Density

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

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Density is the amount of mass per unit volume.

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 little 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 would spread further apart compared to 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.

Scientists can find the density of a material 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:

density = \frac{mass}{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 of 0.45 cubic metres (m3) if it has a mass of 0.2 kg?

\rho  = \frac{m}{V}

\rho = \frac{0.2}{0.45}

\rho = 0.44~kg/m^{3}

Question

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

\rho  = \frac{m}{V}

\rho = \frac{2200}{4}

\rho = 550~kg/m^{3}

The units for density

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

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

Question

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

\rho  = \frac{m}{V}

\rho = \frac{30}{15}

\rho = 2~g/cm^{3}

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1 g/cm3 is equal to 1,000 kg/m3

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