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.

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.

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 are 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 because an individual iron atom is heavier than an aluminium atom.

Scientists can measure how tightly packed the particles are by measuring the mass of a certain volume of the material, for example, one cubic centimetre.

MaterialDensity (g/cm³)
Iron7.8
Ice0.98
Water1
Air0.00129

Calculating density

density = \frac{mass}{volume}

 ρ= \frac{m}{V}

This is when:

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

Example

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

 ρ= \frac{m}{V}

 ρ= \frac{0.2}{0.45}

 ρ= 0.44 \ kg/m^{3}

Question

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

 ρ= \frac{m}{V}

 ρ= \frac{2,200}{4}

 ρ= 550 \ kg/m^{3}

The units for density

The standard unit for mass is kilograms (kg) and for volume is cubic metres (m3). However, in many laboratory situations it is common to measure the mass in grams (g) and volume in cubic centimetres (cm3).

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

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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 a 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 6.531 g/cm3 ?

6.531 multiplied by 1,000 would give 6,531 kg/m3.