Titration calculator

A titration calculator finds the unknown concentration of an acid or alkali from a titration. Work out the moles in the solution you know with n = cV, use the balanced equation to get the moles of the unknown, then divide by its volume: c = n/V. Our Titration Lab runs the titration itself: pick an acid and a base, add titrant drop by drop, and watch the pH curve and the equivalence point appear.

The lab works the other way round from most titration calculators. You give it both concentrations, and it tells you the titre, the volume needed to reach equivalence. So to find an unknown concentration, work it out as below, then type your answer into the lab and check that equivalence lands on your titre.

Try it

Titration Lab

Run a virtual titration and plot the pH curve as you go

Open the simulatorGo to its page

How to use the virtual titration lab

1. Under Set up, choose Acid in flask or Base in flask. The other one goes in the burette.
2. Pick the acid and the base. There are ten acids, including hydrochloric, sulfuric, ethanoic and phosphoric acid, and seven bases, including sodium hydroxide, ammonia and sodium carbonate.
3. Set both concentrations in mol/dm³ and the volume in the flask in cm³.
4. Choose an Indicator. The lab says whether it suits this titration, and how far its colour change is from equivalence.
5. Under Run, pick Dropwise, Quick or Stream, then press Open tap, or Add a drop for one drop of 0.05 cm³.
6. Watch the flask change colour and read the burette, the volume added and the pH. Equivalence and half-equivalence points are marked on the pH curve as you pass them.

It opens on 25 cm³ of 0.1 mol/dm³ ethanoic acid (acetic acid in the US) with 0.1 mol/dm³ sodium hydroxide in the burette and phenolphthalein. mol/dm³ is the same as mol/L, and cm³ is the same as mL. Turn on Show the whole curve to see where the curve is going before you start. The burette holds 50 cm³, and the lab tells you if you will need to refill it. The screen shows results rather than working; the printout, part of the Educator plan, sets out the moles, the mole ratio and the equivalence volume. Practice and help sets questions on titres, pKa and indicators, with worked solutions.

The titration formula

Every titration calculation uses the same three steps:

1. Moles of the solution you know: n = c × V, with V in dm³ (cm³ ÷ 1000).
2. Moles of the unknown, from the mole ratio in the balanced equation.
3. Concentration of the unknown: c = n ÷ V.

For an equation where a mol of acid reacts with b mol of base, the three steps combine into one:

For a 1 to 1 reaction such as HCl with NaOH, this is just c_a V_a = c_b V_b. Our Molarity Calculator handles n = cV on its own.

Worked titration calculations you can check in the lab

Example 1: hydrochloric acid, a 1 to 1 reaction

25.0 cm³ of hydrochloric acid needs 21.40 cm³ of 0.100 mol/dm³ sodium hydroxide to neutralise it. Find the concentration of the acid. HCl + NaOH → NaCl + H₂O, so 1 mol of acid reacts with 1 mol of base.

Check it: set hydrochloric acid to 0.0856 mol/dm³, 25 cm³ in the flask, and sodium hydroxide to 0.1. The lab puts equivalence at 21.40 cm³, pH 7.00, so the answer is right.

Example 2: sulfuric acid, a 1 to 2 reaction

20.0 cm³ of sulfuric acid needs 18.60 cm³ of 0.200 mol/dm³ sodium hydroxide. H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O, so the acid has half as many moles as the base:

Set sulfuric acid to 0.093 mol/dm³ with 20 cm³ in the flask and 0.2 mol/dm³ sodium hydroxide. Equivalence comes at 18.60 cm³. Forgetting the 2 would give 0.186 mol/dm³, double the true value.

Example 3: predict the titre, with two end points

25.0 cm³ of 0.050 mol/dm³ sodium carbonate is titrated with 0.100 mol/dm³ hydrochloric acid. The carbonate reacts with twice its moles of acid, Na₂CO₃ + 2HCl → 2NaCl + H₂O + CO₂, so 1.25 × 10⁻³ mol of carbonate needs 2.50 × 10⁻³ mol of acid, which is 2.50 × 10⁻³ ÷ 0.100 = 0.0250 dm³, or 25.00 cm³.

Choose Base in flask, sodium carbonate at 0.05 and hydrochloric acid at 0.1. The lab shows the titre of 25.00 cm³ at pH 3.98, and a first equivalence point at 12.50 cm³, pH 8.34, where the carbonate has only become hydrogencarbonate. That is why methyl orange, which changes at pH 3.1 to 4.4, is the indicator for this titration.

Example 4: concordant titres and the mean

A student gets titres of 22.50 cm³ (the rough run), 22.15 cm³, 22.10 cm³ and 22.35 cm³. Concordant titres are close to each other, usually within 0.10 cm³: here 22.15 and 22.10. Leave out the rough run and the outlier, and take the mean of the concordant titres: (22.15 + 22.10) ÷ 2 = 22.13 cm³. Use that mean in the calculation. The lab gives one exact titre each time, so this step is always by hand.

Titration curves: reading the pH curve

The pH curve plots the pH in the flask against the volume added. For the lab's opening set-up, ethanoic acid with sodium hydroxide, it looks like this:

Here x is the volume of sodium hydroxide added in cm³ and y is the pH. The curve starts at pH 2.88, rises slowly through the buffer region, then shoots up near 25 cm³. Equivalence is at 25.00 cm³ and pH 8.73, above 7 because the salt, sodium ethanoate, is slightly alkaline. Halfway there, at 12.50 cm³, the pH equals the pKa of the acid, 4.76, which is how you find a pKa from a titration. The lab marks both points.

All four use 25 cm³ of 0.1 mol/dm³ acid and 0.1 mol/dm³ base. With a weak acid and a weak base, the pH only climbs from 6.13 to 7.86 between 24 and 26 cm³, too gradually for any indicator to give a sharp end point. Use a pH meter instead. Our pH calculator guide explains the pH and pKa sums behind these curves.

Choosing an indicator

An indicator works when its colour change falls on the steep part of the curve. These are four of the indicators in the lab:

Try methyl orange with ethanoic acid and sodium hydroxide, and the lab says it is not suitable: it changes 23.05 cm³ before equivalence. Phenolphthalein changes within 0.01 cm³ of it. Test yourself:

What the lab does not do

• No mode for an unknown concentration. It needs both concentrations. Find the unknown by hand, then check it in the lab, as in Examples 1 and 2.
• Acid and base titrations only. Redox titrations, such as potassium manganate(VII), and back titrations need working by hand.
• No experimental error. Every titre is exact, so there are no rough runs or concordant results to pick from, and no meniscus to read.

Common mistakes

• Leaving volumes in cm³. Divide by 1000 to get dm³ before using n = cV.
• Ignoring the mole ratio. Sulfuric acid needs 2 mol of NaOH per mol of acid. Always write the balanced equation first.
• Averaging every titre. Leave out the rough run and any result that is not concordant.
• Expecting pH 7 at equivalence. Only a strong acid with a strong base gives 7. A weak acid with a strong base gives a pH above 7.
• Mixing up end point and equivalence. The end point is where the indicator changes colour. A good indicator puts it within a drop or two of equivalence.

Practise titrations in a short timed paper

Titration calculations come up in High School Chemistry practice, and titration curves in AP Chemistry. In the UK they appear in GCSE Chemistry Higher and A-level Chemistry: Year 2. Each daily paper is a short timed paper of 8 questions worth 25 to 35 marks, and the papers mix topics. For the reaction itself, see our neutralisation guide.

Read next

Chemistry · Acids and basesTitration practical: method, results and calculationsThe titration required practical: equipment, method, results table, concordant titres, working out the acid's concentration, errors and exam tips.