Density and the Particle Model of Matter
Density is mass per unit volume, calculated as density = mass / volume, and it is determined by how heavy a substance's particles are and how closely they are packed, which the particle model explains for solids, liquids and gases. Internal energy is the total kinetic and potential energy of the particles, and heating a substance either raises its temperature or, at constant temperature, changes its state by breaking the bonds between particles.
Before you start
No specific prerequisites - this is a good place to start.
Method
- Use density = mass / volume, and rearrange as mass = density x volume or volume = mass / density. Keep the units consistent: grams with cubic centimetres, or kilograms with cubic metres.
- Measure volume by the right method: a regular solid by measuring its dimensions and multiplying, an irregular solid by displacement in a measuring cylinder or eureka can, and a liquid by pouring it into a measuring cylinder and reading at eye level from the bottom of the meniscus.
- Explain a density difference between states by referring to spacing, not to the mass of individual particles: the particles in a gas are far apart, so the same number of particles occupies a much larger volume, giving a much lower density.
- For change of state questions, remember temperature stays constant during melting and boiling: the energy supplied is doing work to break the bonds between particles rather than increasing their kinetic energy, which is why a heating graph has a flat section.
- Use energy for a change of state = mass x specific latent heat, choosing the latent heat of fusion for melting or freezing and the latent heat of vaporisation for boiling or condensing.
- State that mass is conserved in a change of state: no particles are lost, so the mass of the liquid formed equals the mass of the solid melted, and the change is reversible because no new substance is formed.
Worked example
A metal block has a mass of 240 g. Placed in a measuring cylinder containing 50 cubic centimetres of water, the level rises to 80 cubic centimetres. Calculate the density of the metal in grams per cubic centimetre and in kilograms per cubic metre.
- Find the volume by displacement: 80 - 50 = 30 cubic centimetres.
- Write the equation: density = mass / volume.
- Substitute: 240 / 30 = 8 grams per cubic centimetre.
- Convert to kilograms per cubic metre: 1 gram per cubic centimetre is 1000 kilograms per cubic metre.
- Multiply: 8 x 1000 = 8000 kilograms per cubic metre.
- Sense check: this is a typical density for a metal such as iron, and it is far greater than the 1000 kilograms per cubic metre of water, which is consistent with the block sinking.
Practice questions
Try each question, then tap to reveal the answer.
Q1State the equation for density.Show answer
Answer: Density = mass / volume.
Q2Calculate the mass of 0.5 cubic metres of a material of density 2400 kilograms per cubic metre.Show answer
Answer: Mass = density x volume = 2400 x 0.5 = 1200 kg.
Q3Why is the density of a gas much lower than that of the same substance as a liquid?Show answer
Answer: The particles are much further apart, so the same mass occupies a far greater volume.
Q4Why is melting described as a physical change?Show answer
Answer: No new substance is formed, the mass is unchanged and the change can be reversed by cooling.
Q5Why does the temperature stay constant while a substance boils?Show answer
Answer: The energy supplied is used to break the bonds between the particles rather than to increase their kinetic energy.
Q6Define specific latent heat of fusion.Show answer
Answer: The energy needed to change one kilogram of a substance from solid to liquid with no change in temperature.
Q7Convert a density of 2.7 grams per cubic centimetre into kilograms per cubic metre.Show answer
Answer: 2.7 x 1000 = 2700 kilograms per cubic metre.
Exam-style questions
Written in the style of a GCSE Science exam paper, with a full mark scheme.
Describe how a student could determine the density of a small regular cube of wood, and explain one source of inaccuracy.
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A student heats a beaker of crushed ice at a steady rate and plots temperature against time. Explain the shape of the graph up to the point at which the water boils.
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Free printable worksheet
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This topic is chapter 20 of GCSE Physics Workbook, the whole course as one free printable PDF.
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