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P6.1 Density

GCSE Combined Science · AQA · Chapter P6: Molecules and Matter

A free GCSE Combined Science: Trilogy lesson for AQA (8464) from OBA School: mass per unit volume, units and conversions, why solids, liquids and gases differ, floating and sinking. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

  • Define density and use ρ = m / V with the correct units (kg/m³ or g/cm³)
  • Convert between g/cm³ and kg/m³ and between cm³ and m³, using standard form
  • Rearrange the equation to find the mass (m = ρ V) or the volume (V = m / ρ)
  • Describe how to measure the density of a regular solid, an irregular solid and a liquid
  • Explain differences in density using the particle model, and decide whether an object floats or sinks in water

Key words

  • Density (ρ): The mass per unit volume of a substance. A dense material packs a lot of mass into a small space.
  • Mass (m): The amount of matter in an object, measured in kilograms (kg) with a balance.
  • Volume (V): The amount of space an object takes up, measured in m³ (or cm³).
  • Displacement: Finding the volume of an object from the rise in water level when it is put under water.
  • Meniscus: The curved surface of a liquid in a narrow tube. Read the scale at the bottom of a water meniscus.
  • Resolution: The smallest change a measuring instrument can show, e.g. 1 mm for a metre rule.

What density means

Two objects can be the same size but have very different masses. A cube of lead is much heavier than a cube of cork with the same volume. We say lead has a greater density. Density is the mass per unit volume of a substance.

density = mass ÷ volume ρ = m / V

ρ = density in kilograms per metre cubed (kg/m³)

m = mass in kilograms (kg)

V = volume in metres cubed (m³)

Rearranged: m = ρ V and V = m / ρ

Worked example: a marble floor tile

A marble floor tile is 0.30 m long, 0.30 m wide and 0.020 m thick. Its mass is 4.86 kg. Calculate its density.
V = 0.30 × 0.30 × 0.020 = 0.0018 m³
ρ = m / V = 4.86 ÷ 0.0018

Answer: 2700 kg/m³

Worked example: the mass of air in a sports hall

A sports hall is 20 m × 12 m × 5.0 m. The density of air is 1.2 kg/m³. Calculate the mass of air in the hall.
V = 20 × 12 × 5.0 = 1200 m³
m = ρ V = 1.2 × 1200 = 1440 kg

Answer: about 1400 kg (2 s.f.) – as much as a small car!

Units, conversions and standard form

In the lab, masses are often in grams and volumes in cm³, so density comes out in g/cm³. To use SI units you must convert:

  • mass; Conversion 1 kg = 1000 g; Standard form 1 g = 1 × 10⁻³ kg
  • length; Conversion 1 m = 100 cm; Standard form 1 cm = 1 × 10⁻² m
  • volume; Conversion 1 m³ = 100 × 100 × 100 cm³ = 1 000 000 cm³; Standard form 1 cm³ = 1 × 10⁻⁶ m³
  • density; Conversion 1 g/cm³ = 1000 kg/m³; Standard form multiply g/cm³ by 1000

Worked example: converting a volume and a density

(a) A drinks can holds 330 cm³. Write this in m³. 330 × 10⁻⁶ = 3.3 × 10⁻⁴ m³
(b) Copper has a density of 8.9 g/cm³. In kg/m³: 8.9 × 1000 = 8900 kg/m³

Answer: 3.3 × 10⁻⁴ m³ and 8900 kg/m³

Worked example: the volume of some petrol (always work in kg and m³)

What volume does 0.37 kg of petrol take up? Density of petrol = 740 kg/m³.
V = m / ρ = 0.37 ÷ 740 = 0.000 50 m³

Answer: 5.0 × 10⁻⁴ m³ (= 500 cm³)

Exam tip: A cube 1 m along each side is 100 cm × 100 cm × 100 cm. That is why 1 m³ is a million cm³, not a hundred.

Measuring the density of a solid

Mass: use an electronic balance. Check it reads zero before you put the object on it.

Volume of a regular solid (cube or cuboid): measure the length, width and height and multiply them. Choose an instrument with a suitable range and resolution.

  • metre rule (mm scale); Typical resolution 1 mm; Good for lengths from a few cm up to 1 m
  • vernier callipers; Typical resolution 0.1 mm; Good for small blocks and diameters up to about 15 cm
  • micrometer; Typical resolution 0.01 mm; Good for very small thicknesses, e.g. wire or foil, up to about 25 mm

Volume of an irregular solid (e.g. a stone): use displacement. Part-fill a measuring cylinder with water and read the volume. Lower the object in on a thread until it is fully under water, then read the volume again. The object’s volume is the rise in the reading. (For bigger objects, use a eureka (displacement) can and collect the water that overflows.)

Worked example: the stone in the diagram

Mass of stone = 48.6 g. Volume = 78.0 − 60.0 = 18.0 cm³
ρ = 48.6 ÷ 18.0 = 2.7 g/cm³

Answer: 2.7 g/cm³ = 2700 kg/m³

Measuring the density of a liquid

Measure a volume of the liquid in a measuring cylinder. Find the mass of an empty beaker, pour in the liquid, then find the mass of the beaker and liquid. The mass of liquid is the difference. (Or put the empty beaker on the balance and press “tare” to zero it.)

Worked example: sea water

Volume of sea water = 120 cm³. Mass of empty beaker = 58.6 g. Mass of beaker + sea water = 181.6 g.
Mass of sea water = 181.6 − 58.6 = 123.0 g
ρ = 123.0 ÷ 120 = 1.025 g/cm³

Answer: 1.025 g/cm³ = 1025 kg/m³ – a little denser than pure water

Floating and sinking

The density of pure water is 1000 kg/m³ (1.0 g/cm³). An object with a density less than this floats in water; an object with a greater density sinks. The closer an object’s density is to water’s, the lower it floats.

Key fact: Density is a property of the material, not the size. Cutting a block of wood in half halves its mass and its volume, so its density stays the same.

Why densities differ. Solids and liquids are usually about 1000 times denser than gases, because their particles are packed closely together while gas particles are far apart. Among solids, the mass of each particle also matters: lead atoms are only a little bigger than lithium atoms but have about 30 times the mass, so lead is far denser. Air is denser than hydrogen because nitrogen and oxygen molecules are heavier than hydrogen molecules.

Common mistakes

  • Dividing volume by mass. Density = mass ÷ volume; check the unit (kg/m³ is kg divided by m³).
  • Converting cm³ to m³ by dividing by 100. You must divide by 1 000 000 (10⁶). Saying “lighter” when you mean “less dense”.
  • Forgetting to subtract the beaker’s mass when finding the mass of a liquid.
  • Reading a measuring cylinder from above or below, or at the top of the meniscus, instead of at eye level at the bottom of the meniscus.

Revision questions

Try these, then check your answers below each one.

Question 1. Which statement is the definition of density? (Choose from: Mass per unit volume, Volume per unit mass, Weight per unit area, Mass multiplied by volume.)

Answer: Mass per unit volume

Working: Density is mass per unit volume, ρ = m ÷ V, measured in kg/m³.

Question 2. The diagram shows a block of plastic and its mass. Calculate the density of the plastic.

Answer: 2200 kg/m³

Working: V = 0.25 × 0.10 × 0.040 = 0.0010 m³. ρ = m ÷ V = 2.2 ÷ 0.0010 = 2200 kg/m³.

Question 3. The diagram shows four solid blocks, A to D, and their densities, next to a tank of water. When put in the water, which block will float with the largest fraction of its volume under the surface? (Choose from: A, B, C, D.)

Answer: C

Working: B (1080 kg/m³) and D (2300 kg/m³) are denser than water, so they sink. A and C float. C (940 kg/m³) is closer to 1000 kg/m³, so about 94% of it is under water, compared with 65% for A.

Related lessons

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This lesson is section P6.1 (AGCSC3501) of our free GCSE Combined Science course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Combined Science course.

 

 

 

 

 

 

 

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