Particle Model & Density
The Particle Model of Matter
All matter is made up of tiny particles (atoms or molecules) that are constantly moving. The particle model (also called kinetic theory) explains the behaviour of solids, liquids, and gases by considering how these particles are arranged and how they move.
In a solid, particles are held in a fixed, regular arrangement by strong forces of attraction between them. The particles vibrate about fixed positions but cannot move from place to place. This is why solids have a definite shape and a definite volume.
In a liquid, the particles are still close together but are no longer in a fixed pattern. They can slide over and past one another, which is why liquids can flow and take the shape of their container. Liquids have a definite volume but no fixed shape.
In a gas, particles are far apart with almost no forces of attraction between them. They move randomly at high speeds in all directions, constantly colliding with each other and with the walls of their container. Gases have no fixed shape and no fixed volume — they spread out to fill whatever space is available.
Solid: particles in a fixed regular arrangement, vibrating about fixed positions, very close together. Liquid: particles close together but irregularly arranged, able to slide past each other. Gas: particles widely spaced, moving randomly at high speeds.
What Is Density?
Density tells you how much mass is packed into a given volume. A dense material has a lot of mass in a small space; a less dense material has the same volume but less mass. The equation for density is:
$$\rho = \frac{m}{V}$$
where \(\rho\) (the Greek letter rho) is density in kilograms per cubic metre (kg/m\(^3\)), \(m\) is mass in kilograms (kg), and \(V\) is volume in cubic metres (m\(^3\)). Density can also be expressed in grams per cubic centimetre (g/cm\(^3\)).
For example, if a block of aluminium has a mass of 2.7 kg and a volume of 0.001 m\(^3\): \(\rho = \frac{2.7}{0.001} = 2700\) kg/m\(^3\). This means every cubic metre of aluminium contains 2700 kg of material.
Density = mass ÷ volume, or \(\rho = \frac{m}{V}\). Units: kg/m\(^3\) or g/cm\(^3\). You must be able to recall and rearrange this equation.
Density and States of Matter
The differences in density between solids, liquids, and gases can be explained using the particle model. In solids, particles are packed closely together in a regular arrangement, so there is a lot of mass in a small volume — giving solids a high density. In liquids, particles are still close together (though slightly further apart than in solids), so liquids have a similar density to solids, often just slightly lower.
In gases, particles are far apart with large gaps between them. The same number of particles occupies a much larger volume, so gases have a much lower density than solids or liquids. For example, the density of liquid water is about 1000 kg/m\(^3\), but the density of water vapour (steam at 100 \(^{\circ}\)C) is only about 0.6 kg/m\(^3\) — roughly 1600 times less dense.
Water is unusual because its solid form (ice) is less dense than its liquid form. When water freezes, the particles arrange themselves into a crystalline structure with gaps, making ice about 9% less dense than liquid water. This is why ice floats. Most other substances are denser as solids than as liquids.
Core Practical: Measuring Density
You need to know how to investigate the density of both regular and irregular solids, and of liquids.
Regular solid (e.g. a metal block): Use a balance to measure its mass in grams. Use a ruler or vernier calipers to measure its dimensions (length, width, height) and calculate the volume using \(V = l \times w \times h\). Then use \(\rho = \frac{m}{V}\) to calculate density.
Irregular solid (e.g. a pebble): Measure the mass on a balance. Fill a measuring cylinder with a known volume of water, lower the solid gently into the water, and record the new volume. The volume of the solid equals the rise in water level (new volume minus original volume). This is called the displacement method. Then use \(\rho = \frac{m}{V}\).
Liquid: Place an empty measuring cylinder on a balance and zero it (or record its mass). Pour in a known volume of liquid and record the mass. Then use \(\rho = \frac{m}{V}\).
When using a measuring cylinder, always read the volume at the bottom of the meniscus with your eye level with the liquid surface to avoid parallax error. Ensure irregular solids are fully submerged and that no air bubbles are trapped. For regular solids, measure each dimension in at least two places and take an average to reduce the effect of irregularities.
A metal cube has sides of 2.0 cm and a mass of 63.2 g. Calculate its density in g/cm\(^3\).
Volume \(= 2.0 \times 2.0 \times 2.0 = 8.0\) cm\(^3\).
Density \(= \frac{63.2}{8.0} = 7.9\) g/cm\(^3\).
This is close to the density of iron (7.87 g/cm\(^3\)), so the cube is likely made of iron or steel.
To measure the density of an irregular solid: (1) measure its mass on a balance, (2) use the displacement method with a measuring cylinder to find its volume, (3) calculate \(\rho = \frac{m}{V}\).
Watch your units carefully. If mass is in grams and volume in cm\(^3\), density will be in g/cm\(^3\). If mass is in kg and volume in m\(^3\), density will be in kg/m\(^3\). To convert g/cm\(^3\) to kg/m\(^3\), multiply by 1000.
Summary
The particle model explains the properties of solids, liquids, and gases in terms of particle arrangement and movement. Density is mass per unit volume (\(\rho = m/V\)). Solids and liquids have high densities because particles are close together; gases have low densities because particles are far apart. The core practical requires you to measure density using mass balances, rulers, and displacement methods.