Density of materials — AQA GCSE Combined Science

This equation defines density ρ as mass m divided by volume V. To use it, measure mass in kilograms or grams and volume in cubic metres or cubic centimetres, then divide. For example, if m = 0.60 kg and V = 0.00020 m³, then ρ = 0.60 kg ÷ 0.00020 m³ = 3000 kg/m³. Rearranged forms are m = ρV and V = m / ρ, which help find mass or volume when density is known. In calculations, keep units consistent: g with cm³ gives g/cm³, and kg with m³ gives kg/m³. The equation applies to solids, liquids and gases, but gas densities are much lower because particles are far apart. A common task is to identify an unknown material by comparing its calculated density with a table of known values.

Density tells you how much mass is packed into each unit of volume. The relationship density = mass / volume means that for a uniform material, dividing the mass in kilograms by the volume in cubic metres gives the density in kilograms per cubic metre. For example, a 2.0 kg block of volume 0.0010 m³ has density 2.0 ÷ 0.0010 = 2000 kg/m³. Rearranged, mass = density × volume and volume = mass ÷ density. In practice you measure mass with a balance and volume by measuring dimensions of a regular solid, or by displacement of water for an irregular solid. The equation applies to a uniform material; a hollow object has a lower average density than the solid material it is made from.

Density is represented by the Greek letter ρ (rho) and its SI unit is the kilogram per cubic metre, written kg/m³. This unit means the mass in kilograms contained in one cubic metre of material. For example, water has a density of about 1000 kg/m³, so 1 m³ of water has a mass of about 1000 kg. A smaller unit, g/cm³, is often used in laboratory work; 1 g/cm³ = 1000 kg/m³. To convert g/cm³ to kg/m³, multiply by 1000; to convert kg/m³ to g/cm³, divide by 1000. Using the correct unit matters because a numerical answer without the correct unit does not fully communicate the density.

Mass measures the amount of matter in an object and is measured in kilograms (kg). In density calculations, mass is the numerator when using ρ = m ÷ V, so a block with mass 2.4 kg and volume 0.003 m³ has density 2.4 ÷ 0.003 = 800 kg/m³. Mass is not the same as weight: weight is a force in newtons and depends on gravitational field strength, whereas mass in kg stays the same everywhere. When recording or using mass, convert grams to kilograms by dividing by 1000, for example 450 g = 0.45 kg. Always label the quantity with its symbol m and its unit kg, and check that the value is reasonable for the object being described.

Volume measures the space occupied by an object and is measured in cubic metres (m³). In density calculations, volume is the denominator when using ρ = m ÷ V, so a block with mass 2.4 kg and volume 0.003 m³ has density 2.4 ÷ 0.003 = 800 kg/m³. For a regular solid, calculate volume from length × width × height, converting each length to metres first. For example, a block 0.10 m × 0.20 m × 0.15 m has volume 0.003 m³. For an irregular solid, use displacement in a measuring cylinder and convert cm³ to m³ by dividing by 1 000 000. Always label volume with V and m³, and check that the value is reasonable for the object.

The particle model pictures a substance as tiny particles with spaces between them. Those spaces and how the particles move explain bulk properties: solids have particles packed in fixed positions, so shape and volume stay constant; liquids have particles close but able to slide, so volume stays constant while shape changes to fit the container; gases have large spaces and fast random motion, so both shape and volume change and gases are compressible. Density follows because density = mass ÷ volume: a gas has the same mass spread through a much larger volume, so its density is far lower. For example, 1 kg of air occupies about 0.8 m³, giving roughly 1.2 kg/m³, whereas 1 kg of water occupies 0.001 m³, giving 1000 kg/m³.

The three states of matter are solid, liquid and gas. In a solid, particles are closely packed in a regular arrangement and vibrate about fixed positions, so the solid has a definite shape and volume. In a liquid, particles are close but randomly arranged and can slide past each other, so the liquid has a definite volume but takes the shape of its container. In a gas, particles are far apart, move quickly and randomly, and fill any container, so a gas has neither definite shape nor definite volume and is compressible. Heating transfers energy to the particles, increasing their kinetic energy; at melting and boiling points the arrangement changes. Density changes between states because the same mass occupies a different volume, as density = mass ÷ volume.

Density is the mass per unit volume of a material, calculated as density = mass ÷ volume, with units such as kg/m³ or g/cm³. Differences in density arise because the same volume of different materials contains different amounts of matter, and because the spacing and arrangement of particles changes between solids, liquids and gases. For example, 1 cm³ of iron has a mass of about 7.9 g, while 1 cm³ of water has a mass of about 1.0 g, so iron is denser. In general, solids are densest because particles are closely packed, liquids are slightly less dense, and gases are much less dense because particles are far apart. Density also changes with temperature for gases and with pressure.

Simple particle diagrams use small circles or dots to represent particles and show how they are arranged in solids, liquids and gases. In a solid, particles are closely packed in a regular arrangement and vibrate about fixed positions. In a liquid, particles are close together but randomly arranged and can slide past one another. In a gas, particles are far apart, randomly arranged and move quickly in all directions. These diagrams model differences in density, shape and volume: solids keep a fixed shape and volume, liquids take the shape of their container but keep a fixed volume, and gases fill their container. Recognising and drawing these diagrams helps explain why gases are much less dense than solids and liquids.

Density is mass per unit volume, ρ = m ÷ V. In a solid, particles are closely packed in a regular arrangement, so a given volume contains many particles and density is high. In a liquid, particles remain close but are arranged randomly and can slide past one another, so density is slightly lower than the solid but still much greater than a gas. In a gas, particles are far apart with large empty spaces, so the same volume contains far fewer particles and density is low. For example, 1 cm³ of water has a mass of about 1 g, while 1 cm³ of steam at atmospheric pressure has a mass of roughly 0.0006 g. Heating usually decreases density because the particles move further apart while the mass stays the same.

In this required practical you determine density using ρ = m ÷ V. For a regular solid such as a rectangular block, measure length, width and height with a ruler, micrometer or Vernier callipers, calculate volume, then measure mass with a balance and divide. For an irregular solid such as a stone, find mass on a balance, then use a displacement technique: record the starting volume of water in a measuring cylinder, lower the object in fully, and record the new volume; the volume of the object is the difference. For a liquid, measure the mass of an empty measuring cylinder, add a known volume of liquid, measure the new mass, and divide the mass of the liquid by its volume. Repeat readings and calculate a mean to reduce random error.