Density
Density describes how closely packed the particles are in a solid, liquid or gas.
Solids, liquids and gases
All Sub-atomic particles and anything made from them, such as atoms and molecules, are matter. Energy and forces are not 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
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 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.
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.
| Material | Density in grams per cubic centimetre (g/cm³) |
| Iron | 7.8 |
| Ice | 0.98 |
| Water | 1 |
| Air | 0.00129 |
| Material | Iron |
|---|---|
| Density in grams per cubic centimetre (g/cm³) | 7.8 |
| Material | Ice |
|---|---|
| Density in grams per cubic centimetre (g/cm³) | 0.98 |
| Material | Water |
|---|---|
| Density in grams per cubic centimetre (g/cm³) | 1 |
| Material | Air |
|---|---|
| Density in grams per cubic centimetre (g/cm³) | 0.00129 |
Calculating density
Density can be calculated using the equation:
\(density = \frac{mass}{volume}\)
\(p=\frac{m}{V}\)
This is when:
- density (p) 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?
\(p = \frac{m}{V}\)
\(p = \frac{0.2}{0.45}\)
\(p = 0.44~kg/m^{3}\)
Question
What is the density of a metal if 4 cubic metres (m3) of it has a mass of 2,200 kg?
\(p=\frac{m}{V}\)
\(p=\frac{2,200}{4}\)
\(p = 550~kg/m^3\)
The units for density
Although the standard unit for mass is kilograms (kg) and for volume is cubic metres (m3), in many laboratory situations it is the norm to find 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 if 15 cm3 of it has a mass of 30 g?
\(p=\frac {m}{V}\)
\(p=\frac{30}{15}\)
\(p = 2~g/cm^3\)
- 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 of 11.6 g/cm3, or 11,600 kg/m3.
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 653.1g/cm3?
653.1 multiplied by 1,000 gives 653,100 kg/m3.