4.3.1.1Density of materials
The density of a material is defined by the equation:
density = mass / volume ρ = m / V
density, ρ, in kilograms per metre cubed, kg/m³; mass, m, in kilograms, kg; volume, V, in metres cubed, m³.
You should be able to recall and apply this equation to changes where mass is conserved. The Greek letter used for density is rho, ρ — not a letter p.
The particle model can be used to explain the different states of matter, and differences in density.
You should be able to recognise and draw simple diagrams to model the difference between solids, liquids and gases, and to explain the differences in density between the different states of matter in terms of the arrangement of atoms or molecules.
The explanation is about spacing, not about the particles themselves. In a solid the particles are packed closely together in a regular arrangement, so a large mass occupies a small volume and the density is high. In a liquid they are still close together but disordered, so the density is similar to the solid, usually slightly lower. In a gas the particles are far apart, so the same number of particles fills a very much larger volume and the density is very much lower.
Worked example
A block of aluminium has a mass of 0.54 kg and a volume of 0.0002 m³. Calculate its density.
- Write the equation: ρ = m ÷ V.
- Check the units are kilograms and metres cubed — they are.
- Substitute: ρ = 0.54 ÷ 0.0002.
- = 2700.
- Give the unit: kg/m³.
Answer: 2700 kg/m³
Required practical 5
Determining the densities of regular and irregular solid objects and liquids
- For a regular solid: measure its mass on a balance, then measure its dimensions with a ruler, micrometer or Vernier callipers and calculate the volume from them.
- For an irregular solid: measure its mass, then lower it on a thread into a displacement can filled to the spout, and collect the water that overflows in a measuring cylinder. The volume of water collected is the volume of the object.
- For a liquid: measure the mass of an empty measuring cylinder, pour in the liquid, and measure the mass again. The difference is the mass of the liquid, and its volume is read from the cylinder.
- Repeat every measurement and take a mean.
- Calculate the density in each case from ρ = m ÷ V, converting to kilograms and metres cubed.
Common mistake
Watch the units. A volume measured in cm³ with a mass in g gives a density in g/cm³, not kg/m³ — and the two differ by a factor of 1000. Convert before substituting, or state the unit you have actually produced.
- Density
- mass divided by volume, measured in kilograms per metre cubed
4.3.1.2Changes of state
You should be able to describe how, when substances change state — melt, freeze, boil, evaporate, condense or sublimate — mass is conserved.
Mass is conserved because no particles are created or destroyed. The same particles are present before and after; only their arrangement and their spacing change. That is why 1 kg of ice becomes exactly 1 kg of water, even though the volume changes and so the density changes with it.
Changes of state are physical changes, which differ from chemical changes because the material recovers its original properties if the change is reversed.
That is the test to apply. Freeze water and melt it again and you have the same water, with the same properties. Burn a fuel and you cannot reverse it to recover the fuel — the substances themselves have changed, so it is a chemical change.
Common mistake
The mass stays the same during a change of state, but the density does not, because the volume changes. A question about density during melting or boiling is asking about the change in spacing of the particles.
- Change of state
- a physical change in which a substance melts, freezes, boils, evaporates, condenses or sublimates; mass is conserved because no particles are created or destroyed, only their arrangement and spacing change
Before you practise
- density = mass / volume, ρ = m / V, in kg/m³ — recall and apply this equation.
- Solids: particles closely packed in a regular arrangement, so density is high.
- Liquids: particles close together but disordered, so density is similar to the solid.
- Gases: particles far apart, so density is much lower.
- Required practical 5: mass from a balance; volume from dimensions for regular solids, by displacement for irregular ones.
- The six changes of state are melting, freezing, boiling, evaporating, condensing and sublimating.
- Mass is conserved in every change of state, because no particles are created or destroyed.
- Changes of state are physical, not chemical, because reversing the change recovers the original properties.