Density and states of matter
Density
is the of a material: how much mass is packed into each cubic metre. You must recall this equation:
density = mass ÷ volume, or ρ = m/V
| Quantity | Symbol | Unit |
|---|---|---|
| Density | ρ (the Greek letter rho) | kilograms per cubic metre (kg/m³) |
| Mass | m | kilograms (kg) |
| Volume | V | cubic metres (m³) |
g/cm³ is also used for small objects. To convert, 1 g/cm³ = 1000 kg/m³. Water has a density of 1 g/cm³, or 1000 kg/m³.
Example: a metal block has a mass of 270 g and a volume of 100 cm³.
- ρ = m/V = 270 ÷ 100 = 2.7 g/cm³
- In kg/m³: 2.7 × 1000 = 2700 kg/m³
Key terms
The particle model
The says everything is made of tiny particles. How they are arranged and move depends on the state:
| State | Arrangement | Movement |
|---|---|---|
| Solid | Very close together in a regular pattern | Vibrate about fixed positions |
| Liquid | Close together, but in no pattern | Move around each other |
| Gas | Far apart, with lots of space between them | Move quickly and randomly in all directions |
Solids and liquids have similar densities because their particles are close together. Gases are much less dense: their particles are far apart, so the same mass takes up a much bigger volume.
A substance is usually densest as a solid. Water is an exception: ice floats because it is less dense than liquid water.
Key terms
Required practical 5: solids
Regular solid (such as a cuboid):
- Measure its on a balance.
- Measure its length, width and height with a ruler (or vernier callipers for small objects).
- Volume = length × width × height.
- Calculate ρ = m/V.
Irregular solid (such as a stone):
- Measure its mass on a balance.
- Fill a with water until it drips out of the spout. Wait for it to stop.
- Put an empty under the spout.
- Lower the object in gently on a thread. It pushes out, or displaces, its own volume of water into the cylinder.
- Read the volume of water in cm³. This is the object's volume.
- Calculate ρ = m/V.
Key terms
Required practical 5: liquids, variables and accuracy
Liquid:
- Put an empty measuring cylinder on a balance and zero (tare) it.
- Pour in 50 cm³ of the liquid and read the mass.
- Calculate ρ = m/V.
Remember that 1 ml = 1 cm³.
- the object or liquid being tested.
- its density, worked out from mass and volume.
- the same balance and measuring cylinder; for liquids, the temperature.
Hazard: spilt water makes the floor slippery, so wipe it up straight away.
Improving accuracy: read the measuring cylinder at eye level, from the bottom of the curved surface (the ). Measure each length a few times and find a mean.
Exam tip
Check your units match: g with cm³ gives g/cm³; kg with m³ gives kg/m³.