Particle Model: Density, States and the Gas Laws

States of Matter and the Particle Model

The particle model explains the properties of solids, liquids, and gases in terms of particle spacing, movement, and the forces between particles. In a solid, particles are arranged in a regular lattice and can only vibrate; they cannot change position. In a liquid, particles are still close together but can move past one another, which is why liquids flow and take the shape of their container. In a gas, particles are far apart and move quickly in all directions, filling whatever space is available.

When a substance changes state — for example from solid to liquid on melting — energy must be supplied to overcome the forces (bonds) between particles. The particles gain potential energy as they separate, but their kinetic energy — and therefore the temperature — does not rise during the change of state. This is why a temperature–time graph shows a flat plateau while a substance is changing state, even though heat is still being added.

Density

Density describes how much mass is packed into a given volume. The equation is:

$$\rho = \frac{m}{V}$$

where \(\rho\) is density (kg/m³ or g/cm³), \(m\) is mass (kg or g), and \(V\) is volume (m³ or cm³). Solids are generally denser than liquids, and liquids are much denser than gases, because the particles are more closely packed. Water has a density of 1,000 kg/m³ (or 1.0 g/cm³); any object less dense than water will float in it.

Core Practical: Measuring Density

This core practical requires you to measure the density of both regular and irregular solids and liquids. For a regular solid such as a rectangular block, use a ruler to measure length, width, and height, then calculate volume (length × width × height). Use a balance to measure mass. Then apply \(\rho = m/V\).

For an irregular solid, fill a measuring cylinder with water to a known level and record this volume. Carefully lower the solid into the water and record the new water level. The difference between the two readings equals the volume of the solid. This method is sometimes called the displacement method or the Eureka can method when a displacement can is used instead.

For a liquid, measure the mass of an empty container on a balance, then add the liquid and measure the combined mass. Subtract to find the mass of the liquid. Pour the liquid into a measuring cylinder to find its volume. Calculate \(\rho = m/V\).

Internal Energy, Specific Heat Capacity and Latent Heat

The internal energy of a substance is the total kinetic and potential energy of all its particles. When you heat a substance, you increase its internal energy. If the substance is not changing state, the extra energy goes into increasing the kinetic energy of the particles, which we measure as a rise in temperature. The equation is:

$$Q = mc\Delta\theta$$

where \(Q\) is the energy transferred (J), \(m\) is mass (kg), \(c\) is the specific heat capacity (J/kg°C), and \(\Delta\theta\) is the temperature change (°C or K). Water has a specific heat capacity of 4,200 J/kg°C — much higher than most metals — which is why it is used as a coolant and in central heating systems.

The core practical for specific heat capacity (core practical 14.11) involves measuring the temperature change of water as it is heated by an electric immersion heater, recording a temperature–time graph. The same experiment is extended to observe melting ice — showing the flat plateau on the graph where energy is absorbed without a temperature change.

Gas Pressure and the Kinetic Theory

Gas pressure arises because gas particles are constantly moving and colliding with the walls of their container. Each collision exerts a small force on the wall, and the combined effect of billions of collisions per second creates the pressure we measure. If the temperature rises, the particles move faster and hit the walls harder and more often — so pressure increases. If the volume decreases (particles squashed into a smaller space), the particles collide with the walls more frequently — so pressure again increases.

Absolute Zero and the Kelvin Scale

Absolute zero is −273°C. At this temperature, particles would have no kinetic energy and gas pressure would drop to zero. The Kelvin scale uses absolute zero as its starting point: 0 K = −273°C. To convert from Celsius to Kelvin, add 273: \(T(\text{K}) = \theta(\text{°C}) + 273\).

Boyle's Law

For a fixed mass of gas at constant temperature, pressure and volume are inversely proportional. This relationship is Boyle's law:

$$p_1 V_1 = p_2 V_2$$

The kinetic model explains Boyle’s law: compressing the gas into a smaller volume means particles collide with the walls more often per second (shorter distances between collisions), so the pressure rises. Temperature is constant, so particle speed — and therefore force per collision — is unchanged.