# Density

The of an object or substance is its mass divided by its volume:

density = mass ÷ volume

The units of density depend on the units used for mass and volume, but are usually:

• g/cm3 (if mass is measured in g and volume in cm3)

The more dense a substance is, the heavier it feels for its size. The table shows three examples:

SubstanceDensity in g/cm³
Steel7.82
Water1.00
Air0.0013

Notice that the solid (steel) is the most dense, the gas (air) is the least dense, and the density of the liquid (water) is in between.

## Solids

The particles in solids are very close together. They are tightly packed, giving solids high densities.

## Liquids

The particles in liquids are close together. Although they are randomly arranged, they are still tightly packed, giving liquids high densities. The density of a substance as a liquid is usually only slightly less than its density as a solid. For example, the density of solid aluminium is 2.72 g/cm3 and the density of liquid aluminium is 2.38 g/cm3. This means that liquid aluminium floats on top of solid aluminium.

Water is different from most substances: it is less dense as a solid than as a liquid, because its particles move apart slightly on freezing. This is why ice cubes and icebergs float on liquid water.

## Gases

The particles in gases are very far apart, so gases have a very low density.

## Measuring density

You need to know two things to measure the density of a substance:

• the mass of a sample of some of it
• the volume of that sample

The mass is measured using a balance. The volume of a liquid is easily measured using a measuring cylinder. The volume of a solid can be measured by:

• measuring the side of a cube or block of the substance, then using mathematics to calculate its volume, or
• using a displacement can (also called a eureka can) – the sample is lowered into a container of water and the volume of water it displaces or pushes out of the way is the same as the volume of the object