AQA GCSE Physics Foundation (8463), Foundation tier · Particle model of matter › Changes of state and the particle model
Practise Density of materials. 13 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Density tells you how much mass is packed into each unit of volume of a material. You need to recall and use ρ = m / V, explain the different densities of solids, liquids and gases using the particle model, and describe the density required practical. Expect calculations (often with unit conversions), particle-diagram questions and 4 to 6 mark method questions.
Key facts
density = mass ÷ volume, ρ = m / V (recall it: not on the equation sheet)
ρ in kg/m3, m in kg, V in m3
1 g/cm3 = 1000 kg/m3
1 m3 = 1 000 000 cm3; 1 cm3 = 1 ml
Solid: regular, touching, vibrate about fixed positions
Liquid: random, close together, move past each other
Gas: random, far apart, move quickly in all directions
Gases have a much lower density: particles far apart, so less mass per m3
Volume of an irregular object: displacement of water (eureka can and measuring cylinder)
Notes
The particle model of solids, liquids and gases
diagram
In a solid, the particles are touching and packed in a regular arrangement. They vibrate about fixed positions.
In a liquid, the particles are still close together (mostly touching) but in a random arrangement. They can move past each other.
In a gas, the particles are far apart in a random arrangement. They move quickly in all directions.
In particle diagrams, draw the particles the same size in all three states: only their arrangement and spacing change.
Same-sized particles in all three states: only the arrangement and spacing change.
Density
Density is the mass per unit volume of a material: ρ = m / V.
ρ (rho) is density in kg/m3, m is mass in kg and V is volume in m3. You must recall this equation: it is not on the equation sheet.
Density is often given in g/cm3. 1 g/cm3 = 1000 kg/m3. Water has a density of about 1000 kg/m3 (1 g/cm3).
The solid and liquid forms of a substance have similar densities because in both the particles are close together.
The gas form has a much lower density because its particles are far apart: each cubic metre contains far fewer particles, so much less mass.
Required practical: measuring density
diagram
Measure the mass with a top-pan balance.
Regular solid (e.g. a cuboid): measure the length, width and height with a ruler (or vernier callipers for small lengths), then volume = length × width × height.
Irregular solid (e.g. a stone): fill a displacement (eureka) can with water up to the spout, lower the object in and collect the water that overflows in a measuring cylinder. The volume of water displaced equals the volume of the object.
Volume of water collected = volume of the stone.
Or lower the object into a measuring cylinder part-filled with water: volume of object = new reading − starting reading.
Liquid: put an empty measuring cylinder on the balance and zero it, pour in some liquid, then read the mass and the volume.
Read a measuring cylinder at eye level, from the bottom of the meniscus. 1 ml = 1 cm3. Then calculate ρ = m / V.
Read from the bottom of the meniscus, with your eye level with it.
How to answer each type of question
Calculate density (with a unit conversion)
2 to 3 marksGrade 5
Write ρ = m / V.
Check the unit the question wants. For kg/m3, either convert g to kg and cm3 to m3 first, or work in g/cm3 and multiply by 1000 at the end.
Substitute, calculate and give the unit.
Example. A metal block measures 2.0 cm × 3.0 cm × 5.0 cm. Its mass is 243 g. Calculate the density of the metal in kg/m3.
Describe how to measure the density of an object (required practical)
4 to 6 marksGrade 5
Say how you measure the mass: a top-pan balance.
Say how you find the volume: measure the dimensions (regular shape) or use displacement of water (irregular shape).
Say how you calculate the density: mass ÷ volume.
Add a detail that improves accuracy, e.g. read the meniscus at eye level.
Example. Describe a method a student could use to determine the density of a small, irregularly shaped stone. (4 marks)
Show the model answerHide the model answer
Measure the mass of the stone with a top-pan balance (1). Fill a displacement (eureka) can with water up to the spout and, when it stops dripping, put an empty measuring cylinder under the spout (1). Lower the stone gently into the can and collect the water that overflows in the measuring cylinder (1). The volume of water collected equals the volume of the stone, so density = mass ÷ volume (1).
Don’t lose marks
Mixing units, e.g. grams with m3 or kg with cm3, which makes the answer wrong by a factor of 1000 or 1 000 000.
Converting cm3 to m3 by dividing by 100 or 1000 instead of 1 000 000.
Writing that gas particles are bigger, smaller or lighter. The particles are the same; they are just further apart.
Drawing liquid particles spread out like a gas. Liquid particles should mostly be touching.
Taking the final measuring cylinder reading as the object's volume instead of the change in reading.
More tips
Memory tricks
Density triangle: m on top, ρ and V on the bottom. Cover the one you want: ρ = m ÷ V, V = m ÷ ρ, m = ρ × V.
Sense check: water is 1000 kg/m3. Most solids and liquids are between a few hundred and about 20 000 kg/m3; gases at room temperature are only a few kg/m3 or less.
g/cm3 to kg/m3: multiply by 1000. kg/m3 to g/cm3: divide by 1000.
cm3 to m3: divide by 1 000 000 (100 × 100 × 100).
Exam technique
Write ρ = m / V down before you substitute: it is a recall equation, and the correct equation or substitution often earns the first mark.
Look at the unit the question asks for before you start, and convert consistently.
In particle explanations, use comparisons: 'further apart', 'closer together', 'less mass per unit volume'.
In practical questions, name the equipment (top-pan balance, ruler, eureka can, measuring cylinder) and say what you do with each measurement.
What each grade needs
What you need to be able to do, from the first marks up to the top grade.
Grade 3
Draw particle diagrams for the three statesSolid: particles touching in regular rows; liquid: particles touching but jumbled; gas: particles far apart and random.
Grade 4
Recall and use density = mass ÷ volumeSubstitute into ρ = m / V with mass in kg and volume in m3 to get a density in kg/m3.
Grade 5
Rearrange the density equationUse m = ρ × V to find a mass and V = m ÷ ρ to find a volume.
Grade 5
Describe the density required practicalMeasure mass on a balance and find volume from measured dimensions or by displacement of water.
Required practical:Density (method, variables and exam tips)
Quick recall
Cover the answers and test yourself. The app has these as flashcards that come back just before you'd forget them.
Name a measuring instrument the student could use to measure the length, width and height of the block.
A ruler (or vernier callipers).
Name a piece of apparatus a student could use to measure the volume of a liquid.
A measuring cylinder.
Identify the independent variable and the dependent variable.
Independent: the volume (size) of the cube. Dependent: the density of the cube.
Sample questions
Written for this site in the style of AQA exam questions. They are not taken from real past papers.
Question 1Easy3 marks
(a) Which of these is a unit of density? Tick (✓) one box.[1]
kg
m3
kg/m3
N/kg
(b) Name a piece of apparatus a student could use to measure the volume of a liquid.[1]
(c) Name a piece of apparatus a student could use to measure the mass of a solid object.[1]
Show the answer and mark scheme
(a)Answer: kg/m3
(b)Answer: A measuring cylinder.
measuring cylinder (allow burette / pipette)
(c)Answer: A (top-pan) balance.
(top-pan) balance / scales
Question 2Medium5 marks
The density of air is 1.2 kg/m3. A classroom measures 9.0 m by 7.0 m and has a ceiling height of 3.0 m.
(a) Calculate the volume of air in the classroom.[1]
(b) Calculate the mass of the air in the classroom. Give your answer to 3 significant figures.[2]
(c) A student says the air in the classroom has a mass of about a quarter of a tonne. 1 tonne = 1000 kg. Comment on whether the student is correct.[2]
Show the answer and mark scheme
(a)Answer: 189 m3
189 (m3)
(b)Answer: 227 kg
m = 1.2 × 189
227 (kg)
(c)Answer: A quarter of a tonne is 250 kg. The actual mass, 227 kg, is close to this, so the student’s estimate is reasonable.
a quarter of a tonne is 250 kg
227 kg is reasonably close to 250 kg, so the student’s estimate is about right / a fair approximation