LearnovaAll Physics notes
AQA PhysicsParticle model of matter

Density and states of matter

Calculate density and explain changes of state.

Start here

The key idea

Density depends on mass and volume. State changes alter particle arrangement but not particle identity.

Equation to know

density = mass / volume

Density And States Of Matter
solidliquidgas

Use the labels to explain the scientific relationship shown.

Revision notes

The bit that matters

Short notes first. Learn the idea, then use the worked example and questions to check it properly.

1

Density

Density is the mass per unit volume of a substance.Density = mass / volume, written rho = m / V, with density in kg/m3 (or g/cm3), mass in kg and volume in m3.A dense material has a lot of mass packed into a small volume.The density of a material does not depend on how much of it you have.

2

The three states of matter

In a solid the particles are held in a fixed, regular arrangement, vibrating about fixed positions, so solids keep their shape and volume.In a liquid the particles are close together but can move past each other, so liquids flow and take the shape of their container while keeping a fixed volume.In a gas the particles are far apart and move quickly in random directions, so gases fill their container.

3

Measuring density

To find the density of a regular solid, measure its mass with a balance and calculate its volume from its dimensions, then use rho = m / V.For an irregular solid, find its volume by displacement: lower it into a measuring cylinder or eureka can and measure the volume of water it pushes aside.For a liquid, measure the mass of a known volume in a measuring cylinder.

4

Changes of state

Changes of state are physical changes, not chemical ones, because no new substance is formed and the change can be reversed.The mass is conserved during a change of state, so the same mass of liquid water gives the same mass of ice or steam.Melting, freezing, boiling, evaporating, condensing and sublimating all involve energy rearranging the particles, not creating or destroying them.

Key terms

Definitions to learn

Density

The mass per unit volume of a substance.

State of matter

Whether a substance is a solid, liquid or gas.

Displacement method

Finding a volume from the liquid an object pushes aside.

Change of state

A physical change between solid, liquid and gas.

Physical change

A reversible change with no new substance and conserved mass.

Worked example

A block has a mass of 540 g and a volume of 200 cm3. Calculate its density.

1

Use density = mass / volume.

2

Keep the units consistent.

Final answer

2.7 g/cm3

Exam habit

For density calculations, check that mass and volume are in consistent units before dividing.Show the equation, substitution and answer with unit.For state-change questions, describe particle arrangement and movement — not just 'they move faster'.

Watch out

Do not assume melting changes the number of particles.

Examiner tips

How to score full marks

  • 1Watch the units: 1 g/cm3 = 1000 kg/m3, so convert before comparing densities.
  • 2Density questions often need volume by displacement for irregular shapes — describe the method clearly.
  • 3State that mass is conserved during a change of state to gain the explanation mark.
Practice questions

Try these yourself

Start with the core skill, then open the answer only after you have attempted the full question.

1A liquid has a density of 800 kg/m3 and a volume of 0.025 m3. Calculate its mass.
Mark scheme
  1. 1.Use mass = density x volume.
20 kg
2Explain why a gas is easier to compress than a liquid.
Mark scheme
  1. 1.Compare particle spacing.
Gas particles are much further apart, so they can be pushed closer together.
3Describe what happens to particles when a solid melts.
Mark scheme
  1. 1.Discuss energy, movement and arrangement.
Particles gain energy, vibrate more and leave their fixed positions while remaining close together.
4State the equation for density in words.[1 mark]
Mark scheme
  1. 1.Density relates mass and volume.
density = mass / volume (1)
5A block has a mass of 240 g and a volume of 30 cm3. Calculate its density.[2 marks]
Mark scheme
  1. 1.Use rho = m / V.
  2. 2.Substitute m = 240 and V = 30.
rho = m / V (1) = 240 / 30 = 8.0 g/cm3 (1)
6Describe the arrangement and movement of particles in a gas.[2 marks]
Mark scheme
  1. 1.Recall spacing of gas particles.
  2. 2.Recall their movement.
Particles are far apart with large spaces between them (1); they move quickly in random directions (1)
7Describe how you would measure the volume of an irregular stone.[2 marks]
Mark scheme
  1. 1.Use a displacement method.
  2. 2.Read the change in level.
Lower the stone into a measuring cylinder partly filled with water (1); the rise in water level equals the volume of the stone, read in cm3 (1)
8A glass marble has a mass of 12.5 g. When placed in a measuring cylinder the water level rises from 20.0 cm3 to 25.0 cm3. Calculate the density of the glass in g/cm3, then convert it to kg/m3.[3 marks]
Mark scheme
  1. 1.Find the volume from the rise in level.
  2. 2.Use rho = m / V.
  3. 3.Convert using 1 g/cm3 = 1000 kg/m3.
volume = 25.0 - 20.0 = 5.0 cm3 (1); rho = m / V = 12.5 / 5.0 = 2.5 g/cm3 (1); 2.5 × 1000 = 2500 kg/m3 (1)
9Explain, using particle theory, why solids are much denser than gases of the same substance.[3 marks]
Mark scheme
  1. 1.Compare particle spacing in solid vs gas.
  2. 2.State that mass of particles is unchanged.
  3. 3.Link closer spacing to more mass per volume.
In a solid the particles are held very close together in a regular arrangement (1); in a gas the same particles are widely spread out with large spaces between them (1); the particles themselves have the same mass, but many more fit into each cubic centimetre in the solid state, giving a much higher mass per unit volume and therefore a higher density (1)
10An alloy bar has a mass of 405 g. Its volume is found by dropping it into a eureka can and collecting 45.0 cm3 of displaced water. Calculate the density of the alloy. A student suggests it might be a brass alloy with density 8.5 g/cm3. Comment on whether the result is consistent with brass.[3 marks]
Mark scheme
  1. 1.density = mass / volume = 405 / 45.
  2. 2.Compare calculated density to 8.5 g/cm3.
  3. 3.Comment on whether results are consistent.
rho = 405 / 45.0 = 9.0 g/cm3 (1); this is greater than the stated density of brass (8.5 g/cm3) (1); the bar is therefore not consistent with being brass — it could be a different alloy or the measurement has some uncertainty/error (1)
11Explain why ice floats on liquid water, using the concept of density. What would be the consequence for aquatic life if ice were denser than water?[4 marks]
Mark scheme
  1. 1.Ice has a lower density than liquid water.
  2. 2.Lower density means ice floats.
  3. 3.If ice sank, lakes would freeze from the bottom.
  4. 4.Organisms could not survive in fully frozen lakes.
Ice has a lower density than liquid water (about 917 kg/m3 compared with 1000 kg/m3) because the hydrogen bonds in ice hold the molecules in an open lattice structure with more space between them (1); a less dense solid floats on a denser liquid, so ice forms on the surface (1); this creates an insulating layer that slows further freezing; if ice were denser it would sink, and lakes could freeze solid from the bottom up (1), making it impossible for aquatic organisms to survive in cold climates as there would be no liquid water refuge (1)
12Describe fully the differences in particle arrangement, spacing and movement between a liquid and a gas. In your answer explain why liquids have a definite volume but gases do not.[4 marks]
Mark scheme
  1. 1.Liquid: particles close together, touching, can move past each other.
  2. 2.Gas: particles far apart, move rapidly in random directions.
  3. 3.Liquid volume fixed because particles are attracted and stay close.
  4. 4.Gas fills container because particles move freely and spread out.
In a liquid the particles are close together and touch one another, held by intermolecular forces but able to slide past each other; they vibrate and move around within the liquid (1); in a gas the particles are widely separated with large empty spaces between them, and they move rapidly in random directions, colliding with the walls and each other (1); a liquid has a fixed volume because the attractive forces between particles are strong enough to keep them close together and prevent them from spreading out (1); a gas has no fixed volume because the particles have enough kinetic energy to overcome the attractive forces and move freely, so they spread out to fill any container (1)
13A student has an irregularly shaped piepiece of material and wants to find its density precisely. Describe in detail the complete experimental procedure, including the equipment needed, measurements taken, how the density is calculated, and two sources of error and how to reduce them.[4 marks]
Mark scheme
  1. 1.Equipment: balance, measuring cylinder or eureka can, water.
  2. 2.Measure mass with balance.
  3. 3.Find volume by displacement.
  4. 4.Calculate density = mass / volume.
  5. 5.Two errors and how to reduce them.
Measure the mass of the object on an electronic balance and record it (1); fill a measuring cylinder with enough water to submerge the object; record the initial water level; lower the object gently into the water using a thread and record the new water level; the volume equals the change in level (or use an overflow eureka can and measure the volume of displaced water in a measuring cylinder) (1); calculate density = mass / volume (1); one source of error is air bubbles clinging to the object, which make the displaced volume appear larger than it should — gently agitating the object removes bubbles (1); another source is reading the water level at the wrong angle — always read the bottom of the meniscus at eye level to avoid parallax error (1) — award max 4
Official exam-board sources
Specification Past papers
Browse all Physics topics