Density of materials

Density is mass per unit volume:

$\rho = \dfrac{m}{V}$

• $\rho$ in kg/m³ (or g/cm³).
• $m$ in kg (or g).
• $V$ in m³ (or cm³).

Rearranged: $m = \rho V$ and $V = m/\rho$.

Density of common materials

• Water: 1000 kg/m³ (= 1 g/cm³).
• Air: ~1.2 kg/m³.
• Iron: 7800 kg/m³.
• Gold: 19 300 kg/m³.

If a substance is denser than water, it sinks; if less dense, it floats. (For solids, this is exact; for fluids, it's the same idea.)

Why solids and liquids have similar densities

Particles in solids and liquids are tightly packed — there is no big "empty" space between them. A solid is only slightly denser than its liquid form because the regular lattice packs slightly tighter than the random arrangement in a liquid. Water is famously the opposite — ice floats because its lattice has gaps.

Why gases have low density

Particles in gases are very far apart compared to their size. A litre of air has roughly the same number of molecules as a millilitre of water — but spread through 1000 times the volume.

Required practical 5 — measuring density

Regular solid (cube/cuboid):

1. Use a ruler/calipers to measure dimensions; calculate $V = l \times w \times h$.
2. Use a balance for $m$.
3. $\rho = m/V$.

Irregular solid:

1. Use a balance for $m$.
2. Lower into a measuring cylinder/eureka can with water; measure displaced volume.
3. $\rho = m/V$.

Liquid:

1. Place an empty measuring cylinder on a balance; tare to zero.
2. Pour in a known volume of liquid; record mass.
3. $\rho = m/V$.

Conversions

• 1 g/cm³ = 1000 kg/m³.
• 1 cm³ = 1 × 10⁻⁶ m³.
• 1 mL = 1 cm³.