Density and states of matter
What you'll learn
- How the particle model explains solids, liquids and gases.
- How to recall and use the density equation, ρ=mV\rho = \frac{m}{V}ρ=Vm.
- How to measure the density of solids and liquids in the core practical.
- Why changes of state conserve mass and are physical changes.
Matter is made of particles
Matter is anything that has mass and takes up space. In GCSE Physics, we often explain matter using a simple particle model: we imagine materials as being made of tiny particles.
A particle means a tiny unit of matter, such as an atom (a single chemical building block) or a molecule (a group of atoms joined together).
Kinetic theory
Kinetic theory is the idea that particles in matter are always moving, and that the way they move and are arranged explains the properties of solids, liquids and gases.
The diagram below shows the key differences in particle arrangement and movement in the three states of matter.
The three states of matter
Solids
In a solid, particles are close together in a fixed, usually regular, arrangement. They cannot move from place to place, but they do vibrate about fixed positions.
This explains why solids have:
- a fixed shape
- a fixed volume
- very little compressibility, meaning they are hard to squash into a smaller volume
Liquids
In a liquid, particles are still close together, but they are arranged randomly. They can move around and slide past each other.
This explains why liquids:
- have a fixed volume
- take the shape of the bottom of their container
- are difficult to compress
Gases
In a gas, particles are far apart and move quickly in random directions.
This explains why gases:
- have no fixed shape
- have no fixed volume
- spread out to fill their container
- are easy to compress
Using the particle model to compare compressibility
Why can a gas be compressed much more easily than a liquid?
- In a gas, the particles are far apart, so there is a lot of empty space between them.
- When the gas is compressed, the particles are pushed closer together, mainly reducing the empty space rather than squashing the particles themselves.
- In a liquid, the particles are already close together, so there is very little empty space to reduce. This makes liquids difficult to compress.
Particle model headline
The state of a substance depends on how its particles are arranged and how they move.
Density: how much mass is packed into a volume
Mass is a measure of how much matter an object contains. It is measured in kilograms, kg.
Volume is the amount of three-dimensional space an object or substance takes up. It is measured in cubic metres, m³.
Density
Density is the mass per unit volume of a substance. A dense material has a lot of mass packed into a small volume.
The symbol for density is ρ\rhoρ, pronounced “rho”. You need to recall and use this equation:
ρ=mV\rho = \frac{m}{V}ρ=Vmwhere:
- ρ\rhoρ is density in kilograms per cubic metre, kg/m³
- mmm is mass in kilograms, kg
- VVV is volume in cubic metres, m³
Calculating density from mass and volume
A block has a mass of 2.40 kg and a volume of 0.00080 m³. Calculate its density.
- Choose the density equation because you are given mass and volume: ρ=mV\rho = \frac{m}{V}ρ=Vm.
- Substitute the values with units: ρ=2.40 kg0.00080 m3\rho = \frac{2.40\ \text{kg}}{0.00080\ \text{m}^3}ρ=0.00080 m32.40 kg.
- Calculate the division: ρ=3000 kg/m3\rho = 3000\ \text{kg/m}^3ρ=3000 kg/m3.
Unit sanity check
If mass is in kilograms and volume is in cubic metres, your density answer will be in kg/m³. In school practical work you may also use grams per cubic centimetre, g/cm³.
Forgetting to convert volume
Centimetres cubed are much smaller than metres cubed. If the question asks for kg/m³, do not leave the volume in cm³.
Core practical: investigating density
In the core practical, you need to measure the density of solids and liquids. The main idea is always the same:
- Measure the mass.
- Measure or calculate the volume.
- Use ρ=mV\rho = \frac{m}{V}ρ=Vm.
The diagram below shows useful methods for finding volume for a regular solid and an irregular solid.
Density of a regular solid
A regular solid has a simple shape, such as a cube or cuboid.
For a cuboid, measure its length, width and height using a ruler or calipers, then calculate:
V=L×W×HV = L \times W \times HV=L×W×HThen measure its mass using a balance and calculate density.
Density of an irregular solid
An irregular solid has a shape that is difficult to measure with a ruler, such as a stone. Use water displacement:
- Measure the mass of the object using a balance.
- Put water in a measuring cylinder and record the initial volume.
- Lower the object fully into the water.
- Record the final volume.
- The object’s volume is the final volume minus the initial volume.
Using displacement to find density
A stone has a mass of 56.3 g. The water level in a measuring cylinder rises from 60 mL to 90 mL when the stone is submerged. Calculate the density of the stone.
- Find the volume displaced by the stone: V=90 mL−60 mL=30 mLV = 90\ \text{mL} - 60\ \text{mL} = 30\ \text{mL}V=90 mL−60 mL=30 mL. Since 1 mL=1 cm31\ \text{mL}=1\ \text{cm}^31 mL=1 cm3, the volume is 30 cm³.
- Use density equals mass divided by volume: ρ=56.3 g30 cm3\rho = \frac{56.3\ \text{g}}{30\ \text{cm}^3}ρ=30 cm356.3 g.
- Calculate the density: ρ=1.88 g/cm3\rho = 1.88\ \text{g/cm}^3ρ=1.88 g/cm3. If needed in kg/m³, this is 1880 kg/m³.
Density of a liquid
To find the density of a liquid:
- Measure the mass of an empty measuring cylinder.
- Add a known volume of liquid.
- Measure the mass of the cylinder plus liquid.
- Subtract to find the mass of the liquid.
- Use ρ=mV\rho = \frac{m}{V}ρ=Vm.
Good practical technique
Read the measuring cylinder at eye level and use the bottom of the meniscus, which is the curved surface of the liquid.
Including the container mass
For a liquid, the balance measures the container and the liquid together. You must subtract the empty container’s mass to get the liquid’s mass.
Why density changes between states
The density of a substance depends on how closely packed its particles are.
In solids, particles are usually very close together, so solids are often dense. In liquids, particles are also close together, so liquids usually have similar densities to solids, although often slightly lower. In gases, particles are far apart, so gases have much lower densities.
Explaining why a gas has a lower density
Steam is water as a gas. Liquid water is much denser than steam. Explain why using particles.
- The particles in liquid water are close together, so a given volume contains many particles and therefore more mass.
- The particles in steam are much farther apart, so the same volume contains fewer particles.
- Since density is mass divided by volume, the steam has less mass in the same volume and therefore a lower density.
Not every solid is denser than every liquid
Ice floats on water because solid ice has a structure with more gaps than liquid water. The particle model still explains this: lower density means the same mass takes up more volume.
Changes of state and conservation of mass
A change of state is when a substance changes between solid, liquid and gas without becoming a new substance.
The main changes of state are:
- melting: solid to liquid
- freezing: liquid to solid
- evaporating: liquid to gas from the surface
- boiling: liquid to gas throughout the liquid
- condensing: gas to liquid
- sublimating: solid directly to gas
Mass is conserved
Mass is conserved means the total mass stays the same, as long as no material enters or leaves the system.
When a substance changes state, the particles are rearranged and move differently, but the particles themselves are still the same. No atoms disappear. No new atoms are made.
That means melting, freezing, evaporating, boiling, condensing and sublimating are physical changes. In a physical change, no new substance is formed, and the original properties can be recovered if the change is reversed.
For example, water can freeze to ice and then melt back to water. It is still water.
A chemical change is different because new substances are formed. Some chemical changes are difficult to reverse, and reversing the conditions does not necessarily recover the original material.
Conservation of mass during evaporation
A sealed container contains liquid water. Some of the water evaporates into water vapour. What happens to the total mass?
- The container is sealed, so no water particles can escape from the system.
- During evaporation, liquid water particles become gas particles, but they are still water particles.
- The total mass stays the same because the same particles are still inside the container.
Thinking evaporated mass has vanished
If water evaporates from an open beaker, the mass measured in the beaker may decrease because water vapour has escaped into the room. The mass has not been destroyed.
In the exam
- For particle-model explanations, always link the property to both arrangement and movement of particles.
- For density calculations, write the equation, substitute with units, then calculate. Check whether the answer should be in kg/m³ or g/cm³.
- For changes of state, say that mass is conserved in a closed system because the particles are the same; only their arrangement and motion change.
Check yourself
- Why can a gas be compressed more easily than a liquid?
- A metal cube has mass and side length given in cm. What steps would you take to find its density in kg/m³?
- What is the difference between a physical change of state and a chemical change?
