Topic 3: Particle model of matter

Everything around us is built from tiny particles, and the way those particles are arranged and how fast they move explains whether a substance is a solid, a liquid or a gas. This topic uses a simple particle model to make sense of density, heating, melting, boiling and the pressure a gas pushes outwards. Mastering a handful of equations lets you predict how matter behaves when energy is added or removed.

Density and how to measure it

Density tells you how much mass is packed into a given volume. It is calculated with density = mass / volume, where mass is in kilograms (kg), volume is in cubic metres (m^3) and density comes out in kg/m^3. A material with closely packed, heavy particles has a high density, while one with widely spaced particles has a low density. To measure the density of a regular solid, find its mass on a balance and calculate its volume from its dimensions. For an irregular solid, lower it into a measuring cylinder or displacement can full of water; the volume of water pushed aside equals the volume of the object. For a liquid, measure its volume in a cylinder and find its mass by weighing the cylinder full and empty, then subtracting.

The particle model and the three states of matter

The particle model pictures matter as made of tiny particles in constant motion. In a solid the particles are packed tightly in a regular pattern and can only vibrate about fixed positions, so solids keep a fixed shape and volume. In a liquid the particles are still close together but can move past one another, so liquids flow and take the shape of their container while keeping a fixed volume. In a gas the particles are far apart and move quickly in all directions, so a gas has neither fixed shape nor fixed volume and can be compressed. The same number of particles usually takes up the least space as a solid and the most as a gas, which is why density is normally highest in the solid state.

Internal energy

Internal energy is the total energy stored by all the particles inside a substance. It is made up of two parts: the kinetic energy of the moving particles and the potential energy stored in the forces and spacing between them. Heating a substance transfers energy to its particles and raises the internal energy. This either makes the particles move faster, which increases their kinetic energy and raises the temperature, or it breaks the bonds between particles during a change of state, which increases the potential energy without changing the temperature.

Specific heat capacity versus specific latent heat

Specific heat capacity is the energy needed to raise the temperature of 1 kg of a substance by 1 degree Celsius, measured in J/kg per degree C. The energy involved is found from change in thermal energy = mass x specific heat capacity x temperature change. Specific latent heat is different: it is the energy needed to change the state of 1 kg of a substance with no change in temperature, measured in J/kg, and is found from E = m L, where E is energy in joules, m is mass in kilograms and L is the specific latent heat. Specific latent heat of fusion applies to melting or freezing, while specific latent heat of vaporisation applies to boiling or condensing. Worked example: to melt 2 kg of ice with a specific latent heat of fusion of 334000 J/kg, use E = m L = 2 x 334000 = 668000 J, so 668000 joules are needed.

Changes of state as physical changes

Melting, freezing, boiling, evaporating and condensing are all changes of state. They are physical changes, not chemical ones, because no new substance is made and the change can be reversed. The number and type of particles stay exactly the same, so the mass is conserved: if you melt 50 g of ice you get 50 g of water. During a change of state the temperature stays constant even though energy is still being transferred, because that energy goes into breaking or forming the bonds between particles rather than speeding them up. On a heating graph this appears as a flat section where the temperature does not rise while the substance changes state.

Particle motion in gases and gas pressure

In a gas the particles move quickly in random directions and constantly collide with the walls of their container. Each collision pushes on the wall, and the combined effect of billions of collisions creates gas pressure, which acts at right angles to the surface. The temperature of a gas is linked to the average kinetic energy of its particles: heating a gas makes the particles move faster, so they hit the walls harder and more often. If the volume is kept the same, raising the temperature therefore increases the pressure, which is why a sealed container of gas can become dangerous when heated.

Higher tier: pressure and volume

(Higher tier) For a fixed mass of gas kept at a constant temperature, the pressure and volume are inversely related: if you squeeze the gas into a smaller volume the particles hit the walls more often, so the pressure rises. This relationship is written as pressure x volume = constant, or p1 V1 = p2 V2 when comparing two situations. For example, if a gas at a pressure of 100000 Pa occupies a volume of 0.02 m^3 and is squeezed to 0.01 m^3 at the same temperature, the new pressure is (100000 x 0.02) / 0.01 = 200000 Pa. Doing work on a gas by compressing it quickly can also transfer energy to the particles and raise the gas temperature.