Density

Jonny Nelson explains density with a GCSE Physics practical experiment

Density describes how closely packed the particles are in a solid, liquid or gas.

curriculum-key-fact
Density is the amount of mass per unit volume.

Solids, liquids and gases

All matter contains particles. The difference between the different states of matter is how the particles are arranged:

  • in a solid – particles are tightly packed in a regular structure
  • in a liquid – particles are tightly packed but free to move past each other
  • in a gas – particles are spread out and move randomly
Solid cube: side length 1 unit, 64 particles in tightly packed lattice. Liquid cube: 1 unit, contains approx 30 particles. Gas cube: side length 10 units contains 15 scattered particles.Changing the state of a material will change its density

There is only a small difference between the density of a liquid and its corresponding solid, eg water and ice. This is because the particles are tightly packed in both states. The same number of particles in a gas spread further apart than in the liquid or solid states. The same mass takes up a bigger volume. This means the gas is less dense.

Density also depends on the material. A piece of iron with the same dimensions as a piece of aluminium will be heavier because the atoms are more closely packed and each iron atom has much more mass than each aluminium atom.

Scientists can measure density by measuring the mass of a certain volume of the material, for example, one cubic centimetre.

MaterialDensity in grams per cubic centimetre (g/cm3)
Iron7.8
Ice0.98
Water1
Air0.00129

Calculating density

Density can be calculated using the equation:

\text{density} = \frac{\text{mass}}{\text{volume}}

\rho = \frac{m}{V}

This is when:

  • density (ρ) is measured in kilograms per metre cubed (kg/m3)
  • mass (m) is measured in kilograms (kg)
  • volume (V) is measured in metres cubed (m3)

Example

What is the density of a material if 0.45 cubic metres (m3) of it has a mass of 0.2 kg?

\rho = \frac{m}{V}

\rho = \frac{0.2}{0.45}

\rho = 0.44 kg/m3

Question

What is the density of a material if 4 cubic metres (m3) of it has a mass of 2,200 kg?

\rho = \frac{m}{V}

\rho = \frac{2,200}{4}

\rho = 550 kg/m3

The units for density

Although the standard unit for mass is kilograms (kg) and for volume it is cubic metres (m3), in many laboratory situations the norm is to find mass in grams (g) and volume in cubic centimetres (cm3).

Calculating density using grams and centimetres cubed will give a density unit of grams per centimetre cubed (g/cm3).

Question

What is the density of a material if 15 cm3 of it has a mass of 30 g?

\rho = \frac{m}{V}

\rho = \frac{30}{15}

\rho = 2 g/cm3

curriculum-key-fact
1 g/cm3 is equal to 1,000 kg/m3
  • To convert from kg/m3 to g/cm3, divide by 1,000.
  • To convert from g/cm3 to kg/m3, multiply by 1,000.

Aluminium has a density of 2.7 g/cm3, or 2,700 kg/m3. Lead has density 11.6 g/cm3, or 11,600 kg/m3.

Example

Iron has a density of 7.9 g/cm3 - what is this in kg/m3?

7.9 multiplied by 1,000 gives 7,900 kg/m3.

Question

What is the density of an object in kg/m3 if it is 653.1 g/cm3?

653.1 multiplied by 1,000 would give 653,100 kg/m3.