Density
Density tells you how much mass is packed into each unit of volume. It explains why a steel bolt sinks and a much heavier log floats, and it is one of the required practicals.
Part 1 of 3: Learn it
In short
- Density = mass ÷ volume, ρ = m ÷ V.
- 1 g/cm³ = 1000 kg/m³, so multiply by 1000 to go from g/cm³ to kg/m³.
- Use a displacement can (or a measuring cylinder) to find the volume of an irregular object.
Where this is in your specification
Spec points: AQA 4.3.1.1, Edexcel Topic 14, OCR P1.1
| Board | Topic: Particle model, density and gas pressure |
|---|---|
| AQA 8463 | 4.3 (8463); 6.3 (8464) |
| Edexcel 1PH0 | Topic 14 |
| OCR J249 | P1 |
The equation
| Symbol | Quantity | Unit |
|---|---|---|
| ρ (rho) | density | kg/m³ (or g/cm³) |
| m | mass | kg (or g) |
| V | volume | m³ (or cm³) |
Keep the units matched: grams with cm³ gives g/cm³, kilograms with m³ gives kg/m³. Water is about 1 g/cm³, which is 1000 kg/m³.
Density and the particle model
In a solid the particles are packed closely in a regular pattern; in a liquid they are close but can move past each other; in a gas they are far apart and move quickly in all directions.
So for the same substance, the solid and liquid are much denser than the gas. Changing state does not change the mass: the particles are rearranged, not lost. Water is the well-known exception where the solid (ice) is a little less dense than the liquid, which is why ice floats.
The required practical
- Regular solid: measure the mass on a balance, measure the length, width and height with a ruler or vernier callipers, and work out volume = l × w × h.
- Irregular solid: fill a displacement (eureka) can to the spout, lower the object in and collect the water that overflows in a measuring cylinder. The volume of water equals the object's volume.
- Liquid: put a measuring cylinder on a balance, zero it, pour in a known volume and read the mass.
A 600 g object has a volume of 200 cm³. Find its density.
Show the answer
ρ = 600 ÷ 200 = 3 g/cm³ (3000 kg/m³).
Part 2 of 3: See it worked
Worked examples
Example 1
A metal block measures 5.0 cm × 4.0 cm × 2.0 cm and has a mass of 108 g. Find its density in g/cm³ and in kg/m³.
- Volume = 5.0 × 4.0 × 2.0 = 40 cm³
- ρ = m ÷ V = 108 ÷ 40 = 2.7 g/cm³
- In kg/m³: 2.7 × 1000 = 2700 kg/m³
Answer: 2.7 g/cm³, which is 2700 kg/m³ (the density of aluminium).
Example 2
A stone of mass 0.30 kg makes 120 cm³ of water overflow from a displacement can. What is its density in kg/m³?
- V = 120 cm³ = 120 ÷ 1 000 000 m³ = 0.00012 m³
- ρ = 0.30 ÷ 0.00012
- ρ = 2500 kg/m³
Answer: 2500 kg/m³.
Common mistakes
- Mixing units, such as grams with m³.
- Converting cm³ to m³ by dividing by 100 or 1000. There are 100 × 100 × 100 = 1 000 000 cm³ in 1 m³.
- Saying a gas is less dense because its particles are lighter. They are the same particles, just much further apart.
- Forgetting to zero the balance before adding the liquid.
Convert 0.8 g/cm³ to kg/m³.
Show the answer
0.8 × 1000 = 800 kg/m³.
Part 3 of 3: Test yourself
Check yourself
Answer each one in your head or on paper first, then open it to check.
A 600 g object has a volume of 200 cm³. Find its density.
ρ = 600 ÷ 200 = 3 g/cm³ (3000 kg/m³).
Convert 0.8 g/cm³ to kg/m³.
0.8 × 1000 = 800 kg/m³.
Why is a gas less dense than the liquid of the same substance?
The same mass of particles is spread over a much bigger volume, because the particles in a gas are far apart.
Jobs that use this
- Civil engineer (s'ouvre dans un nouvel onglet)
- Chemist (s'ouvre dans un nouvel onglet)
- Laboratory technician (s'ouvre dans un nouvel onglet)
Each link opens the job profile on the National Careers Service (England). In the rest of the UK: My World of Work (Scotland), Careers Wales, nidirect careers (Northern Ireland).
Ces fiches sont en anglais car elles suivent les programmes d'examen britanniques.
Full lessons and marked practice for this course are coming soon to Brainlag Learn. See courses