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This lesson covers the concept of density, its definition, the equation linking density to mass and volume, and the practical methods used to measure the density of regular and irregular solids. This is a key topic in the Edexcel GCSE Combined Science specification (1SC0) Particle Model unit.
Density is a measure of how much mass is contained in a given volume. It tells us how tightly packed the particles are in a substance.
$$\rho = \frac{m}{V}$$
| Symbol | Quantity | Unit |
|---|---|---|
| (\rho) (rho) | Density | kilograms per cubic metre (kg/m³) or grams per cubic centimetre (g/cm³) |
| (m) | Mass | kilograms (kg) or grams (g) |
| (V) | Volume | cubic metres (m³) or cubic centimetres (cm³) |
Exam Tip: The Greek letter (\rho) (rho) is used for density — do not confuse it with the letter p. Make sure your handwriting clearly distinguishes the two.
You must be able to rearrange the equation for any of the three quantities:
| To find | Rearrangement |
|---|---|
| Density | (\rho = \frac{m}{V}) |
| Mass | (m = \rho \times V) |
| Volume | (V = \frac{m}{\rho}) |
A useful memory aid is the formula triangle:
graph TD
A["m"] --- B["ρ × V"]
Cover the quantity you want to find:
| Material | Density (kg/m³) | Density (g/cm³) |
|---|---|---|
| Air | 1.2 | 0.0012 |
| Water | 1000 | 1.0 |
| Ice | 917 | 0.917 |
| Aluminium | 2700 | 2.7 |
| Iron/Steel | 7800 | 7.8 |
| Gold | 19 300 | 19.3 |
Exam Tip: You should know that the density of water is 1000 kg/m³ (or 1.0 g/cm³). This is a very commonly used value in calculations.
To convert between the two common density units:
A block of aluminium has a mass of 5.4 kg and a volume of 0.002 m³. Calculate its density.
$$\rho = \frac{m}{V} = \frac{5.4}{0.002} = 2700 \text{ kg/m³}$$
A gold ring has a mass of 19.3 g and a volume of 1.0 cm³. Calculate its density.
$$\rho = \frac{m}{V} = \frac{19.3}{1.0} = 19.3 \text{ g/cm³}$$
For a regularly shaped solid (cuboid, cylinder, sphere):
For an irregularly shaped solid (e.g. a stone, a key), the volume cannot be calculated from dimensions. Instead, use the displacement method:
Alternatively, use a eureka can (displacement can):
graph LR
A["Object placed in eureka can"] --> B["Water displaced through spout"]
B --> C["Volume measured in cylinder"]
C --> D["ρ = m / V"]
Whether an object floats or sinks depends on its density compared with the density of the liquid:
| Condition | Result |
|---|---|
| Object density < liquid density | Object floats |
| Object density > liquid density | Object sinks |
| Object density = liquid density | Object is neutrally buoyant (stays at any depth) |
Exam Tip: A common exam question asks you to explain why ice floats on water. Always state that ice is less dense than water, and link this to the particle arrangement.
A student measures the mass of a stone as 150 g. She places it in a measuring cylinder containing 40 cm³ of water. The water level rises to 98 cm³. Calculate the density of the stone.
Step 1 — Find the volume:
$$V = V_2 - V_1 = 98 - 40 = 58 \text{ cm}^3$$
Step 2 — Calculate density:
$$\rho = \frac{m}{V} = \frac{150}{58} = 2.59 \text{ g/cm}^3 \text{ (to 3 s.f.)}$$
| Misconception | Correction |
|---|---|
| Heavy objects always sink | It depends on density, not just mass — a large ship floats because it has a low average density |
| Density and mass are the same thing | Density is mass per unit volume — two objects can have the same mass but very different densities |
| All metals sink in water | Some metals (e.g. lithium, sodium, potassium) are less dense than water and float |