What is density?
Mass is how much matter is in something. Volume is how much space it takes up. Density joins the two: it is the mass in each unit of volume.
ρ = m ÷ V (ρ is the Greek letter "rho").
A cube of iron and a cube of wood of the same size have the same volume, but the iron has much more mass. So iron is denser. The reason is the particles: in iron they are heavier and packed more tightly.
Density is a property of the substance. A small iron nail and a big iron block both have density about 7.9 g/cm³. Cutting a thing in half halves its mass and its volume, so the density stays the same.
Units of density
The SI unit is kilogram per cubic metre (kg/m³). In the lab we often use grams per cubic centimetre (g/cm³), which is the same as g/mL.
- 1 g/cm³ = 1000 kg/m³
- Water ≈ 1 g/cm³ = 1000 kg/m³
- Air ≈ 0.0012 g/cm³ = 1.2 kg/m³
| Substance | Density (g/cm³) |
|---|---|
| Cork | 0.24 |
| Wood (pine) | about 0.5–0.6 |
| Ice | 0.92 |
| Water | 1.00 |
| Aluminium | 2.7 |
| Iron | 7.9 |
| Mercury | 13.6 |
| Gold | 19.3 |
Rearranging: m = ρ × V and V = m ÷ ρ.
Measuring density in the lab
Regular solid (a box shape)
Find mass on a balance. Measure length, width and height with a ruler; V = l × w × h. Then ρ = m ÷ V.
Irregular solid (a stone, a key)
Find mass on a balance. Put water in a measuring cylinder and read the level. Lower the object in gently on a thread. The rise in level is the object's volume (displacement method). 1 mL = 1 cm³.
Liquid
Weigh an empty measuring cylinder. Pour in, say, 50 mL of liquid and weigh again. The difference is the liquid's mass. ρ = m ÷ 50 cm³.
Tips: read the water level at the bottom of the curved surface (the meniscus), at eye level; remove air bubbles; make sure the object is fully under water.
Floating and sinking
- An object floats in a liquid if its density is less than the liquid's density.
- It sinks if its density is more.
- If they are equal, it stays wherever you put it (like a fish or a submarine that has balanced itself).
Liquids that do not mix form layers: the densest at the bottom. Oil (about 0.9 g/cm³) floats on water. Ice (0.92) floats with about nine-tenths under water, which is why most of an iceberg is hidden.
A steel ship floats because it is hollow: its total mass divided by its total volume (steel plus air inside) is less than water's density. Salt water is denser than fresh water, so it is easier to float in the sea.
Density, temperature and uses
When most things are heated they expand: same mass, more volume, so lower density. That is why hot air rises (hot-air balloons) and warm water rises in a pot. Water is special: it is densest at about 4 °C, and ice is less dense than water, so lakes freeze from the top and fish survive below.
Solids are usually densest, then liquids, then gases, because particles are closest in solids.
Uses: checking if a gold ornament is pure; testing milk with a lactometer; checking battery acid or sugar content with a hydrometer; separating plastics for recycling by letting some float and some sink; choosing light, strong materials (aluminium, carbon fibre) for aircraft and bicycles; designing life jackets and ships.
Try it: the float-or-sink test
Collect a coin, an eraser, a grape, a small wood piece and an ice cube. Write your guess (float or sink) for each. Test them in water. Then dissolve 3–4 spoons of salt in the water and test the grape again. What changed, and why? (The salt water is denser.)
Key formulas and definitions
- Density ρ = m ÷ V
- Mass m = ρ × V
- Volume V = m ÷ ρ
- 1 g/cm³ = 1000 kg/m³; 1 mL = 1 cm³; 1 L = 1000 cm³
- Floats if ρ(object) < ρ(liquid); sinks if ρ(object) > ρ(liquid)
Worked examples
1. A block has mass 240 g and volume 100 cm³. Find its density.
ρ = m ÷ V = 240 ÷ 100 = 2.4 g/cm³.
2. Will the block above float or sink in water?
2.4 g/cm³ is more than water's 1 g/cm³, so it sinks.
3. A wooden box is 10 cm × 5 cm × 4 cm and has mass 120 g. Find its density.
V = 10 × 5 × 4 = 200 cm³. ρ = 120 ÷ 200 = 0.6 g/cm³. It floats in water.
4. Water in a measuring cylinder reads 40 mL. A stone of mass 75 g is lowered in and the reading becomes 65 mL. Find the stone's density.
V = 65 − 40 = 25 mL = 25 cm³. ρ = 75 ÷ 25 = 3 g/cm³.
5. Find the mass of 2 m³ of water (density 1000 kg/m³).
m = ρ × V = 1000 × 2 = 2000 kg.
6. Convert 7.9 g/cm³ to kg/m³.
Multiply by 1000: 7.9 × 1000 = 7900 kg/m³.
7. An empty cylinder weighs 60 g. With 50 cm³ of oil it weighs 105 g. Find the oil's density.
Mass of oil = 105 − 60 = 45 g. ρ = 45 ÷ 50 = 0.9 g/cm³.
8. A gold-coloured ring has mass 38.6 g and volume 2.5 cm³. Is it pure gold (19.3 g/cm³)?
ρ = 38.6 ÷ 2.5 = 15.44 g/cm³. This is less than 19.3, so it is not pure gold; it is mixed with a lighter metal.
Common mistakes
- Thinking heavy things always sink. A huge log floats; a tiny pin sinks. Compare density, not mass.
- Thinking a bigger piece of the same material has a bigger density. Mass and volume grow together, so density stays the same.
- Mixing units: dividing grams by m³, or kg by cm³. Put mass and volume in matching units first.
- Reading the displacement volume as the final water level. The volume of the object is the rise: final − initial.