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Physics · Particle model of matter

Density of materials

Use \(\rho = m \div V\), explain differences in density using the particle model, and describe how to find the density of regular and irregular solids and liquids (Required Practical 5).

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Warm-up

Answer each one, then check.

  1. 1

    What is the unit of mass in physics calculations?

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    Kilograms (kg)

  2. 2

    How do you find the volume of a cuboid?

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    length \(\times\) width \(\times\) height

  3. 3

    Convert 1 cm³ to m³.

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    \(1 \times 10^{-6}\) m³

  4. 4

    What are the three states of matter?

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    Solid, liquid and gas

  5. 5

    What does displacement mean when finding volume?

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    The volume of water pushed out or the rise in water level

Learning Objectives

  1. 1Recall and apply the equation for density.
  2. 2Explain differences in density between solids, liquids and gases using the arrangement of particles.
  3. 3Describe how to measure the density of regular and irregular solids and of liquids.
  4. 4Convert between g/cm³ and kg/m³.

DENSITY

density \(=\) mass \(\div\) volume \(\rho = \dfrac{m}{V}\)

Density is in kilograms per metre cubed (kg/m³), mass in kilograms (kg) and volume in metres cubed (m³). Mass is conserved when a substance changes state.

Why the Densities Differ

  • Solids

    Particles are packed closely in a regular arrangement: high density.

  • Liquids

    Particles are close but randomly arranged: similar to solids, usually slightly lower.

  • Gases

    Particles are far apart: very low density.

  • Mass is conserved

    When a substance changes state the number of particles is unchanged, so the mass stays the same.

Required Practical 5: Method

Find the density of a solid or liquid.

  1. 1 Mass

    Measure the mass on a balance (for a liquid, subtract the container's mass).
  2. 2 Regular solid: volume

    Measure length, width and height with a ruler or micrometer and use \(V = l \times w \times h\).
  3. 3 Irregular solid: volume

    Lower it into water in a measuring cylinder, or a displacement can; the volume is the rise in water level (or the volume collected).
  4. 4 Liquid: volume

    Read it from a measuring cylinder at eye level.
  5. 5 Calculate

    \(\rho = m \div V\); repeat and find a mean.

Density of a Block

A metal block has a mass of 0.60 kg and a volume of 0.00020 m³. Calculate its density.

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  1. 1 Write the equation \(\rho = m \div V\)
  2. 2 Substitute \(\rho = 0.60 \div 0.00020\)
  3. 3 Answer \(\rho = 3000\) kg/m³

Answer3000 kg/m³

Unit Conversion

A cube of side 4.0 cm has a mass of 512 g. Calculate the density in kg/m³.

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  1. 1 Volume \(4.0^3 = 64\) cm³ \(= 64 \times 10^{-6}\) m³
  2. 2 Mass \(512\) g \(= 0.512\) kg
  3. 3 Density \(0.512 \div (64 \times 10^{-6}) = 8000\) kg/m³

Answer8000 kg/m³ (or 8.0 g/cm³)

Irregular Solid by Displacement

A stone of mass 45 g is lowered into a measuring cylinder. The water level rises from 50 cm³ to 68 cm³. Calculate the density in g/cm³.

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  1. 1 Volume of stone \(68 - 50 = 18\) cm³
  2. 2 Density \(45 \div 18 = 2.5\) g/cm³

Answer2.5 g/cm³ (2500 kg/m³)

Watch Out

Common mistakes.

  • Units

    Convert cm³ to m³ (× 10⁻⁶) and g to kg (÷ 1000) before using kg/m³.

  • Reading volume

    Read the bottom of the meniscus at eye level.

  • Mass conserved

    Density changes with volume, not with mass, when a substance changes state.

Which Floats?

Water has a density of 1000 kg/m³. A block has a mass of 0.80 kg and a volume of 0.0010 m³. Calculate its density and say if it floats.

1. Calculate the density.

2. Compare with water.

A good answer shows: Density \(= 0.80 \div 0.0010 = 800\) kg/m³. This is less than 1000 kg/m³, so it floats.

Can I...?

  1. 1Recall the equation for density.
  2. 2Use correct units.
  3. 3Convert cm³ to m³.
  4. 4Explain density using particles.
  5. 5Describe measuring density of a regular solid.
  6. 6Describe measuring density of an irregular solid.
  7. 7Read a measuring cylinder.
  8. 8Say why mass is conserved.

Summary & Exam Focus

  • \(\rho = m \div V\).
  • Solids and liquids have close particles: high density; gases: far apart, low density.
  • Mass is conserved in changes of state.
  • Volume of an irregular object: use displacement.

Exam focus

A metal block has a mass of 0.60 kg and a volume of 0.00020 m³. Calculate its density. (2 marks) (2 marks)

Substitute and include kg/m³.

Key terms

The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.

Density
Mass per unit volume of a material.
Displacement
The volume of water moved aside by an object placed in it.
Meniscus
The curved surface of a liquid in a tube.
Regular
A solid with a shape whose volume can be worked out from its dimensions.
Particle model
A model in which matter is made of tiny moving particles.
Conserved
Stays the same in total.

Practice questions

Have a go at each one before you open its answer.

  1. Question 1 Calculate 2 marks

    A block of metal has a mass of 0.60 kg and a volume of 0.00020 m³. Calculate the density of the metal. Use the equation: density = mass ÷ volume

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    Model answer

    \(0.60 \div 0.00020 = 3000\) kg/m³

    Mark scheme

    • Correct substitution — 1 mark
    • 3000 kg/m³ — 1 mark
  2. Question 2 Calculate 4 marks

    A cube has sides of length 4.0 cm and a mass of 512 g. Calculate the density of the cube in kg/m³.

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    Model answer

    \(V = 64\) cm³ = \(6.4 \times 10^{-5}\) m³; \(m = 0.512\) kg; \(\rho = 0.512 \div 6.4 \times 10^{-5} = 8000\) kg/m³

    Mark scheme

    • Volume = 64 cm³ — 1 mark
    • Converts to m³ and kg — 1 mark
    • Correct substitution — 1 mark
    • 8000 kg/m³ — 1 mark
  3. Question 3 Use the diagram 3 marks

    A student measures the volume of a stone using a measuring cylinder. The mass of the stone is 45 g. Use the diagram to calculate the density of the stone in g/cm³.

    A measuring cylinder with water at 50 cm cubed and, with a stone added, at 68 cm cubed.
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    Model answer

    Volume \(= 68 - 50 = 18\) cm³; \(\rho = 45 \div 18 = 2.5\) g/cm³

    Mark scheme

    • Volume of stone = 18 cm³ — 1 mark
    • Correct substitution — 1 mark
    • 2.5 g/cm³ — 1 mark
  4. Question 4 Explain 3 marks

    Explain, in terms of particles, why the density of a gas is much lower than the density of a solid.

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    Model answer

    In a gas the particles are far apart, but in a solid they are packed closely together. The same mass of material occupies a much greater volume in a gas, so the density is lower.

    Mark scheme

    • Particles far apart in a gas — 1 mark
    • Close together in a solid — 1 mark
    • More volume for the same mass so lower density — 1 mark
  5. Question 5 Describe 6 marks

    Describe how to determine the density of an irregularly shaped solid, such as a stone. Your answer should include the apparatus, the measurements and the calculation.

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    Model answer

    See levels-of-response scheme.

    Mark scheme

    • Level 3 (5 to 6 marks): a complete method with a balance to measure mass, a measuring cylinder or displacement can with water, the volume from the change in water level, the calculation of density = mass ÷ volume and a repeat or precaution — 5 to 6 marks
    • Level 2 (3 to 4 marks): a method covering mass and volume but with some detail missing — 3 to 4 marks
    • Level 1 (1 to 2 marks): simple statements about measuring mass or volume — 1 to 2 marks
  6. Question 6 Explain 2 marks

    1.0 kg of ice melts. Explain what happens to the mass and to the density.

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    Model answer

    The mass stays at 1.0 kg because mass is conserved. The density increases because the volume decreases as ice becomes water.

    Mark scheme

    • Mass stays the same (conserved) — 1 mark
    • Density changes because the volume changes — 1 mark

Quick check

  1. The equation for density is...

    1. A\(\rho = V \div m\)
    2. B\(\rho = m \div V\)
    3. C\(\rho = m \times V\)
    4. D\(\rho = m + V\)
    Show answerHide answer

    B: \(\rho = m \div V\)

    Mass divided by volume.

  2. A material has mass 20 kg and volume 4 m³. The density is...

    1. A80 kg/m³
    2. B0.2 kg/m³
    3. C5 kg/m³
    4. D16 kg/m³
    Show answerHide answer

    C: 5 kg/m³

    20 ÷ 4 = 5.

  3. In which state are the particles furthest apart?

    1. ASolid
    2. BLiquid
    3. CThey are all the same
    4. DGas
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    D: Gas

    The particles in a gas are far apart.

  4. The volume of an irregular solid is found by...

    1. Adisplacement
    2. Bweighing it
    3. Cmeasuring its colour
    4. Dheating it
    Show answerHide answer

    A: displacement

    The rise in water level equals its volume.

  5. When a liquid boils, the mass...

    1. Aincreases
    2. Bstays the same
    3. Cdecreases
    4. Dbecomes zero
    Show answerHide answer

    B: stays the same

    Mass is conserved in a change of state.

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