Density and the Particle Model

What density tells us

A block of wood and a metal block can have the same volume but very different masses. The metal block usually has more mass packed into that volume, so it has a greater density. Density therefore connects two measurements: mass and volume.

Density is defined as mass per unit volume:

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

Here, $\rho$ is density in kilograms per metre cubed (kg/m³), $m$ is mass in kilograms (kg), and $V$ is volume in metres cubed (m³). “Per cubic metre” means the mass that each cubic metre of the material would have.

The equation can also be rearranged:

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

For a uniform material, a larger sample has more mass and more volume in the same proportion, so its density remains the same. Density is not simply another word for mass: a small, dense object may have less mass overall than a large, less dense object.

Matter as particles

The particle model treats matter as being made from tiny particles, which may be atoms or molecules. It is a model: the circles used in a drawing are not life-sized pictures, but they help us represent particle arrangement and movement.

The particles are the substance itself; they are not separate objects embedded in an otherwise continuous material. The spaces in a particle diagram represent space between particles.

Solids, liquids and gases

In a solid, particles are very close together in a regular arrangement. They vibrate about fixed positions but do not move past one another. This explains why a solid keeps a fixed shape and volume and is very difficult to compress.

In a liquid, particles are also close together, but their arrangement is irregular. They can move past neighbouring particles, so a liquid flows and takes the shape of the bottom of its container. Because there is very little empty space between its particles, a liquid is also difficult to compress and keeps an approximately fixed volume.

In a gas, particles are widely separated and move randomly in all directions. A gas therefore has no fixed shape or volume: it spreads out to fill its container. The large spaces between particles also mean that a gas can be compressed.

A good particle diagram should therefore show:

• a solid with equal-sized particles close together in ordered rows;
• a liquid with equal-sized particles close together but irregularly arranged;
• a gas with equal-sized particles far apart and randomly arranged.

Using arrangement to explain density

Density depends on how much mass is present in a particular volume. If the particles have the same mass, a volume containing more particles has more mass and therefore a greater density.

Particles in solids and liquids are close together, so solids and liquids commonly have much greater densities than gases. Their densities can also be fairly similar because changing between solid and liquid often causes a much smaller change in particle spacing than changing into a gas.

Gas particles are much farther apart. The same mass of substance therefore occupies a much greater volume in the gas state. Since $\rho=m/V$, increasing the volume while keeping the mass constant reduces the density considerably.

State alone does not give the exact density: density also depends on the substance and the masses and arrangement of its atoms or molecules. It is therefore unsafe to claim that every solid is denser than every liquid. Even for one substance, exceptions occur; ice is less dense than liquid water because freezing produces an unusually open particle arrangement.

Density when state changes

During a change of state in a closed system, mass is conserved: particles are rearranged, not created or destroyed. If the volume changes while the mass stays constant, the density changes. For example, when a fixed mass of liquid becomes a gas, its particles spread much farther apart and occupy a larger volume, so the gas has a lower density.

This is how the equation and particle model work together: the equation describes the change mathematically, while the particle arrangement explains why the volume—and therefore the density—changes.

Density

Recall:

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

• $\rho$: density in kg/m³