Particle theory & states of matter

What you will learn

the five statements of the particle model of matter,
how particle arrangement and motion explain solids, liquids and gases,
how the particle model explains melting, boiling, evaporation, condensation and sublimation,
how to calculate density using $\rho = m/V$ ,
how the particle model explains diffusion, gas pressure, and expansion on heating.

Worked example 0 Real-world example: why does a balloon shrink in the freezer?

A party balloon is fully inflated at room temperature ( $25$ °C). After 30 minutes in the freezer ( $-15$ °C) it looks half-deflated.

The number of gas particles inside is unchanged — the balloon is still sealed.
Cooling slows the particles down: they collide with the rubber wall less often and with less force.
Outside air pressure, unchanged, now pushes the balloon inward more than the inside gas pushes out.
The balloon shrinks until the pressures balance.

Key idea: gas pressure comes from particles hitting the container walls. Temperature controls how hard and how often they hit.

1. The particle model

The particle model makes five claims:

All matter is made of tiny particles (atoms or molecules).
Particles are in constant motion.
Particles have forces of attraction between them.
Particles have spaces between them.
The higher the temperature, the faster the particles move.

2. Solids, liquids and gases

Particle arrangement in the three common states. Dots represent particles; arrows show motion.

Property	Solid	Liquid	Gas
Shape	Fixed	Takes container	Fills container
Volume	Fixed	Fixed	Variable
Particle spacing	Very close	Close	Far apart
Particle motion	Vibrate on spot	Slide past each other	Move freely, fast
Compressible?	No	Barely	Yes, easily

3. Changes of state

Adding or removing heat changes the energy of particles and can change the state.

Melting (solid → liquid): particles gain enough energy to break the regular arrangement.
Freezing (liquid → solid): particles slow and settle into the lattice.
Evaporation / boiling (liquid → gas): particles escape attractive forces.
Condensation (gas → liquid): particles slow and re-attract.
Sublimation (solid → gas directly, e.g. dry ice, naphthalene): particles escape the lattice straight to gas.

Worked example 1 Reading a heating curve

Ice at $-10$ °C is heated steadily. Describe what happens to the temperature as it is heated.

From $-10$ to $0$ °C: temperature rises (ice warms).
At $0$ °C: temperature stays constant while ice melts. All energy goes into breaking the solid lattice.
From $0$ to $100$ °C: temperature rises (liquid water warms).
At $100$ °C: temperature stays constant while water boils to steam.
Above $100$ °C (sealed system only): steam warms further.

Key idea: during a state change, heat added goes into rearranging particles, not into raising temperature.

4. Density

Density is mass per unit volume — how tightly packed matter is.

Density

Definition

\rho = \dfrac{m}{V}

where $\rho$ is density, $m$ is mass, $V$ is volume.

Typical units

g/cm $^3$ for solids and liquids in labs.
kg/m $^3$ for engineering.
Water: $1$ g/cm $^3 = 1000$ kg/m $^3$ .

Worked example 2 Density of a rock

A rock has mass $240$ g and, when lowered into a measuring cylinder, displaces $80$ cm $^3$ of water. Find its density.

\rho = \dfrac{m}{V} = \dfrac{240}{80} = 3.0 \text{ g/cm}^3.

The rock is denser than water ( $1.0$ g/cm $^3$ ), so it sinks.

Worked example 3 Floating and sinking

Oil has density $0.92$ g/cm $^3$ ; water has $1.00$ g/cm $^3$ ; honey has $1.4$ g/cm $^3$ .

If all three are poured into a glass, they separate: honey at the bottom, water in the middle, oil on top. Dense things sink; less dense things float.

Key idea: floating/sinking is decided by density, not by weight. A huge log floats; a small iron nail sinks.

5. Diffusion, pressure and expansion

Diffusion: particles spread from where they are crowded to where they are not (smell of cooking filling a house).
Gas pressure: gas particles collide with container walls; more collisions (or harder collisions) = higher pressure.
Expansion on heating: particles move faster and take up slightly more space; bridges, railway tracks and power lines all include expansion joints.

Worked example 4 Why tyres are checked cold

Car tyre pressure is specified “cold” (before driving).

Driving heats the tyre; gas particles move faster.
Faster particles hit the tyre walls harder and more often.
Pressure rises — up to $10\%$ in hot weather.
A tyre that reads “correct” when hot is actually under-inflated when cold.

Key idea: in a sealed container, pressure rises with temperature because particle collisions become more energetic.

Practice: Year 7

Fluency

Tier 1: recall and identify

State the five statements of the particle model.
Describe the spacing and motion of particles in a solid, liquid and gas.
Name the state change for each: (a) solid → liquid, (b) gas → liquid, (c) solid → gas directly.
What does density measure? Give its formula.
A block has mass $120$ g and volume $40$ cm $^3$ . Find its density.
Water has density $1.0$ g/cm $^3$ . Will a substance with density $0.8$ g/cm $^3$ float or sink in water?
Define diffusion. Give one everyday example.
Why does a balloon shrink in a freezer?
Why does a bridge have expansion joints?
A liquid turns to gas below its boiling point. What is this process called?

Reasoning

Tier 2: explain and reason

Explain, using the particle model, why gases can be compressed but liquids cannot.
Explain why heat added during melting does not raise the temperature.
A drop of food colouring added to still water spreads out over hours. Explain using particle motion.
Why does hot air rise? Link to density.
A student says “when steel is heated, its atoms get larger.” Correct this statement using the particle model.
Using the particle model, explain why a gas fills its container completely while a liquid does not.

Problem solving

Tier 3: apply to a novel context

A metal cube has side $3$ cm and mass $216$ g. Find the density. Is it likely aluminium ( $2.7$ g/cm $^3$ ) or iron ( $7.9$ g/cm $^3$ )?
A liquid of mass $500$ g has volume $625$ mL. Find its density in g/cm $^3$ (recall $1$ mL $=1$ cm $^3$ ). Would it float or sink on water?
A sealed bottle of air is left in a hot car. Explain, using the particle model, why it may burst.
Compare the energy transfer when $100$ g of water at $0$ °C is warmed to $10$ °C with when $100$ g of ice at $0$ °C melts to water at $0$ °C. Which change requires more energy? Why?

Challenge

Reasoning

Harder reasoning

Ice is less dense than liquid water (which is unusual). Explain using the particle model why water expands on freezing, and give one environmental consequence of this.
A pressure cooker cooks food faster than an open pot. Explain using the particle model why increasing the pressure raises the boiling point of water.
A hydrogen balloon and an identical helium balloon are released at the same time. Explain using particle theory which rises faster and why.
A diver surfaces too fast from a deep dive and gets “the bends” — nitrogen bubbles form in the blood. Explain using gas pressure and dissolving behaviour.

Answers

Answer key

Attempt the practice first. When you're ready to check, expand the answers below.

Show the full answer key

Year 7 answers

Fluency

Tier 1: recall and identify

(i) All matter is made of tiny particles. (ii) Particles are in constant motion. (iii) Particles have forces of attraction between them. (iv) Particles have spaces between them. (v) Higher temperature means faster motion.
Solid: particles touching, arranged regularly, vibrating on the spot. Liquid: particles touching, disordered, sliding past. Gas: particles far apart, moving fast and randomly.
(a) Melting. (b) Condensation. (c) Sublimation.
Density is mass per unit volume. Formula: $\rho = m/V$ .
$\rho = 120/40 = 3.0$ g/cm $^3$ .
Float — it is less dense than water.
Diffusion is the spreading of particles from high to low concentration. Example: the smell of perfume spreading through a room.
Cooling slows the gas particles, reducing collisions with the wall. Outside pressure pushes the balloon inward until the pressures balance.
Expansion joints allow the bridge materials to expand in heat and contract in cold without cracking.
Evaporation.

Reasoning

Tier 2: explain and reason

Gases have large spaces between particles that can be squeezed closer. Liquid particles are already touching, so there is almost no space left to compress.
During melting, the heat energy goes into breaking the forces holding the solid lattice, rearranging particles rather than speeding them up. Speed — and therefore temperature — stays constant.
Dye particles collide randomly with water particles, gradually spreading from the crowded area into less crowded water until evenly distributed.
Heated air particles move faster and spread apart, so hot air has lower density than the cooler air around it. Denser cool air sinks beneath, pushing hot air up.
Atoms do not change size. Heating makes them vibrate more, increasing the average spacing between them, which makes the whole object larger.
Gas particles move fast with large spaces and negligible attractive forces, so they spread to fill any container. Liquid particles still attract each other, so they stay together at the bottom while taking the container’s shape.

Reasoning

Tier 3: apply to a novel context

Volume = $3^3 = 27$ cm $^3$ . Density = $216/27 = 8.0$ g/cm $^3$ . Close to iron ( $7.9$ g/cm $^3$ ), not aluminium.
Density = $500/625 = 0.8$ g/cm $^3$ . Less dense than water, so it floats.
The car’s interior heats the trapped air. Particles move faster and hit the bottle walls harder and more often, raising pressure. If the pressure exceeds the bottle’s strength, it bursts.
Warming $100$ g of water by $10$ °C transfers energy into faster motion. Melting $100$ g of ice transfers energy into breaking all the solid-lattice bonds. Melting requires considerably more energy because bond-breaking is “expensive” — this is why ice is so effective for cooling drinks.

Reasoning

Challenge

Liquid water particles have weak but flexible bonds. When freezing, water molecules form a hexagonal crystal with more empty space than in the liquid — so ice is less dense. Consequence: lakes freeze from the top down, insulating water below and allowing fish to survive winter.
A sealed pressure cooker traps steam, raising the gas pressure above the water. Higher external pressure makes it harder for water particles to escape as vapour, so water must reach a higher temperature before it boils — around $120$ °C. Hotter water cooks food faster.
Hydrogen particles have smaller mass than helium, so at the same temperature they move faster (same kinetic energy, lower mass means higher speed). The hydrogen balloon has lower density than helium and rises faster. (Hydrogen is also flammable — one reason helium is used in practice.)
At depth, high water pressure dissolves more nitrogen from the breathing air into the blood. Surfacing drops the pressure rapidly; dissolved nitrogen comes out of solution as bubbles in blood vessels, blocking flow. Slow ascents allow nitrogen to be exhaled gradually.

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