Particle Model, Density and Pressure
The Particle Model of Matter
The particle model explains the properties of solids, liquids and gases in terms of how their particles are arranged and how they move. In a solid, particles are held in fixed positions in a regular arrangement by strong forces between them. They vibrate about fixed points but cannot move from place to place — this explains why solids have a fixed shape and a fixed volume.
In a liquid, particles are close together but can slide past each other because the forces between them are weaker than in a solid. Liquids have a fixed volume but take the shape of their container. In a gas, particles are far apart with negligible forces between them. They move rapidly in random directions, colliding with each other and the walls of their container. Gases fill any container and can be compressed because of the large spaces between particles.
In a solid, particles are in fixed positions (vibrating only). In a liquid, particles are close but can flow past each other. In a gas, particles are far apart and move randomly. Gases can be compressed because of the large spaces between particles; solids and liquids cannot.
What Is Density?
Density tells you how much mass is packed into a given volume. A dense material has a large amount of mass in a small volume. The equation is:
$$\rho = \frac{m}{V}$$
Where \(\rho\) is density (\(\text{kg/m}^3\) or \(\text{g/cm}^3\)), \(m\) is mass (kg or g), and \(V\) is volume (\(\text{m}^3\) or \(\text{cm}^3\)). You must be able to rearrange the equation to find mass (\(m = \rho \times V\)) or volume (\(V = \frac{m}{\rho}\)). To convert between units: \(1 \text{ g/cm}^3 = 1000 \text{ kg/m}^3\). A common exam error is failing to convert grams to kilograms before calculating in SI units.
Question: A metal cube has a mass of 216 g and a volume of \(80 \text{ cm}^3\). Calculate its density in \(\text{g/cm}^3\).
Answer: Write the equation: \(\rho = \frac{m}{V}\). Substitute: \(\rho = \frac{216}{80} = 2.7 \text{ g/cm}^3\). This is the density of aluminium. To express in SI units: \(2.7 \text{ g/cm}^3 = 2700 \text{ kg/m}^3\).
Measuring Density (PAG P1)
To measure the density of a regular solid (such as a cuboid), measure its mass on a balance and calculate its volume using a ruler: \(V = l \times w \times h\). For a cylinder, use \(V = \pi r^2 h\). Then apply \(\rho = m/V\).
For an irregular solid (such as a pebble), use a displacement method. Fill a eureka can until water overflows at the spout. Gently lower the object into the water and collect the displaced water in a measuring cylinder — its volume equals the volume of the object. Alternatively, use a measuring cylinder directly: record the initial water level, submerge the object, and measure the new level. The volume of the object equals the rise in water level.
For a liquid, measure the mass of an empty measuring cylinder, pour in the liquid, and measure the total mass. The liquid’s mass is the difference. Read the volume from the graduated scale at the bottom of the meniscus. Apply \(\rho = m/V\).
Density of a regular solid: measure mass and calculate volume using a ruler, then \(\rho = m/V\). Density of an irregular solid: measure mass on a balance, find volume by water displacement (eureka can or measuring cylinder), then apply \(\rho = m/V\). Read the measuring cylinder at the bottom of the meniscus.
Why Densities Differ
The particle model explains why densities differ between states of matter. In solids, particles are closely and regularly packed, giving high density. In liquids, particles are slightly further apart and less ordered, so density is a little lower. In gases, particles are very widely spaced, so density is dramatically lower — typically about a thousand times less than the same substance in liquid form. Crucially, mass is conserved during any change of state: the number of particles does not change, only their arrangement and spacing. When ice melts to water, the same particles are present but occupy a slightly different volume. When water boils to steam, the vast increase in volume means density falls dramatically.
An important exception is water: ice is slightly less dense than liquid water, which is why ice floats. This unusual behaviour occurs because water molecules form an open lattice structure in the solid state, taking up more volume per molecule than in the liquid state.
Pressure in Fluids
Pressure in a gas arises because gas particles constantly collide with the walls of their container, exerting a force on each unit of area. In a liquid or gas (both are fluids), pressure acts in all directions and increases with depth below the surface. The qualitative reason is that a deeper column of fluid has more weight of fluid above it pressing down, increasing the force on any surface at that depth.
For Higher tier, the pressure at a depth in a fluid can be calculated using:
$$p = h \times \rho \times g$$
Where \(p\) is pressure (Pa), \(h\) is the depth of the fluid (m), \(\rho\) is the density of the fluid (\(\text{kg/m}^3\)), and \(g\) is the gravitational field strength (10 N/kg on Earth). This equation shows that pressure increases with depth (greater \(h\)), with denser fluids (greater \(\rho\)), and in stronger gravitational fields. For example, a diver at 10 m depth in sea water (density approximately \(1025 \text{ kg/m}^3\)) experiences a pressure of \(p = 10 \times 1025 \times 10 = 102{,}500 \text{ Pa}\) from the water alone, in addition to atmospheric pressure above.
Worked example: A submarine is at a depth of 200 m in sea water (\(\rho = 1025 \text{ kg/m}^3\)). Calculate the pressure due to the water at this depth. \(p = h\rho g = 200 \times 1025 \times 10 = 2{,}050{,}000 \text{ Pa}\) (or 2.05 MPa). Always state the unit — pascals (Pa) — in the final answer.
Pressure in a gas is caused by particles colliding with the container walls. Heating a gas at constant volume increases particle speed, so collisions become more frequent and more forceful — pressure rises. In a fluid column, pressure increases with depth.
Heating a gas at constant volume increases the kinetic energy of the particles. They move faster, collide with the container walls more frequently, and each collision exerts a greater force. Both effects increase the pressure. This is why sealed containers such as aerosol cans carry warnings about exposure to heat — the rising pressure could exceed the container’s strength and cause it to burst.