Particle model of matter – GCSE Combined Science Physics

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Watch an ice cube sitting in a pan on the cooker. At first it is a hard solid. Then it turns to water, and after a while the water bubbles and turns into steam, which is a gas that you cannot see.

It is the same stuff all the way through, which is water. What changes is how the tiny particles inside it are arranged, how close they are and how fast they move. A particle is a very small piece of matter, such as an atom or a molecule, and everything around you is made of them.

Picture a school hall. In a solid the particles are like students sitting in neat rows, shaking a little in their seats. In a liquid they are like a crowd in the corridor at break, close together but sliding past each other, and in a gas they are like runners spread out across a huge field, dashing about in all directions.

This picture is called the particle model, and it helps to explain a lot. It explains why things have different densities, why they change state when heated, how much energy that takes and why a gas pushes on its container. You will also use it to do some short calculations, so keep a calculator ready.

By the end you will be able to do three things. You will describe solids, liquids and gases using the particle model, and calculate density from mass and volume. You will also calculate the energy needed to heat something up or to melt or boil it, and explain gas pressure in terms of collisions.

Solids, liquids and gases

In a solid the particles are packed close together in a regular pattern, and strong forces hold them in place. They cannot move around, but they do vibrate, which means they shake back and forth on the spot. A solid keeps its shape and its volume, and it does not flow, which is why you can pick up a brick.

In a liquid the particles are still close together and touching, but they are not in a regular pattern. They can move past each other, which is why a liquid flows and takes the shape of its container. A liquid has a fixed volume, because the particles are still packed close, and it is hard to squash, which is why hydraulic brakes use liquid.

In a gas the particles are far apart, with a lot of empty space between them, and they move quickly in random directions. There are almost no forces holding them together, so a gas spreads out to fill any container. A gas has no fixed shape and no fixed volume, and it is easy to compress, which means squash into a smaller space.

The arrangement explains the density, which is how much mass is packed into each unit of volume. A solid or a liquid has particles close together, so a lot of mass fits in a small space. A gas has particles far apart, so the same space holds very little mass, and that is why a gas is much less dense.

You can draw a particle diagram for each state. For a solid, draw small circles touching in neat rows. For a liquid, draw circles that touch but are jumbled, with no pattern. For a gas, draw a few circles far apart with plenty of empty space between them.

When a substance changes state, the particles are the same. Nothing new is made and nothing is lost, so the mass stays the same. This is why we call it a physical change. If you reverse the change, the material recovers its original properties. Water that is frozen and melted again is still water. Burning is different, because it makes new substances.

Density and the density practical

Density tells you how heavy something is for its size. A bag of feathers and a bag of the same size filled with stones have the same volume, but the stones have a lot more mass. We say that the stones are more dense, because more mass is packed into each cubic centimetre.

In words: density = mass ÷ volume. In symbols: ρ = m ÷ V, where ρ is the Greek letter rho, m is mass and V is volume. Use it whenever you are given a mass and a volume and asked how dense something is, or how heavy a certain volume will be.

The units depend on what you put in. If the mass is in grams (g) and the volume is in cubic centimetres (cm³), the density is in g/cm³. If the mass is in kilograms (kg) and the volume is in cubic metres (m³), the density is in kg/m³, and 1 g/cm³ is the same as 1000 kg/m³.

To find the density of a regular solid, such as a block, measure its mass on a balance. Measure the length, width and height with a ruler. For a thin or small object, use a micrometer or Vernier callipers, which measure much more precisely than a ruler. Then volume = length × width × height, and density = mass ÷ volume.

For an irregular solid, such as a stone, find the mass on a balance first. Then lower the stone into a displacement can that is filled to the spout, and catch the water that is pushed out in a measuring cylinder. You can also put the stone into a measuring cylinder of water and see how far the level rises. The volume of water moved is the volume of the stone. Read the scale at eye level.

For a liquid, put a measuring cylinder on a balance and note its mass. Pour in some liquid, read the volume at eye level and note the new mass. The mass of the liquid is the new mass minus the mass of the empty cylinder. Then density = mass ÷ volume. Repeat the test and find the mean.

Water has a density of 1 g/cm³. An object that is denser than water sinks, and one that is less dense floats. A steel ship floats because its overall shape contains lots of air. In a change of state the mass is conserved but the volume changes, so the density changes. One kilogram of water that freezes gives one kilogram of ice, but ice takes up more space, so ice is less dense and floats.

Changes of state

There are names for each change of state. A solid turns to a liquid by melting, and a liquid turns to a solid by freezing. A liquid turns to a gas by boiling or evaporating, and a gas turns back to a liquid by condensing, which is what happens to steam on a cold window. A few substances go straight from a solid to a gas. This is called sublimation, as with dry ice.

When you heat a substance, the particles gain energy and move faster, so the temperature rises. At the melting point the particles have enough energy to break free from their fixed places, so the solid melts. At the boiling point they have enough energy to break free from each other completely, and the liquid boils.

Look at the heating curve. The line rises while the substance is just getting hotter. Then it goes flat during melting and during boiling, even though you are still heating it at the same rate.

The temperature stays the same on the flat parts because the energy is being used to change the state, not to speed the particles up. When the change is finished, the temperature starts to rise again. We will see in a later step where that energy goes, and why it is so important.

Cooling curves are the reverse. As a gas cools, its temperature falls. It goes flat while the gas condenses, falls again as the liquid cools, and goes flat again while the liquid freezes. During the flat parts the substance is giving energy out to the surroundings.

The mass does not change in a change of state. If you melt 100 g of ice, you get 100 g of water, because the particles are still there. This is conservation of mass, and it is a good thing to say in an exam answer when you are asked what happens to the mass.

Internal energy and specific heat capacity

Energy is stored inside a system by its particles, which are the atoms and molecules that make it up. This is called internal energy. It is the total of the kinetic energy and the potential energy of all of the particles. Kinetic energy is movement energy, and potential energy is the energy stored because of the positions of the particles and the forces between them.

Heating a system increases the energy of its particles. This either raises the temperature or produces a change of state. When the temperature rises, the particles gain kinetic energy and move faster.

How much the temperature rises depends on three things: the mass of the substance, the type of material and the energy put in. The specific heat capacity is the energy needed to raise the temperature of 1 kg of the substance by 1 °C, and each substance has its own value.

In words: energy = mass × specific heat capacity × temperature change. In symbols: E = m × c × Δθ, where Δθ means the change in temperature. The units are joules (J) for energy, kilograms (kg) for mass, J/kg °C for specific heat capacity and °C for temperature change.

Water has a high specific heat capacity of 4200 J/kg °C, which means it takes a lot of energy to warm it up. That is why the sea stays cool on a sunny day, long after the sand is too hot to walk on. Metals have low values, so they heat up quickly, which is why a metal spoon in hot soup gets hot fast, and why a pan is made from metal.

Do not leave out the temperature change when you calculate. Work out the change by taking the starting temperature from the final temperature, and write down the unit, which is the joule for energy. The equation also works for cooling, and then it gives the energy released. You can measure a specific heat capacity with a heater and a metal block, as in the practicals lesson.

Specific latent heat

Energy is also needed to change the state of a substance. This energy is called latent heat. When a change of state happens, the energy supplied changes the internal energy but not the temperature. The specific latent heat is the energy needed to change the state of 1 kg of a substance with no change in temperature.

It has two types. The specific latent heat of fusion is for a change between solid and liquid. The specific latent heat of vaporisation is for a change between liquid and gas. In words: energy = mass × specific latent heat. In symbols: E = m × L. The unit of L is J/kg, so change grams into kilograms before you start.

During melting or boiling the energy goes into the potential energy of the particles. The particles are pulled free from their neighbours, and the kinetic energy stays the same, which is why the temperature stays the same. Think of lifting a ball up a staircase, where energy is stored in the ball but the ball is not moving any faster.

It takes much more energy to boil water than to melt ice. Boiling pulls the particles completely apart and pushes the air out of the way, so the specific latent heat of vaporisation is much bigger than that of fusion. For water they are about 2 260 000 J/kg and 330 000 J/kg.

When a gas condenses or a liquid freezes, the same amount of energy is given back out. This is why steam burns can be so bad, because the steam releases a lot of energy as it condenses on your skin. Remember to use the right value of L for the change you are asked about, because fusion and vaporisation are very different.

Do not mix up c and L. Specific heat capacity, c, is for a temperature change, E = m × c × Δθ. Specific latent heat, L, is for a change of state with no temperature change, E = m × L. On a heating graph, the sloping parts are where c is used, and the flat parts are where L is used.

You can measure the specific latent heat of fusion of water with a heater. Put crushed ice in two funnels over two beakers. Switch a heater on in one funnel, and leave the other as a control to show how much ice melts by itself. After a set time, measure the mass of water in each beaker. The extra water in the heated beaker was melted by the heater, so L = energy supplied ÷ mass of extra water.

Gas pressure

The molecules of a gas are in constant random motion. They move quickly in all directions, and they hit the walls of their container again and again. Each hit gives the wall a tiny push. All of the tiny pushes together, from billions of particles every second, add up to the pressure of the gas.

The temperature of a gas is related to the average kinetic energy of its molecules. The molecules do not all move at the same speed, but a hotter gas has a higher average kinetic energy. So its molecules move faster on average.

Heat a gas in a sealed container and the particles move faster. They hit the walls harder, and they hit them more often. The pressure goes up, which is why a sealed can left in a fire can burst, and why a tyre pressure goes up on a hot day.

Squash the same amount of gas into a smaller space, with the temperature kept the same. The particles have less room, so they hit the walls more often. The pressure rises, which is how a bike pump works, because pushing the handle squeezes the air into a smaller space.

In the same way, more gas particles in the same space also means more collisions and more pressure. This is how you pump up a football, one stroke at a time. Letting some gas out lowers the pressure, because there are fewer particles to hit the walls.

Always describe the collisions when you explain pressure. Say that the particles hit the walls, and say whether the hits are harder, more often or both. A good answer ties the change to the particles, and does not just say that the gas expands or heats up.

Recap

In a solid the particles are close and vibrate in a regular pattern. In a liquid they are close but slide past each other. In a gas they are far apart and move fast, so gases are easy to compress and have a low density, while solids and liquids do not compress much.

Density = mass ÷ volume, with units of g/cm³ or kg/m³. Measure a regular solid with a ruler, an irregular solid by displacement and a liquid with a measuring cylinder and a balance. To raise the temperature of a substance, the energy is E = m × c × Δθ. To change its state, the energy is E = m × L.

During melting and boiling the temperature stays the same, because the energy goes into the potential energy of the particles. The mass does not change in a change of state, and the change can be reversed, so it is a physical change. Water has a high specific heat capacity, so it warms up slowly and cools down slowly too.

A gas creates pressure by its molecules colliding with the walls. Heating a gas raises the average kinetic energy of the molecules, so the collisions are harder and more frequent and the pressure goes up. Compressing a gas into a smaller space makes the collisions more frequent, so the pressure goes up.

In an exam you might be asked to calculate a density, or the energy for a temperature change or a change of state. You might be asked how to measure the density of a stone, why the temperature stays constant while a substance melts, or why a gas pressure rises. Write the equation, substitute the numbers, then give the answer with its unit.