any result that does not agree are left out.

Worked Example 1 — Finding the mean titre

Titration	Initial reading / cm³	Final reading / cm³	Titre / cm³
Rough	0.00	26.20	26.20
1	0.00	25.85	25.85
2	0.15	26.00	25.85
3	0.00	25.90	25.90

Each titre is final minus initial: for titration 2, $26.00 - 0.15 = 25.85$ cm³.

The three accurate titres range from 25.85 to 25.90, a spread of 0.05 cm³. All three are concordant. The rough titre is left out.

Mean titre $= (25.85 + 25.85 + 25.90) \div 3 = 25.866 \dots \approx 25.87$ cm³.

Check: the mean lies between the smallest and largest concordant titres ✓. It is given to two decimal places, like the readings. It need not end in 0 or 5, because it is calculated, not read.

Worked Example 2 — A result that does not belong

A student's titres are: rough 24.60, then 23.90, 24.30 and 24.00 cm³. Find the mean titre.

23.90 and 24.00 differ by 0.10 cm³: concordant. 24.30 differs from them by 0.30 and 0.40 cm³: not concordant, so it is left out. Perhaps the student overshot the end point that time.

Mean titre $= (23.90 + 24.00) \div 2 = 23.95$ cm³.

Check: including 24.30 would give 24.07 cm³, pulled upwards by one careless result. Concordance protects the mean from it.

Worked Example 3 — Which indicator, and which colour change?

Ammonia solution is in the flask. Hydrochloric acid of known concentration is in the burette. Choose an indicator and state the colour change at the end point.

Ammonia is a weak base and hydrochloric acid is a strong acid, so the pH jump is in the acidic region: use methyl orange.

At the start, the flask is alkaline, so methyl orange is yellow. As acid is added, the end point is the first permanent orange. If you went on to red, you have overshot.

Check: the colour change goes from the alkali colour to the acid colour, because acid is being added to alkali. If the burette held the alkali instead, the change would run the other way, from red to orange.

Worked Example 4 — Finding the cause of a wrong result

A student's titres are concordant, but every one is about 1.6 cm³ larger than the rest of the class's (26.60 cm³ instead of 25.00 cm³). The student says the burette was rinsed with water only. Explain the result.

Water left in the burette dilutes the standard solution. Each cm³ then holds fewer moles than the label says. The analyte in the flask still needs the same number of moles to react completely. So more cm³ must be added.

If the dilution lowered the concentration by 6%, the volume needed rises by a factor of $1 \div 0.94 \approx 1.064$ : from 25.00 to about 26.60 cm³. That matches.

Check: the error affects every titre in the same way, which is why the results still agree with each other. Concordant results show precision. They do not prove accuracy.

That last point deserves practice. For each mistake below, decide what happens to the titre.

Sort — what does each mistake do to the titre?

For each mistake, ask: does it change the moles in the flask, the concentration in the burette, or the volume I read? Then put the card in a box.

Eight mistakes and their effect on the titre (standard solution in the burette, analyte in the flask).

Titre too high: burette rinsed with water only · overshooting the end point · an air bubble in the jet escapes during the titration · conical flask rinsed with analyte.
Titre too low: pipette rinsed with water only · stopping when the pink colour fades on swirling.
No effect: the conical flask is still wet with distilled water · washing the inside of the flask with distilled water during the titration.

Three classic mistakes

Trap 1 — Calling the solution the "titre"

The titre is a volume, the volume delivered from the burette in one titration. The solution in the burette is the standard solution. Writing "the titre was 0.100 mol/dm³" makes no sense: a titre is measured in cm³.

Trap 2 — Including the rough titre in the mean

The rough titration is done quickly and usually overshoots. It tells you where to slow down. The mean uses only the concordant accurate titres.

Trap 3 — Stopping at a colour that fades

Near the end point, each drop makes a flash of colour where it lands. If the colour disappears when you swirl, the analyte is not yet used up. The end point is the first colour that stays.

Try it yourself

Work each one on paper first. Open a hint only when you are stuck.

Burette readings (initial, final) in cm³: rough (0.00, 22.40); 1st (0.50, 22.30); 2nd (22.30, 44.45); 3rd (0.00, 21.80). Find each titre and the mean titre.

Hint 1
Each titre is final minus initial.

Hint 2
The titres are 22.40, 21.80, 22.15 and 21.80. Which accurate ones agree within 0.10 cm³?

Full answer
Titres: rough 22.40; 1st $22.30 - 0.50 = 21.80$ ; 2nd $44.45 - 22.30 = 22.15$ ; 3rd 21.80. The 1st and 3rd are concordant (identical). The 2nd differs by 0.35 and is left out, as is the rough. Mean $= 21.80$ cm³. Check: the 2nd titration started at 22.30, so it was done without refilling the burette. That is allowed, because a titre is a difference.
You titrate ethanoic acid (in the flask) with sodium hydroxide solution (in the burette). Which indicator do you use, and what colour change do you look for?

Hint 1
Is ethanoic acid strong or weak? Is sodium hydroxide strong or weak?

Hint 2
Weak acid with strong base: the pH jump is in the alkaline region.

Full answer
Phenolphthalein. The flask starts acidic, so the indicator is colourless. The end point is the first permanent pale pink. Methyl orange would change colour far too early, while there is still plenty of acid left, because its range (3.2 to 4.4) lies below the jump.
Explain why rinsing the pipette with water only makes the titre too low, while rinsing the burette with water only makes it too high.

Hint 1
What does each piece of equipment control: the moles in the flask, or the concentration of what you add?

Hint 2
A diluted analyte means fewer moles to react with. A diluted standard means fewer moles per cm³ added.

Full answer
Pipette: water dilutes the analyte, so the fixed 25.0 cm³ holds fewer moles. Fewer moles of analyte need fewer moles of standard, so a smaller volume: titre too low. Burette: water dilutes the standard, so each cm³ carries fewer moles. The analyte still needs the same moles, so more cm³ are needed: titre too high. The same mistake, water, has opposite effects because the two pieces of equipment protect different numbers.
Group A's titres are 26.40, 26.45 and 26.40 cm³. Group B's are 25.10, 24.70 and 25.30 cm³. The true titre is 25.00 cm³. Which group is more precise? Which is more accurate? Suggest one cause for each group's problem.

Hint 1
Precise means the results agree with each other. Accurate means they are close to the true value.

Hint 2
A mistake repeated the same way each time moves every result together. A mistake that varies scatters them.

Full answer
Group A is precise (spread 0.05 cm³) but not accurate: every titre is about 1.4 cm³ too high. That suggests an error repeated every time, such as a burette rinsed with water, or a standard solution weaker than its label. Group B is closer to the true value on average (mean of all three ≈ 25.03 cm³) but not precise: the spread is 0.60 cm³, so no two titres are concordant. That suggests careless end points, such as overshooting or stopping at a fading colour, which vary from run to run. Group B should repeat until titres agree. Group A must find the error in its method, because repeating will only give the same wrong answer.

The bigger idea

The burette has a long history. In 1806 the French chemist François-Antoine-Henri Descroizilles described a graduated tube for measuring alkalis, controlled by covering an air hole with a finger. Joseph Louis Gay-Lussac developed a tube with a spout that he called a burette. Then Karl Friedrich Mohr added a short rubber tube at the bottom, squeezed shut by a metal clip he designed, so the flow could be controlled drop by drop. His 1855 textbook on titration methods made the technique standard in laboratories.

Why has it lasted? Because it turns an invisible count of particles into a length of liquid that a person can read to 0.05 cm³. With a 25.0 cm³ portion and a titre of about 25 cm³, that is a reading good to about one part in 500. Today many laboratories use automatic titrators that follow the pH with an electrode instead of watching a colour. The principle is unchanged: react the unknown with the known, and measure how much of the known it took.

The next lecture takes the mean titre you have learned to measure and turns it into a concentration, using $n = c V$ and the mole ratio.

Key concepts in this lesson

A titration finds the concentration of an analyte by measuring the volume of a standard solution of known concentration needed to react with it exactly.
The titre is the volume delivered from the burette in one titration, read at the bottom of the meniscus to the nearest 0.05 cm³.
The equivalence point is where the reactants are in the exact ratio of the balanced equation, and the end point is where the indicator changes colour permanently.
Phenolphthalein suits titrations with a strong base, methyl orange suits titrations with a strong acid, and either works for strong acid with strong base.
Rinsing with the right solution protects the moles and the concentration, while water in the conical flask has no effect because it adds no moles.
The mean titre uses only concordant accurate titres, usually within 0.10 cm³, and concordant results show precision but not necessarily accuracy.