Density

This lesson covers the concept of density as required by the AQA GCSE Combined Science Trilogy specification (8464, section 6.3.1). Density links the mass of a substance to the volume it occupies and is essential for understanding why some objects float and others sink.

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What Is Density?

Density is defined as the mass per unit volume of a substance. It tells you how much matter is packed into a given space.

$\rho = \frac{m}{V}$ρ=Vm​

Symbol	Quantity	Unit
$\rho$ρ (rho)	Density	kilograms per cubic metre (kg/m³) or grams per cubic centimetre (g/cm³)
$m$m	Mass	kilograms (kg) or grams (g)
$V$V	Volume	cubic metres (m³) or cubic centimetres (cm³)

Exam Tip: The density equation is one of the equations you must recall from memory — it is NOT given on the AQA equation sheet. Make sure you can write it from memory: $\rho = m / V$ρ=m/V.

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Rearranging the Density Equation

You must be able to rearrange the equation to find any quantity:

To find	Formula
Density	$\rho = \frac{m}{V}$ρ=Vm​
Mass	$m = \rho \times V$m=ρ×V
Volume	$V = \frac{m}{\rho}$V=ρm​

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Units and Conversions

Quantity	SI Unit	Alternative Unit
Mass	kg	g
Volume	m³	cm³
Density	kg/m³	g/cm³

• To convert from g/cm³ to kg/m³, multiply by 1000.
• To convert from kg/m³ to g/cm³, divide by 1000.

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Typical Densities of Common Materials

Material	Density (kg/m³)	Density (g/cm³)	State
Air	1.2	0.0012	Gas
Cork	120	0.12	Solid
Ice	920	0.92	Solid
Water	1000	1.0	Liquid
Aluminium	2700	2.7	Solid
Iron/Steel	7800	7.8	Solid
Copper	8900	8.9	Solid
Gold	19 300	19.3	Solid

Key patterns:

• Solids generally have the highest density (particles closely packed).
• Liquids have intermediate density.
• Gases have the lowest density (particles far apart).
• Ice is less dense than water — this is unusual. In ice, water molecules form an open crystalline structure with gaps.

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The Particle Model and Density

The density of a material depends on:

1. The mass of each particle — heavier particles mean greater density.
2. How closely packed the particles are — tighter packing means greater density.

This is why solids are generally denser than liquids, and liquids are denser than gases. The particles are the same, but their spacing differs.

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Worked Example 1

A block of metal has a mass of 540 g and a volume of 200 cm³. Calculate its density.

$\rho = \frac{m}{V} = \frac{540}{200} = 2.7 \text{ g/cm³}$ρ=Vm​=200540​=2.7 g/cm³

The metal is likely aluminium (density = 2.7 g/cm³).

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Worked Example 2

A gold bar has a density of 19 300 kg/m³ and a volume of 0.0005 m³. Calculate its mass.

$m = \rho \times V = 19\,300 \times 0.0005 = 9.65 \text{ kg}$m=ρ×V=19300×0.0005=9.65 kg

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Worked Example 3

A substance has a mass of 3.6 kg and a density of 1200 kg/m³. Calculate its volume.

$V = \frac{m}{\rho} = \frac{3.6}{1200} = 0.003 \text{ m³}$V=ρm​=12003.6​=0.003 m³

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Floating and Sinking

Condition	Result
Object density < liquid density	Object floats
Object density > liquid density	Object sinks
Object density = liquid density	Object is neutrally buoyant

Exam Tip: If a question asks whether an object floats or sinks, calculate or compare its density with the density of the liquid. If the object's density is less than the liquid's density, it floats.

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Common Misconceptions

Misconception	Correction
Heavy objects always sink	It is density, not mass, that determines floating or sinking — a large ship floats because its overall density (including the air inside) is less than water
All solids are denser than all liquids	Not true — cork (solid, 120 kg/m³) is much less dense than mercury (liquid, 13 600 kg/m³)
Density and mass are the same thing	Density is mass per unit volume — a small piece of lead has less mass than a large block of wood, but lead has a higher density

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Summary

• Density = mass per unit volume: $\rho = m / V$ρ=m/V.
• This equation must be recalled from memory for the AQA exam.
• Common units: kg/m³ or g/cm³ (multiply by 1000 to convert g/cm³ to kg/m³).
• Solids are generally the densest, gases the least dense.
• Density determines whether an object floats or sinks.
• The particle model explains density differences: denser materials have particles that are more closely packed or heavier.

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Worked Example 4 — Conversion Between Units

A plastic sample has a density of 0.95 g/cm³. What is its density in kg/m³?

$0.95 \text{ g/cm³} \times 1000 = 950 \text{ kg/m³}$0.95 g/cm³×1000=950 kg/m³

Because 1 g = 0.001 kg and 1 cm³ = $10^{-6}$10−6 m³, the conversion factor is $0.001 / 10^{-6} = 1000$0.001/10−6=1000. A helpful memory aid: the density of water is 1 g/cm³ = 1000 kg/m³, so to go from g/cm³ to kg/m³ you always multiply by 1000.

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Worked Example 5 — Identifying an Unknown Metal

A student measures a cube of unknown metal. Each side is 2.0 cm. The mass is 70.2 g. Use $\rho = m/V$ρ=m/V and the typical densities table to identify the metal.

Volume: $V = 2.0 \times 2.0 \times 2.0 = 8.0 \text{ cm³}$V=2.0×2.0×2.0=8.0 cm³

Density: $\rho = \frac{70.2}{8.0} = 8.78 \text{ g/cm³}$ρ=8.070.2​=8.78 g/cm³

Comparing with the table, 8.9 g/cm³ corresponds to copper. The slight difference (8.78 vs 8.9) is within experimental uncertainty caused by measuring dimensions with a ruler rather than a vernier calliper.

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Worked Example 6 — Mixing Two Liquids

A measuring cylinder contains 100 cm³ of water (density 1.0 g/cm³). 50 cm³ of ethanol (density 0.80 g/cm³) is poured in and the liquids mix completely. What is the density of the mixture? (Assume no volume change on mixing.)

Mass of water: $100 \times 1.0 = 100$100×1.0=100 g Mass of ethanol: $50 \times 0.80 = 40$50×0.80=40 g Total mass: $140$140 g Total volume: $150$150 cm³

$\rho = \frac{140}{150} = 0.93 \text{ g/cm³}$ρ=150140​=0.93 g/cm³

The density of the mixture lies between the two component densities — this is always the case for a well-mixed solution with no volume change.

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