8.1 Changes of state and the particle model — Learn

Prerequisites: Section 2.1, especially the idea that matter is made of particles; Chapter 1, especially energy stores and energy transfers.

By the end of this section you can: use the particle model to describe a solid, a liquid and a gas; calculate density from mass and volume; describe how to measure the density of a solid or a liquid; list the changes of state; and explain why mass is conserved when a substance changes state.

1. The three states of matter

Everything around you is made of tiny particles: atoms, or groups of atoms called molecules. The particle model describes how these particles are arranged and how they move. The model explains the three states of matter.

• In a solid, the particles are close together in a regular pattern. They vibrate about fixed positions, so a solid keeps its own shape.
• In a liquid, the particles are still close together, but they are not in a fixed pattern. They move around each other, so a liquid flows and takes the shape of its container.
• In a gas, the particles are far apart. They move quickly and randomly, so a gas fills any container.

The particles themselves do not change during a change of state. Only their arrangement and their energy change.

Worked example 1. Describe the difference between a solid and a gas using the particle model.

A model answer is:

• In a solid, the particles are close together and held in a regular pattern. They can only vibrate about fixed positions.
• In a gas, the particles are far apart and move quickly in random directions. The forces between them are very weak.

2. Density

Density tells you how much mass there is in each unit of volume. It is defined by this equation.

where $\rho$ is the density in kilograms per metre cubed ($\text{kg/m}^3$), $m$ is the mass in kilograms and $V$ is the volume in metres cubed. The Greek letter $\rho$ is called rho.

Density is a property of a material. A large block of ice and a small block of ice have the same density, because both the mass and the volume grow together.

Worked example 2. The block of ice in the chapter problem has a volume of $2.5 \times 10^{-3}\,\text{m}^3$. The density of ice is $920\,\text{kg/m}^3$. Calculate the mass of the block.

We need the mass, so we rearrange $\rho = \dfrac{m}{V}$ to make $m$ the subject.

The block has a mass of $2.3\,\text{kg}$.

Worked example 3. A piece of metal has a mass of $67.5\,\text{g}$ and a volume of $25\,\text{cm}^3$. Calculate its density in $\text{g/cm}^3$ and in $\text{kg/m}^3$.

To change $\text{g/cm}^3$ into $\text{kg/m}^3$, multiply by 1000, because there are 1000 g in a kilogram and $10^6\,\text{cm}^3$ in a cubic metre.

3. Measuring density

You can find the density of a material in the laboratory. The method depends on the shape of the object.

• A regular solid, such as a block or a cylinder. Measure its length, width and height with a ruler. Calculate the volume, then use $\rho = \dfrac{m}{V}$.
• An irregular solid, such as a stone. Find its volume by displacement. Lower it into water in a measuring cylinder and read how much the water level rises. The rise is the volume of the solid.
• A liquid. Measure the mass of an empty container, then the mass of the container with the liquid. The difference is the mass of the liquid. Measure the volume with a measuring cylinder.

Worked example 4. An empty beaker has a mass of $120\,\text{g}$. When $100\,\text{cm}^3$ of a liquid is poured in, the total mass is $204\,\text{g}$. Calculate the density of the liquid.

The mass of the liquid is the total mass minus the mass of the beaker.

The liquid has a density of $0.84\,\text{g/cm}^3$, which is $840\,\text{kg/m}^3$.

4. Why the states have different densities

The particle model explains the densities of the three states.

In a solid and a liquid, the particles are packed closely together, so the density is high. Solids and liquids usually have similar densities.

In a gas, the particles are far apart, with large empty spaces between them. The same mass of gas therefore fills a much larger volume, so a gas has a much lower density than a solid or a liquid.

Water is unusual in one way. Ice is less dense than liquid water. When water freezes, the particles are held in an open pattern that takes up more space. That is why ice floats on water, and why water expands when it freezes.

5. Changes of state

A substance can change from one state to another. Each change has its own name.

A change of state is a physical change. The particles stay the same, and no new substance is made. If you reverse the change, the material gets back its original properties. This makes a change of state different from a chemical change, where a new substance forms.

Mass is conserved during a change of state. When ice melts, the mass of the water equals the mass of the ice. The particles have not been created or destroyed; they have only moved further apart.

Worked example 5. A $2.3\,\text{kg}$ block of ice melts completely. Explain what happens to the mass and to the volume, and why.

A model answer is:

• The mass stays at $2.3\,\text{kg}$. The same particles are present before and after melting, so no mass is lost.
• The volume decreases. In liquid water the particles are packed a little more closely than in the open ice pattern.

6. Density and the particle model

The figure lets you set the mass and the volume of a block of material. It shows the density and compares it with the density of water.

Predict first. Do not move the sliders yet. Write down your answers.

1. The block of ice has a mass of $2.3\,\text{kg}$ and a volume of $2.5 \times 10^{-3}\,\text{m}^3$. Will it float or sink in water?
2. If you increase the volume but keep the mass the same, what happens to the density?

Test. Move the sliders to make the ice block. Note the density. Then change the volume and watch the density and the floating line. Finally, set a mass and volume that give a density greater than $1000\,\text{kg/m}^3$.

Explain. The water line shows a density of $1000\,\text{kg/m}^3$. A material floats only if its density is less than the density of the liquid. Explain, using particles, why a smaller density means the material floats. Write your answer in two or three sentences.

Watch out. Density carries a unit, and the unit must match the numbers you put in. If the mass is in grams and the volume is in cubic centimetres, the density comes out in $\text{g/cm}^3$, not $\text{kg/m}^3$. Do not mix grams with metres or kilograms with centimetres. Write the unit next to every value, then convert at the end. Re-check by asking whether the density is sensible: a solid is usually between $500$ and $10\,000\,\text{kg/m}^3$, and air is about $1.2\,\text{kg/m}^3$.

Progress check

Return to the chapter problem. The station stores water as a block of ice.

1. The block has a volume of $2.5 \times 10^{-3}\,\text{m}^3$ and the density of ice is $920\,\text{kg/m}^3$. Calculate the mass of the block.
2. When the ice melts, what happens to the mass? Give a reason.
3. The liquid water from the melted block has a smaller volume than the ice. Explain this using the particle model.

You should now be able to

• use the particle model to describe a solid, a liquid and a gas;
• define density and use $\rho = \dfrac{m}{V}$;
• measure the density of a regular solid, an irregular solid and a liquid;
• explain why a gas has a much lower density than a solid or a liquid;
• list the changes of state and describe each one;
• explain why mass is conserved during a change of state;
• explain why ice is less dense than liquid water.