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KS3 Science · Year 7Chapter 5 · Diffusion and density
Year 7 · Chapter 5

Diffusion and density

By the end of this chapter you will be able to

  • Describe diffusion using the random movement of particles and concentration
  • Name the factors that change the rate of diffusion, including temperature and state
  • Use density = mass / volume, with units of g/cm cubed
  • Measure the volume of a regular and an irregular solid
  • Predict whether an object floats or sinks by comparing its density with that of the liquid

You should already know

  • Particles and the particle model (Chapter 4 of this book)
  • Reading a measuring cylinder and using a table (Chapter 1 of this book)

Where this leads

  • Atoms and elements, which use the particle idea further (Chapter 6)

National Curriculum for England, Key Stage 3 science, Year 7. Content: C2 diffusion is the random movement of particles, from a higher to a lower concentration, in gases and liquids, C3 density = mass / volume; measuring the density of regular and irregular solids and liquids; density and floating.

Exercise P  Do you remember?

1
FIn the particle model, what do we call the particles in a gas? Write the word for how they are spaced: close or far apart.
2
FWhat is the name of the change when a liquid turns into a gas? Write the word.
3
FWhat is the volume of a cube that is 2 cm long, 2 cm wide and 2 cm high? Write the number of cubic centimetres.
4
FWhat is 60 divided by 10? Write the number.
5
FWhat is the unit of mass commonly used in the lab? Write the unit.
5.1

Diffusion and the particle model

Year 7
C2: diffusion is the random movement of particles, from a higher to a lower concentration, in gases and liquids
Video lesson: Diffusion and the particle modelComing soon
Story. Ben sprays perfume at one end of a classroom. A minute later, a pupil at the other end smells it. “How did the perfume get all the way over here?” asks Ben. His teacher says, “The particles of perfume are moving at random, and they spread out until they are everywhere.”

The particles in a gas or a liquid are always moving at random. Diffusion is the spreading of particles from a region of higher concentration to a region of lower concentration, as a result of this random movement. The concentration is the number of particles in a given space.

Diffusion happens in gases and in liquids, but not in solids, because the particles of a solid are held in fixed positions.

higher concentrationlower concentration
Particles spread from a region of higher concentration (left) to a region of lower concentration (right).

Key ideas

  • Diffusion is the random movement of particles from higher to lower concentration.
  • It happens in gases and liquids, not in solids.
  • Particles move at random, so the net movement is from high to low concentration.
  • Diffusion continues until the particles are evenly spread.
Worked example 5.1.1
In which direction do particles diffuse: from the higher concentration to the lower concentration, or the other way? Write the words.

Method. Read the definition.

  1. Read the definition. Diffusion is the movement from a higher concentration to a lower concentration.
    higher to lower
  2. Apply it. So the particles move from the higher concentration to the lower one.
    higher to lower
  3. Write the answer.
    from higher to lower concentration

Check. The net movement is in this direction. ✓

Worked example 5.1.2
Can particles diffuse in a solid? Write yes or no.

Method. Think about the particles of a solid.

  1. Think about the particles. The particles of a solid are held in fixed positions, so they cannot spread through it.
    fixed positions
  2. Decide. So diffusion does not happen in a solid, and the answer is no.
    no
  3. Write the answer.
    no

Check. Diffusion needs particles that can move past each other. ✓

Worked example 5.1.3
Perfume spreads across a room. Is this an example of diffusion? Write yes or no.

Method. Check the movement.

  1. Check the movement. The perfume particles are in the air, and they spread out from high to low concentration.
    spread out
  2. Decide. So this is diffusion, and the answer is yes.
    yes
  3. Write the answer.
    yes

Check. Gases diffuse in the air. ✓

Watch out

Watch out: diffusion is not caused by particles pushing each other. It is caused by the random movement of each particle, which means particles end up spreading out.

Exam tip

Exam tip. When you explain diffusion, use the words random movement, higher concentration and lower concentration.

Try it (with your teacher, or a grown-up at home). With a grown-up, place a drop of food colouring in a jar of still water, and do not stir it. Look at the jar every few minutes. Describe how the colour spreads, and say which way the particles of colour move.

Exercise 5A  Diffusion and the particle model

1
FWhat is the name of the spreading of particles from higher to lower concentration? Write the word.
2
FDo particles diffuse from a lower concentration to a higher concentration? Write yes or no.
3
FIn which two states does diffusion happen? Write the two words.
4
FDoes diffusion happen in a solid? Write yes or no.
5
FWhat is the name for the number of particles in a given space? Write the word.
6
FRuby sprays perfume at one end of a room. Which end has the higher concentration of perfume particles, at the start? Write the words.
7
FIs diffusion a random process, or does it happen in one direction only? Write one word: random or one-way.
8
PSDoes the net diffusion of food colouring stop when the colour is spread evenly? Write yes or no.
9
PSA pupil says that perfume particles are pushed by the air to the other end of the room. Is the pupil right? Write yes or no.
10
PSWorking scientifically: a pupil wants to show diffusion in a jar of water. Name one thing to keep the same in a fair test. Accept any one: the same jar, the same amount of water, the same drop size.
11
RExplain why diffusion happens in a liquid even though the particles are close together. Write one sentence.
12
RChallenge: explain why diffusion stops being observable once the particles are evenly spread, even though the particles keep moving. Write one sentence.
5.2

Factors that affect diffusion

Year 7
C2: the rate of diffusion depends on the temperature and on whether the substance is a gas or a liquid
Video lesson: Factors that affect diffusionComing soon
Story. Ruby and Ali put one drop of food colouring into a glass of cold water and another into a glass of warm water. “The warm one turns colour much faster,” says Ali. His teacher says, “Faster particles diffuse faster. Let us find out how much faster, with the times we recorded.”

The rate of diffusion depends on how fast the particles are moving. Particles that have more energy move faster, so they spread more quickly. Diffusion is faster in warm substances than in cold ones.

Diffusion is much faster in a gas than in a liquid, because gas particles move more quickly and are further apart, so they travel further between collisions.

The class recorded how long one drop of food colouring took to spread evenly through the same volume of water at three temperatures.

Water temperatureTime to spread evenly (minutes)
cold water30
room temperature water15
warm water5

Key ideas

  • Diffusion is faster at a higher temperature, because particles move faster.
  • Diffusion is much faster in a gas than in a liquid.
  • In a fair test, keep the drop size and the volume of water the same.
  • Use the times in a table to compare the rates.
Worked example 5.2.1
Which water temperature gave the fastest diffusion of the food colouring? Write the words.

Method. Find the shortest time.

  1. Read the table. The shortest time is 5 minutes, for the warm water.
    5 minutes
  2. Decide. So warm water gave the fastest diffusion.
    warm water
  3. Write the answer.
    warm water

Check. The warm water spread the colour in 5 minutes. ✓

Worked example 5.2.2
How many times longer did the cold water take than the warm water? Write the number.

Method. Divide the cold time by the warm time.

  1. Read the times. The cold water took 30 minutes and the warm water took 5 minutes.
    30 and 5
  2. Divide. Divide 30 by 5 to find how many times longer.
    30 / 5 = 6
  3. Write the answer.
    6

Check. 5 x 6 = 30. ✓

Worked example 5.2.3
Is diffusion faster in a gas or in a liquid? Write the word.

Method. Use the fact about gas particles.

  1. Read the fact. Gas particles move more quickly and are further apart than liquid particles.
    more quickly
  2. Decide. So diffusion is faster in a gas.
    gas
  3. Write the answer.
    gas

Check. Perfume spreads in air much faster than it spreads through water. ✓

Watch out

Watch out: a faster rate does not mean the particles diffuse to a different place; it means they reach an even spread in less time.

Exam tip

Exam tip. When you compare rates, use the temperature as the reason: higher temperature, particles faster, diffusion faster.

Try it (with your teacher, or a grown-up at home). With a grown-up, put one drop of food colouring into a glass of cold tap water, and a second drop into a glass of warm tap water (not hot). Time how long each glass takes to become an even colour. Use the same drop size and the same volume of water.

Exercise 5B  Factors that affect diffusion

1
FHow long, in minutes, did the cold water take to spread the colour evenly? Write the number of minutes.
2
FWhich water temperature was the slowest for diffusion? Write the words.
3
FDoes diffusion get faster as the temperature goes up? Write yes or no.
4
FHow many minutes faster was the room-temperature water than the cold water? Write the number of minutes.
5
FWhich is faster: diffusion in a gas, or diffusion in a liquid? Write the word.
6
FWhat is the time for the warm water, in minutes? Write the number of minutes.
7
PSHow many times longer than the warm water did the room-temperature water take? Write the number.
8
PSA pupil says diffusion in cold water is faster because the particles are closer together. Is the pupil right? Write yes or no.
9
PSAli says that a drop of food colouring in warm water spreads evenly in less time than in cold water, because the warm particles move faster. Is Ali right? Write yes or no.
10
PSWorking scientifically: a pupil says the times in the table are not reliable because the drops were different sizes. Is this a reasonable criticism? Write yes or no.
11
RExplain why diffusion is faster at a higher temperature. Write one sentence.
12
RChallenge: explain why the same food colouring diffuses faster in a gas than in a liquid, at the same temperature. Write one sentence.
5.3

Density: mass, volume and density

Year 7
C3: density = mass / volume; use the units g/cm cubed and calculate density from mass and volume
Video lesson: Density: mass, volume and densityComing soon
Story. Ali picks up two small blocks of the same size. One feels much heavier than the other. “They look the same size, so why is one heavier?” he asks. His teacher says, “Compare the mass of each block with its volume. That comparison is the density.”

Density is the mass of a substance in a given volume. It is found using:

density = mass / volume

Mass is measured in grams (g) and volume in cubic centimetres (cm³), so density is measured in grams per cubic centimetre (g/cm³). Pure water has a density of 1 g/cm³.

The table gives the mass and volume of four samples, with their densities.

SampleMass (g)Volume (cm³)Density (g/cm³)
wooden block40500.8
stone90303.0
metal cube80108.0
plastic cube25500.5

Key ideas

  • density = mass / volume
  • Density is measured in g/cm³.
  • A heavy object of small volume can have a high density.
  • Pure water has a density of 1 g/cm³.
Worked example 5.3.1
A block has a mass of 40 g and a volume of 50 cm³. What is its density? Write the number of g/cm³.

Method. Use density = mass / volume.

  1. Write the values. The mass is 40 g and the volume is 50 cm³.
    40 and 50
  2. Divide. Density = 40 divided by 50.
    40 / 50 = 0.8
  3. Write the answer.
    0.8 g/cm³

Check. Check: 0.8 x 50 = 40. ✓

Worked example 5.3.2
A stone has a mass of 90 g and a volume of 30 cm³. What is its density? Write the number of g/cm³.

Method. Use density = mass / volume.

  1. Write the values. The mass is 90 g and the volume is 30 cm³.
    90 and 30
  2. Divide. Density = 90 divided by 30.
    90 / 30 = 3
  3. Write the answer.
    3 g/cm³

Check. Check: 3 x 30 = 90. ✓

Worked example 5.3.3
A cube has a density of 2 g/cm³ and a volume of 15 cm³. What is its mass? Write the number of grams.

Method. Rearrange: mass = density x volume.

  1. Rearrange. Mass = density x volume.
    mass = density x volume
  2. Multiply. Mass = 2 x 15.
    2 x 15 = 30
  3. Write the answer.
    30 g

Check. Check: 30 divided by 15 is 2. ✓

Watch out

Watch out: density is mass divided by volume, not volume divided by mass. Check the units: g and cm³ give g/cm³.

Exam tip

Exam tip. Write the formula first, then put in the numbers, then give the unit g/cm³.

Try it (with your teacher, or a grown-up at home). With a teacher, weigh a small wooden block and a small metal object on balance scales. Measure the length, width and height of the block with a ruler, and work out its volume. Then find the density of the block using density = mass / volume.

Exercise 5C  Density: mass, volume and density

1
FWhat is the density of the metal cube in the table? Write the number of g/cm³.
2
FWhat is the density of pure water? Write the number of g/cm³.
3
FWhat is the density of the plastic cube? Write the number of g/cm³.
4
FWhat is the mass of a block of density 3 g/cm³ and volume 10 cm³? Write the number of grams.
5
FWhat is the volume of a sample of mass 60 g and density 3 g/cm³? Write the number of cm³.
6
FWhat is the density of the wooden block, from its mass of 40 g and volume of 50 cm³? Write the number of g/cm³.
7
PSA cube has a mass of 16 g and a volume of 8 cm³. What is its density? Write the number of g/cm³.
8
PSWhich sample has the greatest density: the stone or the metal cube? Write the words.
9
PSA pupil says the wooden block is denser than the stone because it is bigger. Is the pupil right? Write yes or no.
10
PSA block has a mass of 30 g and a density of 0.5 g/cm³. What is its volume? Write the number of cm³.
11
PSTwo blocks have the same mass of 20 g. One has a volume of 10 cm³ and the other has 20 cm³. Which block is denser? Write the volume in cm³.
12
PSWorking scientifically: explain why a bigger block is not always less dense than a smaller block. Write one sentence.
13
RChallenge: two cubes both have a mass of 45 g. One has a density of 3 g/cm³ and the other has a density of 1 g/cm³. Write the volume of the denser cube, in cm³.
5.4

Measuring volume and density

Year 7
C3: measure the density of regular and irregular solids, using a ruler and a measuring cylinder (displacement)
Video lesson: Measuring volume and densityComing soon
Story. Omar has a stone that will not fit in a ruler-measured box. “How do I find its volume?” he asks. His teacher says, “Use a measuring cylinder. The water level rises by the volume of the stone.”

A regular solid has a simple shape, so its volume can be found from its length, width and height: volume = length x width x height, in cm³.

An irregular solid has no simple shape. Put it into water in a measuring cylinder. The water level rises by the same volume as the solid, because the solid pushes the water out of its way. This is called displacement. One millilitre (mL) is the same as one cubic centimetre (cm³).

length 5 cmwidth 4 cmheight 2 cm
A regular block, labelled with its length, width and height.
0102030405060before: 40 cm³after: 55 cm³measuring cylinder (mL)
A measuring cylinder: the water rises from 40 cm³ to 55 cm³ after the stone is added.

Key ideas

  • Regular solid: volume = length x width x height.
  • Irregular solid: volume = the rise in water level, in a measuring cylinder.
  • 1 mL = 1 cm³.
  • Then density = mass / volume.
Worked example 5.4.1
A regular block is 5 cm long, 4 cm wide and 2 cm high. What is its volume? Write the number of cm³.

Method. Multiply the three lengths.

  1. Write the values. Length 5 cm, width 4 cm, height 2 cm.
    5, 4, 2
  2. Multiply. Volume = 5 x 4 x 2.
    5 x 4 x 2 = 40
  3. Write the answer.
    40 cm³

Check. Forty 1 cm cubes fill the block. ✓

Worked example 5.4.2
A stone is put into a measuring cylinder. The level rises from 40 cm³ to 55 cm³. What is the volume of the stone? Write the number of cm³.

Method. Find the rise in the water level.

  1. Read the levels. The level was 40 cm³ before, and 55 cm³ after.
    40 and 55
  2. Subtract. The rise, which is the volume of the stone, is 55 minus 40.
    55 - 40 = 15
  3. Write the answer.
    15 cm³

Check. 40 + 15 = 55. ✓

Worked example 5.4.3
The regular block (5 cm by 4 cm by 2 cm) has a mass of 32 g. What is its density? Write the number of g/cm³.

Method. Use density = mass / volume, with the volume from the first example.

  1. Write the values. Mass 32 g, volume 40 cm³.
    32 and 40
  2. Divide. Density = 32 / 40.
    32 / 40 = 0.8
  3. Write the answer.
    0.8 g/cm³

Check. 0.8 x 40 = 32. ✓

Watch out

Watch out: read the bottom of the water surface at eye level. Use the scale on the measuring cylinder, not the top of the cylinder.

Exam tip

Exam tip. For an irregular solid, always subtract the starting level from the final level.

Try it (with your teacher, or a grown-up at home). With a teacher, put a stone into a measuring cylinder half full of water. Read the level before and after. Subtract to find the volume of the stone, in cm³. Then weigh the stone and calculate its density.

Exercise 5D  Measuring volume and density

1
FWhat is the formula for the volume of a regular block? Write the words.
2
FWhat is the volume of a block 3 cm long, 2 cm wide and 4 cm high? Write the number of cm³.
3
FWhat is the volume of a regular block 5 cm by 4 cm by 2 cm? Write the number of cm³.
4
FWhat is 1 mL in cm³? Write the number.
5
FThe water level in a measuring cylinder rises from 40 cm³ to 55 cm³ when a stone is added. What is the volume of the stone? Write the number of cm³.
6
FWhat is the density of the irregular stone, if its mass is 45 g and its volume is 15 cm³? Write the number of g/cm³.
7
FWhich measuring tool is used to find the volume of an irregular solid by displacement? Write the words.
8
FWhich measurement is needed, along with the volume, to find density? Write one word.
9
PSA regular block has a volume of 40 cm³ and a mass of 32 g. Is its density 0.8 g/cm³? Write yes or no.
10
PSA measuring cylinder reads 60 cm³ before a stone is added, and 72 cm³ after. What is the volume of the stone? Write the number of cm³.
11
PSA stone of mass 36 g has a volume of 12 cm³. What is its density? Write the number of g/cm³.
12
PSWorking scientifically: a pupil reads the top of the water surface instead of the bottom of the curve. Name one effect this could have on the volume. Write one sentence.
13
RChallenge: a pupil measures the volume of a stone by displacement, and gets 15 cm³. Then the pupil calculates its density. The mass is 45 g. Write the density, and say whether it is more or less than water. Write the density and the word: more or less.
5.5

Density, floating and sinking

Year 7
C3: density and floating: an object floats in a liquid if it is less dense than the liquid, and sinks if it is denser
Video lesson: Density, floating and sinkingComing soon
Story. Priya drops four small objects into a beaker of water. Two float and two sink. “Why does a plastic cube float, but a metal cube sinks?” she asks. Her teacher says, “Compare the density of each object with the density of the water.”

An object floats in a liquid if its density is less than the density of the liquid. It sinks if its density is more than the density of the liquid.

Pure water has a density of 1 g/cm³. So an object with a density below 1 g/cm³ floats in water, and one with a density above 1 g/cm³ sinks.

water (density 1 g/cm³)woodenstonemetalplastic
A beaker of water with four samples: the wooden block and the plastic cube float, the stone and the metal cube sink.

The four samples from section 5.3 are used here.

SampleMass (g)Volume (cm³)Density (g/cm³)
wooden block40500.8
stone90303.0
metal cube80108.0
plastic cube25500.5

Key ideas

  • An object floats if it is less dense than the liquid.
  • An object sinks if it is denser than the liquid.
  • Pure water has a density of 1 g/cm³.
  • The shape of the object does not decide whether it floats; the density does.
Worked example 5.5.1
Does the plastic cube float or sink in water? Write the word.

Method. Compare the density with water.

  1. Read the density. The plastic cube has a density of 0.5 g/cm³.
    0.5
  2. Compare. 0.5 is less than 1, the density of water, so the cube floats.
    floats
  3. Write the answer.
    float

Check. It is less dense than water. ✓

Worked example 5.5.2
Does the stone float or sink in water? Write the word.

Method. Compare the density with water.

  1. Read the density. The stone has a density of 3 g/cm³.
    3
  2. Compare. 3 is more than 1, so the stone is denser than water.
    more than 1
  3. Write the answer.
    sink

Check. A denser object sinks. ✓

Worked example 5.5.3
Which of the four samples has the lowest density? Write the name.

Method. Compare the four densities.

  1. Read the densities. The densities are 0.8, 3, 8 and 0.5 g/cm³.
    0.8, 3, 8, 0.5
  2. Decide. The smallest is 0.5, for the plastic cube.
    plastic cube
  3. Write the answer.
    the plastic cube

Check. The plastic cube is the least dense sample. ✓

Watch out

Watch out: a heavy object does not always sink. The plastic cube is light for its size, so it floats. Compare density, not mass.

Exam tip

Exam tip. To predict floating or sinking, compare the density of the object with the density of the liquid. Say the numbers.

Try it (with your teacher, or a grown-up at home). With a grown-up, drop a small wooden or plastic object and a small metal object into a bowl of water. Predict which will float and which will sink, using density. Then test your predictions, and write down whether they were correct.

Exercise 5E  Density, floating and sinking

1
FDoes an object with a density of 0.8 g/cm³ float or sink in water? Write the word.
2
FDoes an object with a density of 3 g/cm³ float or sink in water? Write the word.
3
FWhat is the density of pure water? Write the number of g/cm³.
4
FDoes the metal cube float or sink? Write the word.
5
FDoes the plastic cube float or sink? Write the word.
6
FWhich two samples float in water? Write the two names.
7
FWhich two samples sink in water? Write the two names.
8
PSA pupil says a heavy object always sinks. Is the pupil right? Write yes or no.
9
PSA new object has a density of 1.2 g/cm³. Does it float or sink in water? Write the word.
10
PSA new object has a density of 0.9 g/cm³. Does it float or sink in water? Write the word.
11
PSAli says the plastic cube would sink in a liquid with a density of 0.3 g/cm³. Is Ali right? Write yes or no.
12
PSWorking scientifically: a pupil predicts that the stone will float in a liquid of density 4 g/cm³. Is the prediction correct? Write yes or no.
13
RChallenge: explain why the plastic cube floats in water, but would sink in a liquid with a density of 0.4 g/cm³. Write one sentence.

Chapter summary

SkillMethod
DiffusionRandom movement of particles from higher to lower concentration, in gases and liquids.
Rate of diffusionFaster at a higher temperature. Much faster in a gas than in a liquid.
Densitydensity = mass / volume, in g/cm³. Pure water is 1 g/cm³.
VolumeRegular solid: length x width x height. Irregular solid: displacement in a measuring cylinder (1 mL = 1 cm³).
FloatingFloats if less dense than the liquid; sinks if denser.

Can you…?

  • I can describe diffusion, using random movement and concentration
  • I can explain how temperature and state change the rate of diffusion
  • I can use density = mass / volume, with the units g/cm³
  • I can find the volume of a regular and an irregular solid
  • I can predict whether an object floats or sinks, using density

Key terms

diffusion
the spreading of particles from higher to lower concentration, due to random movement
concentration
the number of particles in a given space
density
the mass of a substance in a given volume; density = mass / volume
displacement
the rise in water level when a solid is put into the water
float
stay on the surface, because the object is less dense than the liquid
sink
move to the bottom, because the object is denser than the liquid
g/cm³
the unit of density: grams per cubic centimetre

Exercise 5Z  Check-up

1
What is the process in which particles spread from higher to lower concentration? Write the word.
2
In which state does diffusion not happen? Write the word.
3
At which water temperature did food colouring spread fastest in the class data? Write the words.
4
What is the density formula? Write the words.
5
A block has a mass of 40 g and a volume of 50 cm³. What is its density? Write the number of g/cm³.
6
What is the mass of a block with density 2 g/cm³ and volume 15 cm³? Write the number of grams.
7
A regular block is 3 cm long, 2 cm wide and 4 cm high. What is its volume? Write the number of cm³.
8
The water level rises from 40 cm³ to 55 cm³ when a stone is added. What is the stone's volume? Write the number of cm³.
9
Does an object with a density of 0.5 g/cm³ float or sink in water? Write the word.
10
Explain why diffusion is faster in warm water than in cold water. Write one sentence.

Total 16 marks. Allow about 16 minutes.

Exercise 5X  Practice test questions

1
FWhich process moves particles from higher to lower concentration by random movement? Write the word.[1 mark]
2
RExplain why a gas diffuses faster than a liquid. Write one sentence.[2 marks]
3
PSA block has a mass of 60 g and a volume of 20 cm³. What is its density? Write the number of g/cm³.[2 marks]
4
PSA stone is put into a measuring cylinder. The level rises from 25 cm³ to 40 cm³. What is the volume of the stone? Write the number of cm³.[2 marks]
5
FDoes an object of density 2 g/cm³ float or sink in water? Write the word.[1 mark]
6
FWhich is more dense: the wooden block at 0.8 g/cm³ or the stone at 3 g/cm³? Write the name.[1 mark]
7
FWrite the density of pure water, in g/cm³. Write the number.[1 mark]
8
RExplain why a plastic cube floats in water. Write one sentence.[2 marks]
9
PSA cube has a mass of 16 g and a volume of 8 cm³. What is its density? Write the number of g/cm³.[2 marks]
10
RWrite one reason why the same drop size and the same volume of water must be used in a diffusion test. Write one sentence.[2 marks]
← Chapter 4: States of matter and the particle modelChapter 6: Atoms, elements and the periodic table →

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