Density and the equation density = mass / volume, the particle model of solids, liquids and gases, the changes of state, and how the particle model explains gas pressure.

What this dot point is asking

CCEA Double Award wants you to use density = mass / volume, describe the particle model of the three states, name the changes of state, and use the particle model to explain gas pressure. The density calculation and the particle explanations are both common.

Density

A dense material has a lot of mass packed into a small volume. To measure density, find the mass on a balance and the volume by measurement (regular shape) or by displacement in water (irregular shape).

The particle model and the three states

This is why solids are usually densest and gases least dense: the closer the particles, the more mass in a given volume.

Changes of state

Heating or cooling moves a substance between states by changing how the particles are arranged and how fast they move:

• Melting (solid to liquid) and freezing (liquid to solid);
• Evaporating or boiling (liquid to gas) and condensing (gas to liquid);
• Subliming (solid straight to gas).

Changes of state are physical changes: the particles themselves are unchanged, so the mass is conserved.

Gas pressure

Measuring volume for density

To use $\rho = m/V$ you need the volume as well as the mass. For a regular solid (a cube or cylinder), measure the sides with a ruler and calculate the volume. For an irregular solid, lower it into a measuring cylinder of water (or a displacement can) and the rise in water level gives the volume, because the object pushes aside its own volume of water. For a liquid, pour a known volume into a measuring cylinder and find its mass on a balance, remembering to subtract the mass of the empty cylinder. Keeping the units of mass and volume consistent (grams with cubic centimetres, or kilograms with cubic metres) is essential.

Examples in context

Example 1. Why ice floats

Ice is less dense than liquid water because its particles form an open structure, so it floats. This is unusual; most substances are denser as solids than as liquids.

Example 2. A car tyre on a hot day

On a hot day the air in a tyre warms, the particles move faster, and the pressure rises, which is why tyre pressures are checked when cold.

Example 3. Hot air balloons

Heating the air in a balloon makes its particles spread out, lowering the density of the air inside below that of the cooler air outside. The less dense air inside makes the balloon float upward, the same reason a cork floats on water.

Try this

Q1. State the equation for density and a possible unit. [2 marks]

• Cue. $\rho = m/V$; units $\text{g/cm}^3$ or $\text{kg/m}^3$.

Q2. A liquid has a mass of $80\ \text{g}$ and a volume of $100\ \text{cm}^3$. Find its density. [2 marks]

• Cue. $\rho = 80/100 = 0.80\ \text{g/cm}^3$.

Q3. In which state are the particles furthest apart? [1 mark]

• Cue. A gas.