Density of Materials

This lesson covers the concept of density as required by the AQA GCSE Physics specification (4.3.1). Density is a fundamental property of matter that relates the mass of a substance to the volume it occupies. Understanding density is essential for explaining why some objects float and others sink, and for identifying different materials based on their physical properties.

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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. A material with a high density has a lot of mass in a small volume, while a material with a low density has less mass spread over the same volume.

The equation for density is:

density = mass / volume

p = m / V

Where:

• p (the Greek letter rho) = density, measured in kilograms per cubic metre (kg/m3) or grams per cubic centimetre (g/cm3)
• m = mass, measured in kilograms (kg) or grams (g)
• V = volume, measured in cubic metres (m3) or cubic centimetres (cm3)

Exam Tip: You must be able to recall and apply the density equation from memory. It is one of the equations NOT given on the equation sheet, so you must learn it. Remember: density = mass / volume, or p = m / V.

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Units of Density

Density can be expressed in two common sets of units:

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

Converting Between Units

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

For example:

• Water has a density of 1.0 g/cm3 = 1000 kg/m3
• Aluminium has a density of 2.7 g/cm3 = 2700 kg/m3

Exam Tip: In exam calculations, always check what units the question gives you and what units your answer should be in. If the mass is in grams and the volume is in cm3, your answer will be in g/cm3. If the question asks for kg/m3, you must convert.

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Density of Common Materials

Material	Density (kg/m3)	Density (g/cm3)	State
Air	1.2	0.0012	Gas
Hydrogen	0.09	0.00009	Gas
Cork	120	0.12	Solid
Ice	920	0.92	Solid
Water	1000	1.0	Liquid
Aluminium	2700	2.7	Solid
Steel	7800	7.8	Solid
Copper	8900	8.9	Solid
Lead	11340	11.34	Solid
Gold	19300	19.3	Solid
Mercury	13600	13.6	Liquid

Patterns in Density

• Solids generally have the highest densities because particles are closely packed together.
• Liquids have intermediate densities — particles are close together but can move past one another.
• Gases have the lowest densities because particles are widely spaced and move freely.
• Ice is less dense than water — this is unusual and explains why ice floats on water. In ice, the water molecules form an open crystalline structure with spaces between them.

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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 — particles packed more tightly together mean greater density.

graph LR
    subgraph Solid["Solid (High Density)"]
        S1["O O O O"]
        S2["O O O O"]
        S3["O O O O"]
    end
    subgraph Liquid["Liquid (Medium Density)"]
        L1["O  O  O"]
        L2[" O  O  O"]
        L3["O  O  O"]
    end
    subgraph Gas["Gas (Low Density)"]
        G1["O      O"]
        G2["   O      "]
        G3["O      O"]
    end

    style Solid fill:#3498db,color:#fff
    style Liquid fill:#2ecc71,color:#fff
    style Gas fill:#e74c3c,color:#fff

In the diagram above:

• In a solid, particles are packed closely in a regular arrangement — high density.
• In a liquid, particles are close but arranged randomly — slightly lower density than the solid (in most cases).
• In a gas, particles are widely spaced and move randomly — very low density.

Exam Tip: When explaining density differences using the particle model, you must refer to the spacing between particles (not the size of particles). A common mistake is to say gas particles are "smaller" — they are the same size, just further apart.

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Rearranging the Density Equation

You need to be able to rearrange the density equation to find any of the three quantities:

To Find	Formula
Density	p = m / V
Mass	m = p x V
Volume	V = m / p

Worked Example 1

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

Step 1: Write down the known values: m = 540 g, V = 200 cm3

Step 2: Use the equation: p = m / V

Step 3: Substitute: p = 540 / 200

Step 4: Calculate: p = 2.7 g/cm3

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

Worked Example 2

A gold bar has a density of 19300 kg/m3 and a volume of 0.0005 m3. Calculate its mass.

Step 1: Write down the known values: p = 19300 kg/m3, V = 0.0005 m3

Step 2: Rearrange: m = p x V

Step 3: Substitute: m = 19300 x 0.0005

Step 4: Calculate: m = 9.65 kg

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Floating and Sinking

An object will float in a fluid if its density is less than the density of the fluid. An object will sink if its density is greater than the density of the fluid.

Object	Density (g/cm3)	Water (1.0 g/cm3)	Result
Cork	0.12	Less dense	Floats
Ice	0.92	Less dense	Floats
Steel	7.8	More dense	Sinks
Wood (oak)	0.6	Less dense	Floats

Ships are made of steel, which is denser than water. However, ships float because they are designed to be hollow — the overall density of the ship (steel + air inside) is less than the density of water.

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Common Exam Mistakes

• Forgetting to convert units — mixing g with m3, or kg with cm3.
• Using the wrong formula — confusing density with mass or volume.
• Saying particles are "smaller" in a gas — the particles are the same size, just further apart.
• Forgetting that density = mass / volume is NOT on the equation sheet — you must memorise it.
• Not including the correct units in your final answer.

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Summary

• Density is the mass per unit volume of a substance: p = m / V.
• Density is measured in kg/m3 or g/cm3.
• To convert g/cm3 to kg/m3, multiply by 1000.
• Solids generally have the highest density, gases the lowest.
• Density differences are explained by how closely packed the particles are.
• An object floats if its density is less than the density of the fluid it is placed in.
• You must be able to recall the density equation — it is not given on the exam equation sheet.

Exam Tip: A common 3-mark calculation question will ask you to calculate density, mass, or volume. Always show your working clearly: write the formula, substitute the values, calculate, and include units. Even if your final answer is wrong, you can gain marks for correct working.

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Further Worked Examples

Worked Example 3: Finding Volume

A quantity of mercury has a mass of 2.72 kg and a density of 13 600 kg/m3. Calculate the volume occupied by the mercury.

Step 1: State the known values: m = 2.72 kg, p = 13 600 kg/m3.

Step 2: Rearrange the equation for volume: V = m / p.

Step 3: Substitute: V = 2.72 / 13 600.

Step 4: Calculate: V = 2.0 x 10^-4 m3 (or 200 cm3).

Step 5: Sanity-check the answer — mercury is very dense, so a small volume is expected for roughly 2.7 kg. The answer is reasonable.

Worked Example 4: Identifying an Unknown Material

A cube of unknown metal has sides of length 2.0 cm and a mass of 71.2 g. Identify the metal using the density table above.

Step 1: Volume of cube: V = 2.0 x 2.0 x 2.0 = 8.0 cm3.

Step 2: Density: p = m / V = 71.2 / 8.0 = 8.9 g/cm3.

Step 3: Match to the table: 8.9 g/cm3 corresponds to copper.

Common mistake: Students often substitute the length of one side into the equation instead of the volume. For a cube, you must cube the side length before dividing mass by volume. A missing cube on the side length is one of the most frequent calculation errors in this topic.

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Why Ice Floats: A Particle-Model Case Study

Ice has a density of 920 kg/m3, but liquid water has a density of 1000 kg/m3. This is highly unusual — for most substances, the solid form is denser than the liquid. The reason lies in the structure of the water molecule and the hydrogen bonds between molecules.

• In liquid water, the molecules are free to move past one another and pack fairly closely.
• When water freezes, each molecule forms hydrogen bonds with four neighbours, locking the molecules into a regular open crystalline lattice.
• The lattice contains hexagonal gaps, so the molecules in ice are actually further apart on average than in liquid water.
• More spacing between the same molecules means lower mass per unit volume — so ice is less dense than water and floats.

This effect is important for aquatic ecosystems. Because ice floats, a layer of ice forms on top of ponds and lakes in winter, insulating the liquid water beneath and allowing fish and other organisms to survive.

Common mistake: Students sometimes claim that "water expands when frozen because the particles get bigger." The particles (water molecules) do not change size — the arrangement becomes more open, so the spacing increases. It is the arrangement that changes, not the particles themselves.

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Answering at different grade levels

Exam-style question (4 marks): "A student measures a block of brass. It has a mass of 42 g and dimensions 2.0 cm by 1.5 cm by 1.4 cm. Calculate the density of the brass in kg/m3 and explain why brass sinks in water."

Grade 4–5 answer: Volume = 2 x 1.5 x 1.4 = 4.2 cm3. Density = mass / volume = 42 / 4.2 = 10 g/cm3. Brass sinks because it is denser than water.

Grade 8–9 answer: Using p = m / V, the volume is V = 2.0 x 1.5 x 1.4 = 4.2 cm3, giving p = 42 / 4.2 = 10 g/cm3. Converting to SI units, p = 10 x 1000 = 10 000 kg/m3. The density of water is 1000 kg/m3, and since the brass has a density ten times greater, it will sink when placed in water. The particle-model explanation is that brass atoms are closely packed in a regular metallic lattice and are individually much more massive than water molecules, so the same volume of brass contains far more mass than the same volume of water. The upthrust from the water is less than the weight of the brass, so the block sinks. A common misconception is that "heavy objects sink" — in fact, it is the density (not mass alone) that determines whether an object floats or sinks; a large ship made of dense steel can still float because its overall density (including the air inside) is less than that of water.

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AQA alignment: This content is aligned with AQA GCSE Physics (8463) specification section 4.3 Particle model of matter — specifically 4.3.1.1 Density of materials and 4.3.1.2 Changes of state (link to particle arrangement). Assessed on Paper 1.