How to carry out an acid–alkali titration accurately, find a mean titre, and use it to calculate an unknown concentration.
Objectives
Describe how to carry out a titration using a pipette, burette and indicator.
Choose concordant results and calculate a mean titre.
Calculate the concentration of an unknown solution in mol/dm³ and g/dm³.
Use the ratio in the balanced equation, including for sulfuric acid.
Titrations and their calculations explained
Start here
A titration is a careful way to find out how concentrated a solution is. You add one solution to another, a drop at a time, until they have exactly reacted.
It matters because chemists in labs and factories use it to check the strength of acids, cleaning products and medicines. The method needs careful hands and careful maths.
By the end you will be able to describe how to carry out a titration and choose the right results. You will calculate a mean titre. Then you will use it to find an unknown concentration, including with sulfuric acid.
Course note: the titration method (pipette, burette, indicator, end-point) is part of making salts in Combined Science. Calculating an unknown concentration from a titre is Separate Chemistry. Learn the method first, then the calculations if you need them.
The titration method
A titration finds the volume of one solution that exactly reacts with a fixed volume of another. Use a pipette to put 25.0 cm³ of alkali into a conical flask. A pipette measures one fixed volume very accurately. Fill a burette with acid and note the start reading.
Add a few drops of indicator, a dye that changes colour. Phenolphthalein is pink in alkali and colourless in acid. Methyl orange is yellow in alkali and red in acid. Universal indicator is not used because its colour changes gradually.
Add the acid slowly, swirling the flask, until the colour just changes. This is the end-point. The volume of acid added is the titre.
Titration apparatus. A burette of acid is clamped above a conical flask that holds a measured volume of alkali and a few drops of indicator. The flask stands on a white tile.
Getting accurate results
Rinse the burette with the acid and the pipette with the alkali before you use them. Water left inside would dilute the solutions. Stand the flask on a white tile so the colour change is easy to see. Remove the funnel before you read the burette.
Do a rough titration first. Add the acid quickly to find the approximate end-point. In the later runs, add the acid drop by drop near the end-point, so you do not overshoot.
Read the burette at eye level, at the bottom of the meniscus. The meniscus is the curved surface of the liquid. It is like reading a measuring jug in the kitchen, where you crouch to look level with the line.
Concordant results and the mean titre
Repeat the titration until you have at least two concordant results. Concordant means within 0.10 cm³ of each other. Think of runners finishing a lap in almost the same time. A runner far slower than the rest is the odd one out, called an anomalous result.
The mean titre is the mean of the concordant results only. Ignore the rough titration and any anomalous results.
Results of 22.40, 22.30 and 22.35 cm³ are concordant. The mean titre is (22.40 + 22.30 + 22.35) ÷ 3 = 22.35 cm³.
Bars showing titres in cubic centimetres: rough 23.5, run 1 22.4, run 2 22.3 and run 3 22.35. The three runs are concordant.
The calculation: moles
The calculation has three parts. First find the moles of the solution you know. A mole is a fixed number of particles. It is the unit chemists use to count them.
Moles = concentration × volume in dm³. Always change cm³ to dm³ first by dividing by 1000. So 25.0 cm³ is 0.0250 dm³.
Take 25.0 cm³ of 0.100 mol/dm³ NaOH. Moles of NaOH = 0.100 × 0.0250 = 0.00250 mol. For HCl + NaOH → NaCl + H₂O, the ratio is 1 : 1. So this reacts with 0.00250 mol of HCl.
The calculation: concentration
Next, use the ratio in the equation to find the moles of the other solution. Then divide by its volume in dm³. Concentration = moles ÷ volume in dm³.
Say the HCl titre is 20.0 cm³, which is 0.0200 dm³. Its concentration is 0.00250 ÷ 0.0200 = 0.125 mol/dm³.
To give g/dm³, multiply by the Mr. The Mr is the relative formula mass. For HCl it is 36.5. So 0.125 × 36.5 = 4.56 g/dm³.
Ratios other than 1 : 1
Not every reaction is 1 : 1. Sulfuric acid reacts like this: H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O. One mole of sulfuric acid reacts with two moles of sodium hydroxide.
Think of a recipe. If each cake needs 2 eggs, then 3 cakes need 6 eggs. The balanced equation is the recipe.
Say 25.0 cm³ of 0.200 mol/dm³ NaOH needs 20.0 cm³ of sulfuric acid. Moles of NaOH = 0.200 × 0.0250 = 0.00500. Moles of H₂SO₄ = 0.00500 ÷ 2 = 0.00250. Concentration = 0.00250 ÷ 0.0200 = 0.125 mol/dm³.
Recap
Rinse the apparatus, use a white tile, do a rough run, and add acid drop by drop near the end-point.
Use only concordant results for the mean titre.
Write the equation. Moles = concentration × volume in dm³. Use the ratio. Divide by the volume in dm³.
Show every change from cm³ to dm³. Give the unit, and about three significant figures.
Key points
Pipette the alkali into a flask with indicator, add acid from a burette to the end-point and record the titre.
Concordant results are within 0.10 cm³. Use only those for the mean titre.
Moles = concentration × volume in dm³. Use the equation ratio, then concentration = moles ÷ volume.
Multiply mol/dm³ by Mr to give g/dm³.
Worked examples
Example 1
Titres are 21.20, 20.40, 20.50 and 20.45 cm³. The first is a rough titration. Calculate the mean titre using the concordant results.
Ignore the rough result of 21.20.
The concordant results are 20.40, 20.50 and 20.45.
Mean = (20.40 + 20.50 + 20.45) ÷ 3 = 20.45 cm³.
Answer: 20.45 cm³
Common slips
Slip: Mean = (21.20 + 20.40 + 20.50 + 20.45) ÷ 4. The rough titration is not included.
Slip: Mean = 20.40 + 20.50 + 20.45 = 61.35. Divide the total by the number of results.
Slip: Mean = 20.5. The mean of the three is 20.45, not 20.5.
Example 2
25.0 cm³ of sodium hydroxide solution is neutralised by 18.0 cm³ of 0.100 mol/dm³ hydrochloric acid. Calculate the concentration of the sodium hydroxide in mol/dm³. HCl + NaOH → NaCl + H₂O
Moles of HCl = 0.100 × 0.0180 = 0.00180 mol.
The ratio HCl : NaOH is 1 : 1, so moles of NaOH = 0.00180 mol.
Slip: Moles of HCl = 0.100 × 18.0 = 1.80. Change cm³ to dm³ before multiplying: 18.0 cm³ = 0.0180 dm³.
Slip: Moles of NaOH = 0.00180 × 2. The equation has a 1 : 1 ratio.
Slip: Concentration = 0.00180 × 0.0250. Divide the moles by the volume to find a concentration.
Example 3
25.0 cm³ of 0.150 mol/dm³ sodium hydroxide is neutralised by 15.0 cm³ of sulfuric acid. H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O. Calculate the concentration of the acid in g/dm³. Mr of H₂SO₄ = 98.
Moles of NaOH = 0.150 × 0.0250 = 0.003750 mol. Moles of H₂SO₄ = 0.003750 ÷ 2 = 0.001875 mol.
Slip: Concentration = 0.125 ÷ 98. To change mol/dm³ into g/dm³ multiply by Mr.
Questions and answers
Titrations and their calculations practice questions for GCSE Combined Science Chemistry. Try each one, then open the answer. Easy questions come first.
Question 1 Easy
Which apparatus is used to add acid slowly in a titration?
Show answer
Answer: a burette
It has a tap.
It is a burette.
Question 2 Easy
Calculate the mean of the concordant titres 18.20, 18.30 and 18.25 cm³.
Show answer
Answer: 18.25 cm³
(18.20 + 18.30 + 18.25) ÷ 3.
54.75 ÷ 3 = 18.25.
Question 3 Easy
What is the name for the volume of acid added from the burette?
Show answer
Answer: the titre
It is read from the burette.
It is called the titre.
Question 4 Easy
What word describes titration results within 0.10 cm³ of each other?
Show answer
Answer: concordant
They agree closely.
They are concordant.
Question 5 Easy
What name is given to the dye added to show when a titration has reached the end-point?
Show answer
Answer: an indicator
The dye changes colour at the end-point.
It is called an indicator.
Question 6 Easy
Convert a volume of 25.0 cm³ into dm³.
Show answer
Answer: 0.0250 dm³
Divide by 1000.
25.0 ÷ 1000 = 0.0250 dm³.
Question 7 Medium
Calculate the moles of acid in 20.0 cm³ of 0.100 mol/dm³ hydrochloric acid.
Show answer
Answer: 0.00200 mol
20.0 cm³ = 0.0200 dm³.
Moles = 0.100 × 0.0200 = 0.00200.
Question 8 Medium
25.0 cm³ of NaOH is neutralised by 20.0 cm³ of 0.100 mol/dm³ HCl. Calculate the concentration of NaOH in mol/dm³. HCl + NaOH → NaCl + H₂O
Show answer
Answer: 0.0800 mol/dm³
Moles of HCl = 0.00200, so NaOH = 0.00200.
Concentration = 0.00200 ÷ 0.0250 = 0.0800.
Exam-style questions
Longer questions in the style of a written paper, with the marking points. These are Yumio practice questions.
Exam-style question 14 marks
A student titrates 25.0 cm³ of sodium hydroxide solution against 0.100 mol/dm³ hydrochloric acid. The mean titre is 22.5 cm³.
(a) Calculate the moles of hydrochloric acid used. [2 marks]
(b) Calculate the concentration of the sodium hydroxide in mol/dm³. HCl + NaOH → NaCl + H₂O [2 marks]
Show answer and marking points
Answer: (a) 0.00225 mol (b) 0.0900 mol/dm³
(a) 0.100 × 0.0225 (1)
(a) 0.00225 mol (1)
(b) 0.00225 ÷ 0.0250 (1)
(b) 0.0900 mol/dm³ (1)
Exam-style question 26 marks
Describe how to carry out a titration to find the concentration of a sodium hydroxide solution using hydrochloric acid of known concentration, and how to process the results. [6 marks]
Show answer and marking points
Answer: Use a pipette and filler to put 25.0 cm³ of sodium hydroxide in a conical flask and add a few drops of indicator such as methyl orange. Fill a burette with the acid and note the start reading. Add the acid slowly, swirling, until the indicator just changes colour, and record the titre. Do a rough titration first, then repeat with the acid added drop by drop near the end-point until two or more results are concordant, within 0.10 cm³. Calculate the mean of the concordant titres, work out the moles of acid using concentration × volume in dm³, use the 1 : 1 ratio to find the moles of alkali, and divide by 0.0250 dm³ to find the concentration.
pipette used for the alkali, with indicator (1)
burette used for the acid, added until the colour change (1)
swirl and add drop by drop near the end-point (1)
repeat until concordant results within 0.10 cm³ (1)
mean of the concordant titres (1)
moles of acid, the ratio, and concentration = moles ÷ volume (1)
Common mistakes
Including the rough titration in the mean
Use only the concordant results, within 0.10 cm³.
Not converting cm³ to dm³
Divide the volume in cm³ by 1000 before calculating moles or concentration.
Ignoring the ratio in the equation
Check whether it is 1 : 1 or 1 : 2 and use it.
Forgetting to add drops of indicator or to rinse the apparatus
Add a few drops. Rinse the burette with the acid and the pipette with the alkali before you use them.
Using the same number of moles for both solutions when the equation is not 1 : 1
Check the ratio. For H₂SO₄ with NaOH the acid moles are half the alkali moles.
Questions students ask
Is Titrations and their calculations on the Foundation or Higher tier?
Titrations and their calculations is Higher tier content for GCSE Combined Science Chemistry, aimed at around grade 8.
What is a common mistake on Titrations and their calculations?
Including the rough titration in the mean. Use only the concordant results, within 0.10 cm³.
Where are the answers to the Titrations and their calculations questions?
Open Show answer under each question on this page. The questions are Yumio practice questions, not past exam questions.