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GCSE Chemistry · GCSEChapter 9 · Concentration of solutions
GCSE · Chapter 9

Concentration of solutions

By the end of this chapter you will be able to

  • Convert cm3 to dm3 by dividing by 1000
  • Calculate the concentration of a solution in g/dm3
  • Calculate the mass of solute in a given volume of a solution
  • [H] Calculate concentration in mol/dm3, and moles from concentration and volume
  • Predict the mass of product from a reaction in solution, and explain what dilution does

You should already know

  • Moles, Mr and mass (Chapter 8)
  • Balanced equations and mass ratios (Chapter 7)

Where this leads

  • Acids, alkalis and titration (Chapter 10)
  • Electrolysis of solutions (Chapter 11)

GCSE Chemistry. Content follows the GCSE (9-1) subject content for England (Edexcel and AQA). Content references: Convert volumes from cm3 to dm3 and calculate concentration in g/dm3, Calculate the mass of solute from a concentration and a volume, [H] Calculate concentration in mol/dm3 and the number of moles of solute, Use concentration to predict the mass of product in a reaction in solution, Explain dilution of a solution, and how it changes the concentration.

Exercise P  Do you remember?

1
FHow many millilitres are in one litre? Write the number.
2
FWhat is 10 / 250? Write the number as a decimal.
3
FWhat is 40 x 10 / 100? Write the number.
4
FWhat is the Mr of NaOH, with Ar Na = 23, O = 16, H = 1? Write the number.
5
FWhat is 5 x 0.5? Write the number.
9.1

Concentration in g/dm3

GCSE
Convert volumes from cm3 to dm3 and calculate concentration in g/dm3
Video lesson: Concentration in g/dm3Coming soon
Context. A pupil dissolves salt in water to make a solution for a lab. “How strong is the solution?” asks the teacher. The strength of a solution is its concentration: the mass of solute in each cubic decimetre, or litre, of solution.

The concentration of a solution is the mass of solute dissolved in each unit volume of solvent (or solution). In GCSE chemistry it is often given in g/dm3. 1 dm3 = 1000 cm3, so to convert from cm3 to dm3, divide by 1000.

25015050measuring cylinder250 cm<sup>3</sup>= 250 / 1000 dm<sup>3</sup>= 0.25 dm<sup>3</sup>divide by 1000 to convert
Converting a volume from cm3 to dm3
VolumeIn dm3
50 cm30.05
250 cm30.25
500 cm30.5
1000 cm31
Some volumes converted to dm3

Key ideas

  • Concentration (g/dm3) = mass of solute (g) / volume of solution (dm3).
  • To convert cm3 to dm3, divide by 1000.
  • A bigger mass in the same volume gives a higher concentration.
  • Always convert the volume to dm3 before you divide.
Worked example 9.1.1
10 g of solute is dissolved to make 250 cm3 of solution. What is the concentration in g/dm3? Write the number.

Method. Convert the volume to dm3, then divide.

  1. Convert. 250 cm3 = 250 / 1000 = 0.25 dm3.
    0.25 dm3
  2. Divide. concentration = 10 / 0.25 = 40.
    40
  3. Write the answer.
    40

Check. 0.25 x 40 = 10 g. ✓

Worked example 9.1.2
5 g of solute is dissolved in 500 cm3 of solution. What is the concentration in g/dm3? Write the number.

Method. Convert the volume, then divide the mass by it.

  1. Convert. 500 cm3 = 0.5 dm3.
    0.5 dm3
  2. Divide. concentration = 5 / 0.5 = 10.
    10
  3. Write the answer.
    10

Check. Twice the volume gives half the concentration of 20 g/dm3. ✓

Worked example 9.1.3
3 g of solute is in 50 cm3 of solution. What is the concentration in g/dm3? Write the number.

Method. Convert 50 cm3 first.

  1. Convert. 50 cm3 = 0.05 dm3.
    0.05 dm3
  2. Divide. concentration = 3 / 0.05 = 60.
    60
  3. Write the answer.
    60

Check. 0.05 x 60 = 3 g. ✓

Watch out

Watch out: the volume must be in dm3 for g/dm3. Dividing by 50 cm3 directly gives the wrong answer by a factor of 1000.

Exam tip

Exam tip. Write “convert the volume” as your first line. Then the division is simple.

Exercise 9A  Concentration in g/dm3

1
FHow many cm3 are in 1 dm3? Write the number.
2
FConvert 250 cm3 into dm3. Write the number.
3
FConvert 500 cm3 into dm3. Write the number.
4
FConvert 50 cm3 into dm3. Write the number.
5
FConvert 2.5 dm3 into cm3. Write the number.
6
FA solution has 20 g of solute in 1 dm3. What is its concentration in g/dm3? Write the number.
7
F8 g of solute is dissolved in 1 dm3 of solution. What is the concentration? Write the number in g/dm3.
8
F10 g of solute is dissolved in 250 cm3. What is the concentration in g/dm3? Write the number.
9
PSA solution of concentration 15 g/dm3 has volume 2 dm3. What mass of solute is in it? Write the number in g.
10
PSA pupil dissolves 6 g of solute to make 300 cm3 of solution. Find the concentration in g/dm3. Write the number.
11
PSTwo solutions contain 10 g of solute: one in 250 cm3, the other in 500 cm3. Which is more concentrated? Write 250 or 500.
12
RExplain why a concentration in g/dm3 must use the volume in dm3, in one sentence. Accept any sentence that says the unit of concentration uses dm3, so the volume must be in dm3 to match.
13
RA pupil says “25 g in 250 cm3 is 25 g/dm3.” Explain why this is wrong, in one sentence. Accept any sentence that says 250 cm3 is 0.25 dm3, so the concentration is 100 g/dm3.
9.2

Mass of solute from concentration and volume

GCSE
Calculate the mass of solute from a concentration and a volume
Video lesson: Mass of solute from concentration and volumeComing soon
Context. A technician needs 0.4 dm3 of a sodium hydroxide solution at 25 g/dm3. “How much solid do I weigh out?” she asks. Multiply the concentration by the volume to find the mass of solute needed.

If the concentration and the volume are known, the mass of solute is:

mass (g) = concentration (g/dm3) x volume (dm3)

The volume must be in dm3. If it is in cm3, convert it first.

10 g of solutein 0.25 dm3concentration40 g/dm3
A solution made by dissolving 10 g of solute in 0.25 dm3 of water
QuantityUnitFormula
concentrationg/dm3mass (g) / volume (dm3)
concentration [H]mol/dm3moles / volume (dm3)
mass of solutegconcentration x volume (dm3)
moles of solute [H]molconcentration (mol/dm3) x volume (dm3)
Concentration, volume and mass

Key ideas

  • Mass of solute = concentration x volume (in dm3).
  • Volume of solution = mass of solute / concentration.
  • Convert cm3 to dm3 first.
  • The answer has the unit of the solute: grams.
Worked example 9.2.1
A solution has a concentration of 25 g/dm3. What mass of solute is in 0.4 dm3? Write the number in g.

Method. Multiply the concentration by the volume.

  1. Multiply. mass = 25 x 0.4.
    25 x 0.4
  2. Answer. mass = 10 g.
    10
  3. Write the answer.
    10

Check. 10 / 0.4 = 25 g/dm3. ✓

Worked example 9.2.2
What mass of solute is in 50 cm3 of a solution of concentration 60 g/dm3? Write the number in g.

Method. Convert 50 cm3 to dm3 first.

  1. Convert. 50 cm3 = 0.05 dm3.
    0.05
  2. Multiply. mass = 60 x 0.05 = 3.
    3
  3. Write the answer.
    3

Check. 3 / 0.05 = 60 g/dm3. ✓

Worked example 9.2.3
What volume of a solution of concentration 20 g/dm3 contains 5 g of solute? Give the answer in cm3. Write the number.

Method. Divide the mass by the concentration, then convert to cm3.

  1. Divide. volume = 5 / 20 = 0.25 dm3.
    0.25 dm3
  2. Convert. 0.25 x 1000 = 250 cm3.
    250
  3. Write the answer.
    250

Check. 250 / 1000 = 0.25 dm3. ✓

Watch out

Watch out: multiply by the volume in dm3. Using cm3 directly multiplies the answer by 1000 too much.

Exam tip

Exam tip. Write the concentration, the volume in dm3, and the calculation on separate lines.

Exercise 9B  Mass of solute from concentration and volume

1
FWhat is the mass of solute in 1 dm3 of a solution with concentration 30 g/dm3? Write the number in g.
2
FWhat is the mass of solute in 2 dm3 of a solution with concentration 15 g/dm3? Write the number in g.
3
FWhat is the mass of solute in 0.5 dm3 of a solution with concentration 40 g/dm3? Write the number in g.
4
FWhat is the mass of solute in 0.4 dm3 of a solution with concentration 25 g/dm3? Write the number in g.
5
FWhat is the mass of solute in 250 cm3 of a solution with concentration 80 g/dm3? Write the number in g.
6
FWhat is the mass of solute in 100 cm3 of a solution with concentration 50 g/dm3? Write the number in g.
7
PSWhat volume, in dm3, of a solution with concentration 20 g/dm3 contains 5 g of solute? Write the number.
8
PSA solution of concentration 12 g/dm3 is needed to contain 6 g of solute. What volume, in cm3, is needed? Write the number.
9
PSSodium chloride solution has a concentration of 58.5 g/dm3. What mass of salt is in 0.2 dm3? Write the number in g.
10
PSA student makes 500 cm3 of a solution from 15 g of solute. What is the concentration in g/dm3? Write the number.
11
RExplain why a concentrated solution contains more solute per dm3 than a dilute one, in one sentence. Accept any sentence that says it has a larger mass of solute in the same volume.
9.3

Concentration in mol/dm3 [H]

GCSE
[H] Calculate concentration in mol/dm3 and the number of moles of solute
Video lesson: Concentration in mol/dm3 [H]Coming soon
Context. A chemist needs to know how many moles of a substance are in a flask of solution, so that she can predict how much product will form. The concentration in mol/dm3 gives the answer when the volume is known.

[H] Higher tier only. The concentration in mol/dm3 is the number of moles of solute in each dm3 of solution: concentration (mol/dm3) = moles / volume (dm3). So moles = concentration x volume (dm3). To change g/dm3 into mol/dm3, divide by the Mr.

Key ideas

  • mol/dm3 = moles / volume (dm3).
  • moles = mol/dm3 x volume (dm3).
  • Concentration in g/dm3 / Mr = concentration in mol/dm3.
  • Convert cm3 to dm3 first.
Worked example 9.3.1
[H] 0.5 mol of solute is dissolved in 2 dm3 of solution. What is the concentration? Write the number in mol/dm3.

Method. Divide the moles by the volume.

  1. Divide. concentration = 0.5 / 2.
    0.5 / 2
  2. Answer. concentration = 0.25 mol/dm3.
    0.25
  3. Write the answer.
    0.25

Check. 0.25 x 2 = 0.5 mol. ✓

Worked example 9.3.2
[H] How many moles of solute are in 0.25 dm3 of a solution of concentration 0.1 mol/dm3? Write the number.

Method. Multiply the concentration by the volume.

  1. Multiply. moles = 0.1 x 0.25.
    0.1 x 0.25
  2. Answer. moles = 0.025.
    0.025
  3. Write the answer.
    0.025

Check. 0.025 / 0.25 = 0.1 mol/dm3. ✓

Worked example 9.3.3
[H] A solution of NaOH has concentration 40 g/dm3. Find its concentration in mol/dm3. (Mr of NaOH is 40.) Write the number.

Method. Divide the g/dm3 value by the Mr.

  1. Divide. 40 / 40 = 1.
    1
  2. Units. The concentration is 1 mol/dm3.
    1 mol/dm3
  3. Write the answer.
    1

Check. One mole of NaOH is 40 g. ✓

Watch out

Watch out: mol/dm3 and g/dm3 are different units. Convert between them by dividing or multiplying by the Mr, not by 1000.

Exam tip

Exam tip. Write down the units on every line. If the answer has mol, it must be moles; if g, it must be a mass.

Exercise 9C  Concentration in mol/dm3 [H]

1
F[H] What is the concentration, in mol/dm3, of 1 mol of solute in 1 dm3? Write the number.
2
F[H] What is the concentration of 2 mol of solute in 4 dm3? Write the number in mol/dm3.
3
F[H] How many moles are in 2 dm3 of a 0.5 mol/dm3 solution? Write the number.
4
F[H] How many moles are in 0.25 dm3 of a 0.1 mol/dm3 solution? Write the number.
5
PS[H] Convert 50 cm3 to dm3, then find the moles in it at 0.2 mol/dm3. Write the number.
6
PS[H] A solution contains 0.01 mol of solute in 50 cm3. What is its concentration in mol/dm3? Write the number.
7
PS[H] What is the concentration in mol/dm3 of a solution of 4.0 g of NaOH (Mr 40) in 0.25 dm3? Write the number.
8
PS[H] Convert 60 g/dm3 of a solution of NaOH (Mr 40) into mol/dm3. Write the number.
9
PS[H] A solution of 0.2 mol/dm3 has 0.05 dm3 taken from it. How many moles are taken? Write the number.
10
R[H] Explain why mol/dm3 is useful for reactions, in one sentence. Accept any sentence that says it gives the number of moles, which relates to the balanced equation.
9.4

Predicting the mass of product in a reaction in solution

GCSE
Use concentration to predict the mass of product in a reaction in solution
Video lesson: Predicting the mass of product in a reaction in solutionComing soon
Context. A pupil adds magnesium to 50 cm3 of copper sulfate solution, and the copper formed is collected and weighed. “What mass of copper should I expect?” she asks. The concentration of the solution and the balanced equation give the answer.

To predict the mass of product from a reaction in solution: (1) find the moles of solute from its concentration and volume; (2) use the ratio from the balanced equation to find the moles of product; (3) change moles to mass (x Mr). The example below uses a solution of copper sulfate with excess magnesium: Mg + CuSO4 -> MgSO4 + Cu.

Key ideas

  • The method: concentration and volume give the moles of solute; the balanced equation gives the moles of product; mass = moles x Mr.
  • In a reaction with excess of one reactant, all of the other is used up.
  • Use cm3 converted to dm3 for the volume.
  • Check that the answer is sensible: a bigger volume or concentration gives more product.
Worked example 9.4.1
50 cm3 of 0.5 mol/dm3 copper sulfate reacts with excess magnesium. What mass of copper is made? Write the number in g.

Method. Find the moles of CuSO4, then the mass of Cu.

  1. Moles. moles = 0.5 x 0.05 = 0.025 mol.
    0.025
  2. Ratio. CuSO4 : Cu = 1 : 1, so 0.025 mol Cu.
    0.025 mol
  3. Mass. mass = 0.025 x 64 = 1.6 g.
    1.6
  4. Write the answer.
    1.6

Check. Magnesium is in excess, so all the copper sulfate reacts. ✓

Worked example 9.4.2
In the same reaction, what mass of magnesium sulfate, MgSO4, is made? (Mr 120.) Write the number in g.

Method. Use the same moles of product as the moles of copper sulfate.

  1. Moles. The equation gives 1 mol MgSO4 for 1 mol CuSO4: 0.025 mol.
    0.025
  2. Mass. mass = 0.025 x 120 = 3.0 g.
    3.0
  3. Write the answer.
    3

Check. Mass conservation is not needed here: 3.0 g MgSO4 forms. ✓

Worked example 9.4.3
A solution of NaOH at 20 g/dm3 has volume 0.5 dm3. What mass of solute is in it? Write the number in g.

Method. Multiply the concentration by the volume.

  1. Multiply. mass = 20 x 0.5.
    20 x 0.5
  2. Answer. mass = 10 g.
    10
  3. Write the answer.
    10

Check. Check: 10 / 0.5 = 20 g/dm3. ✓

Watch out

Watch out: check which reactant is in excess. If magnesium is in excess, use the copper sulfate to find the product, not the magnesium.

Exam tip

Exam tip. Write each step on its own line: moles of solute, moles of product, mass of product.

Exercise 9D  Reactions in solution

1
FWhat is the moles of solute in 1 dm3 of 0.5 mol/dm3 copper sulfate? Write the number.
2
FWhat is the mass of Cu made from 0.025 mol of CuSO4 (1:1 ratio)? Write the number in g.
3
FWhat mass of MgSO4 is made from 0.025 mol of MgSO4? (Mr 120.) Write the number in g.
4
FIn Mg + CuSO4 -> MgSO4 + Cu, what is the ratio of moles of CuSO4 to Cu? Write the ratio.
5
PSWhat is the moles of CuSO4 in 50 cm3 of 0.5 mol/dm3 solution? Write the number.
6
PSWhat mass of Cu is made when 50 cm3 of 0.5 mol/dm3 copper sulfate reacts completely with excess magnesium? Write the number in g.
7
PSA solution of concentration 40 g/dm3 has volume 250 cm3. What mass of solute is in it? Write the number in g.
8
PSIn a reaction in solution, 0.025 mol of product is expected from 50 cm3 of solution. What is the concentration of the solution in mol/dm3? Write the number.
9
RExplain why magnesium is added in excess in the copper sulfate reaction, in one sentence. Accept any sentence that says it makes sure all the copper sulfate reacts.
10
RExplain why doubling the volume of the copper sulfate solution doubles the mass of copper made, in one sentence. Accept any sentence that says the moles of copper sulfate are doubled, so the product is doubled.
9.5

Dilution

GCSE
Explain dilution of a solution, and how it changes the concentration
Video lesson: DilutionComing soon
Context. A lab has a strong solution and needs a weaker one. “Add water,” says the technician. “Does the amount of solute change?” asks a pupil. The solute does not change, but the solvent is spread through a bigger volume, so the concentration falls.

Dilution means adding solvent (usually water) to a solution. The mass or moles of solute stay the same, but the volume increases, so the concentration decreases. If the volume is doubled, the concentration is halved.

Key ideas

  • Dilution adds solvent; the moles or mass of solute stay the same.
  • The concentration decreases when the volume increases.
  • Doubling the volume halves the concentration.
  • A solution with the same solute in less volume is more concentrated.
Worked example 9.5.1
50 cm3 of a solution of concentration 2 g/dm3 is diluted to 100 cm3. What is the new concentration in g/dm3? Write the number.

Method. The mass of solute stays the same; find it first.

  1. Mass. mass = 2 x 0.05 = 0.1 g.
    0.1 g
  2. New concentration. concentration = 0.1 / 0.1 = 1 g/dm3.
    1
  3. Write the answer.
    1

Check. The volume doubled, so the concentration halved from 2 to 1. ✓

Worked example 9.5.2
[H] A 0.2 mol/dm3 solution is diluted so that the volume doubles. What is the new concentration in mol/dm3? Write the number.

Method. Moles stay the same; divide by the new volume.

  1. Moles. The moles are unchanged.
    the same
  2. Concentration. The concentration halves: 0.2 / 2 = 0.1 mol/dm3.
    0.1
  3. Write the answer.
    0.1

Check. Doubling the volume halves the concentration. ✓

Worked example 9.5.3
A solution of 40 g/dm3 is diluted to 4 times its volume. What is the new concentration in g/dm3? Write the number.

Method. The solute mass is the same; divide by 4.

  1. Factor. The volume is multiplied by 4.
    4
  2. Concentration. 40 / 4 = 10 g/dm3.
    10
  3. Write the answer.
    10

Check. The mass of solute stays at 40 g per dm3 of the original volume. ✓

Watch out

Watch out: dilution lowers the concentration, but it does not change the mass or the moles of solute. Do not divide the mass of solute when you dilute.

Exam tip

Exam tip. Ask: has the amount of solute changed? If not, the new concentration is the old amount divided by the new volume.

Exercise 9E  Dilution

1
FWhen a solution is diluted, does the mass of solute change? Write yes or no.
2
FWhen a solution is diluted, does the concentration increase or decrease? Write the word.
3
FA 20 g/dm3 solution has its volume doubled by adding water. What is the new concentration? Write the number in g/dm3.
4
FA 30 g/dm3 solution is diluted to three times its volume. What is the new concentration? Write the number in g/dm3.
5
PSA solution of concentration 2 g/dm3, volume 50 cm3, is diluted to 100 cm3. What mass of solute is there after dilution? Write the number in g.
6
PSA 4 g/dm3 solution has its volume increased from 0.5 dm3 to 2 dm3. What is the new concentration? Write the number in g/dm3.
7
PS[H] A 0.5 mol/dm3 solution is diluted so that the volume is 5 times larger. What is the new concentration in mol/dm3? Write the number.
8
PS[H] How many moles of solute are in 0.25 dm3 of a 0.1 mol/dm3 solution after it is diluted with water? Write the number.
9
RExplain why adding water to a salt solution makes it less concentrated, in one sentence. Accept any sentence that says the same mass of salt is spread through more solution.
10
RA pupil says, “When I dilute a solution, the mass of solute goes down.” Explain why this is wrong, in one sentence. Accept any sentence that says only the volume increases; the solute is still there.

Chapter summary

SkillMethod
Volume1 dm3 = 1000 cm3; divide cm3 by 1000 to get dm3.
Concentration (g/dm3)mass of solute / volume in dm3.
Mass of soluteconcentration x volume (dm3).
[H] Concentration (mol/dm3)moles / volume (dm3); g/dm3 divided by Mr gives mol/dm3.
Reactions in solutionConcentration x volume gives moles of solute; the ratio gives moles of product; x Mr gives mass.
DilutionAdding water: the mass or moles of solute stay the same; the concentration falls.

Can you…?

  • I can convert cm3 to dm3
  • I can calculate the concentration in g/dm3 and the mass of solute
  • I can use concentration to predict the mass of product in a reaction in solution
  • I can explain dilution and its effect on concentration
  • [H] I can calculate concentration in mol/dm3 and the moles of solute

Key terms

solute
the substance that dissolves in a solvent
solvent
the liquid that dissolves a solute, usually water
concentration
the amount of solute in a given volume of solution
dilution
adding solvent to a solution, which lowers its concentration
mol/dm3
[H] the number of moles of solute in one dm3 of solution

Exercise 9Z  Check-up

1
Convert 500 cm3 into dm3. Write the number.
2
What is the concentration in g/dm3 of 8 g of solute in 1 dm3? Write the number.
3
What is the mass of solute in 0.5 dm3 of a 40 g/dm3 solution? Write the number in g.
4
What is the concentration in g/dm3 of 10 g of solute in 250 cm3? Write the number.
5
What volume, in dm3, contains 5 g of solute at 20 g/dm3? Write the number.
6
[H] What is the concentration in mol/dm3 of 0.5 mol in 2 dm3? Write the number.
7
[H] How many moles are in 0.25 dm3 of a 0.1 mol/dm3 solution? Write the number.
8
A solution of 40 g/dm3 is diluted to double its volume. What is the new concentration in g/dm3? Write the number.
9
In 50 cm3 of 0.5 mol/dm3 copper sulfate reacting with excess magnesium, what mass of copper is made? Write the number in g.
10
Explain why the concentration falls when a solution is diluted, in one sentence. Accept any sentence that says the same mass of solute is spread through a bigger volume.

Total 24 marks. Allow about 24 minutes.

Exercise 9X  Exam-style questions

1
FConvert 250 cm3 into dm3, then find the concentration in g/dm3 when 10 g of solute is dissolved in it. Write the number.[2 marks]
2
FWhat mass of solute is in 0.4 dm3 of a 25 g/dm3 solution? Write the number in g.[2 marks]
3
PSA solution of concentration 15 g/dm3 is needed for an experiment. What volume, in cm3, contains 3 g of solute? Write the number.[3 marks]
4
PS[H] A solution has 0.1 mol of solute in 0.25 dm3. What is its concentration in mol/dm3? Write the number.[2 marks]
5
PSIn a reaction, 50 cm3 of 0.5 mol/dm3 copper sulfate reacts completely. What mass of copper is formed? Write the number in g.[3 marks]
6
PSA 20 g/dm3 solution is diluted so that its volume is 4 times larger. What is the new concentration in g/dm3? Write the number.[2 marks]
7
RExplain why diluting a solution does not change the mass of solute in it, in one sentence. Accept any sentence that says only water is added, so the solute is still present.[2 marks]
8
PS[H] Calculate the concentration in mol/dm3 of a solution of 4.0 g of NaOH (Mr 40) in 0.25 dm3. Write the number.[3 marks]
9
PSA pupil dissolves 6 g of solute in 300 cm3 of water. Find the concentration in g/dm3. Write the number.[2 marks]
10
RExplain how you would use concentration to predict the mass of product from a reaction in solution, in two sentences. Accept any answer that says find the moles of solute from concentration and volume, then use the balanced equation ratio to find the mass of product.[3 marks]
← Chapter 8: The mole, reacting masses and limiting reactantsChapter 10: Reactions of acids and making salts →

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