P3 Particle model of matter

Density tells you how much mass is packed into each unit of volume.

The particle model explains why different states of matter have different densities. In a solid, particles are closely packed in a regular pattern, and in a liquid they are still touching but randomly arranged. Because the particles are close together, solids and liquids have similar and high densities.

In a gas, the same particles are spread much further apart and move randomly in all directions. Because the same mass fills a far larger volume, the density of a gas is much lower (often about 1000 times lower).

Density: ρ = m ÷ V, so density = mass ÷ volume.

Density (ρ) is usually measured in kg/m³, which requires mass in kg and volume in m³.

If you are given mass in g and volume in cm³, the density will be in g/cm³. To convert from g/cm³ to kg/m³, multiply by 1000.

In the solid and the liquid the particles are touching, so a lot of mass fits into each cubic metre. In the gas the particles are far apart and moving in random directions, so the same space holds much less mass.

A 2.5 kg block of metal has a volume of 0.00080 m³. What is its density?

Use ρ = m ÷ V

ρ = 2.5 ÷ 0.00080 = 3125 kg/m³

Mass is conserved when a substance changes state (melts or boils). The volume changes, which means the density changes, but the mass stays exactly the same.

Heavier objects do not always have a higher density. Density depends on both mass and volume.

When a substance expands (like a gas being heated), its particles do not get bigger; they just spread further apart. This increases the volume and decreases the density.

A change of state is a physical change: reversing it gives back the original material with its original properties. Mass is conserved because the particles are only rearranged.

Internal energy is the total kinetic energy (from motion) and potential energy (from position) of all the particles in a system.

Heating a system transfers energy to its particles. This energy can do one of two things:

1. Increase the temperature: the particles gain kinetic energy and move faster.

2. Change the state: the temperature stays the same, but the potential energy of the particles increases as the forces between them are overcome.

Each arrow shows a change of state. Sublimating turns a solid straight into a gas without a liquid stage.

Water vapour from the air condenses into droplets on a cold can of drink. The temperature of the water stays the same while it condenses. What happens to the internal energy of the water?

The temperature is constant, so the average kinetic energy of the particles does not change.

As the gas becomes a liquid, the water transfers energy to the cold can and the potential energy of its particles decreases.

So the internal energy of the water decreases.

Temperature and internal energy are not the same thing. Temperature is linked to the average kinetic energy of the particles; internal energy is the total energy of all of them.

Particles themselves do not melt, boil or expand. The substance changes state because its particles are arranged and move differently.

Evaporation happens only at the surface of a liquid, below its boiling point; boiling happens throughout the liquid at the boiling point.

The temperature rise when something is heated depends on its mass, the material and the energy supplied.

Latent heat is the energy needed for a change of state. During a change of state the energy transferred changes the internal energy (the potential energy of the particles) but not the temperature.

Specific latent heat is the energy needed to change the state of 1 kg of a substance with no change in temperature. The specific latent heat of fusion is for solid ↔ liquid; the specific latent heat of vaporisation is for liquid ↔ gas.

Energy for a change of state: E = mL, so energy for a change of state = mass × specific latent heat.

Energy (E) is in joules (J), mass (m) in kilograms (kg) and specific latent heat (L) in J/kg.

Heating curve for 0.10 kg of ice warmed by a 200 W heater. The sloping parts show a temperature rise within one state; the flat parts show melting at 0 °C and boiling at 100 °C. Boiling lasts far longer because vaporisation needs much more energy per kilogram than fusion.

Use the heating curve. Melting lasts from 42 s to 209 s. Calculate the specific latent heat of fusion of water.

Time spent melting = 209 − 42 = 167 s

Energy supplied = power × time = 200 × 167 = 33 400 J

L = E ÷ m = 33 400 ÷ 0.10 = 334 000 J/kg

A flat part of a heating graph does not mean the heater is off: the energy is increasing the potential energy of the particles, not the temperature.

Specific heat capacity (J/kg °C) is for a temperature change; specific latent heat (J/kg) is for a change of state. Use ΔE = mcΔθ for sloping parts and E = mL for flat parts.

Convert grams to kilograms before using E = mL.

Gas molecules move constantly and randomly. They travel in straight lines between collisions, in all directions, at a wide range of speeds.

Gas temperature is directly linked to the molecules' average kinetic energy. Higher temperature means higher average kinetic energy, so the molecules move faster on average.

Gas pressure is caused by molecules constantly colliding with the walls. Each collision exerts a tiny force.

Heating a gas in a sealed, rigid container increases its pressure. The molecules gain kinetic energy and move faster on average. They hit the walls more frequently and with greater force per collision, increasing the total force and pressure. Cooling the gas has the opposite effect.

The gas particles move in random directions. Each collision with the container wall exerts a small force on it; together these forces cause the gas pressure.

A football is pumped up indoors and then taken outside on a frosty morning. Its volume stays the same. Explain why the pressure of the air inside the ball decreases.

The air inside the ball cools, so the average kinetic energy of its molecules decreases.

The molecules move more slowly on average, so they hit the inside of the ball less often and with less force.

A smaller total force on the walls means a lower pressure.

Molecules do not expand or get bigger when heated; only their speed increases.

Gas pressure is caused by molecules colliding with the container walls, not with each other.

Remember that the molecules move at a range of speeds, not just one single speed.

This practical finds the density of a regular solid, an irregular solid and a liquid by measuring mass and volume.

1. Regular solid: Measure the mass using a top-pan balance. Measure the length, width and height with a ruler (or Vernier callipers/micrometer for small dimensions) and multiply them together to find the volume.

2. Irregular solid: Measure the mass. Fill a displacement (eureka) can up to the spout. Lower the object in gently on a thread and collect the displaced water in a measuring cylinder. This volume is the volume of the object.

3. Liquid: Place an empty measuring cylinder on a balance and zero (tare) it. Pour in a measured volume of the liquid and read the mass directly from the balance.

Density = mass ÷ volume (ρ = m ÷ V).

Mass is measured in grams (g) or kilograms (kg). Volume is measured in cm³ or m³ (1 cm³ is the same as 1 ml).

A ruler has a resolution of 1 mm, Vernier callipers 0.1 mm, and a micrometer 0.01 mm.

Hazards: wipe up spills straight away so nobody slips, and lower heavy objects gently so they do not crack the glassware.

The object on the thread pushes water out of the spout into the measuring cylinder. The volume of displaced water equals the volume of the object.

Wait for the displacement can to stop dripping before you put the measuring cylinder under the spout, and again before you read it.

Read the measuring cylinder at eye level from the bottom of the meniscus to avoid parallax error.

Trapped air bubbles on the object make the volume reading too large, which makes the calculated density too low.

To convert a density from g/cm³ to kg/m³, multiply by 1000.