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# Chapter 7: Ideal gases

In this chapter learners are introduced to the concept of ideal gases. They will explore the different gas laws and learn about the motion of gas particles. The following list provides a summary of the topics covered in this chapter.

• The motion of particles

In grade $$\text{10}$$ learners were introduced to the kinetic molecular theory and the idea that all particles in a substance are constantly moving. In this chapter the motion of particles is applied to gases and is used to help distinguish between real gases and ideal gases.

• Real gases and ideal gases

A real gas is very similar to an ideal gas except at high pressures and low temperatures. The main distinguishing characteristics of a real gas are that the particles have volume, the particles in the gas have an average speed (since each particle is moving at a different speed) and that forces of attraction exist between particles.

• The kinetic theory of gases

The kinetic theory of gases is similar to the kinetic theory of matter that learners learnt about in grade $$\text{10}$$ (states of matter and the kinetic molecular theory). The kinetic theory of gases helps to explain all the gas laws and learners are encouraged to think about what the different laws mean rather than just learning the laws.

• Boyle's law, Charles' law, the pressure-temperature relation (Gay-Lussac's or Amonton's law), the general gas equation and the ideal gas equation

In this book we talk about the pressure-temperature relation. CAPs refers to this as Gay-Lussac's law, while other sources call it Amonton's law. At the time when this law was discovered many scientists were working on the same problems and often it is hard now to say who actually discovered what. Learners should know that different names for the gas laws exist and they should be aware of the other names that exist.

Boyle's law, Charles' law and the pressure-temperature relation all require very specific conditions to be true. These laws are then expanded into the general gas equation and finally the ideal gas equation is introduced. All the gas laws except the ideal gas law compare a sample of gas at two different sets of readings (e.g. two different sets of pressure and temperature readings, while the volume and amount of gas remains the same).

• Temperature and pressure

Although temperature and pressure are given last in CAPs, in this book they are placed with the kinetic theory of gases and the explanation of real and ideal gases since temperature and pressure are key to understanding these topics.

The pressure is a result of the motion of particles in the gas and is a measure of how many times the particles in the gas collide with each other and with the walls of the container. Temperature is a measure of the kinetic energy that the particles have.

We are surrounded by gases in our atmosphere which support and protect life on this planet. Everyday we breathe in oxygen and release carbon dioxide. Green plants take in the carbon dioxide and release oxygen. One way or another we are surrounded by a mix of many different gases, some that we need and some that are harmful to us.

In this chapter, we are going to learn more about gases and about the different gas laws.

• Ratio and proportion - Physical Sciences, Grade 10, Science skills
• Equations - Mathematics, Grade 10, Equations and inequalities
• Graphs - Mathematics, Grade 10, Functions and graphs
• Units and unit conversions - Physical Sciences, Grade 10, Science skills

## 7.1 Motion of particles (ESBNR)

### The kinetic theory of gases (ESBNS)

In grade $$\text{10}$$ you learnt about the kinetic theory of matter. The kinetic theory of matter says that all matter is composed of particles which have a certain amount of energy which allows them to move at different speeds depending on the temperature (energy). There are spaces between the particles and also attractive forces between particles when they come close together.

Now we will look at applying the same ideas to gases.

The main assumptions of the kinetic theory of gases are as follows:

• Gases are made up of particles (e.g. atoms or molecules). The size of these particles is very small compared to the distance between the particles.

• These particles are constantly moving because they have kinetic energy. The particles move in straight lines at different speeds.

• There are attractive forces between particles. These forces are very weak for gases.

• The collisions between particles and the walls of the container do not change the kinetic energy of the system.

• The temperature of a gas is a measure of the average kinetic energy of the particles.

From these assumptions we can define the pressure and temperature of any gas.

Pressure
The pressure of a gas is a measure of the number of collisions of the gas particles with each other and with the sides of the container that they are in.
Temperature
The temperature of a substance is a measure of the average kinetic energy of the particles.

If the gas is heated (i.e. the temperature increases), the average kinetic energy of the gas particles will increase and if the temperature is decreased, the average kinetic energy of the particles decreases. If the energy of the particles decreases significantly, the gas liquefies (becomes a liquid).

One of the assumptions of the kinetic theory of gases is that all particles have a different speed. However, this is only the case for a real gas. For an ideal gas we assume that all particles in the gas have the same speed.

So for an ideal gas we can simply talk about the speed of particles. But for a real gas we must use the average speed of all the particles.

### Ideal gases and non-ideal gas behaviour (ESBNT)

When we look at the gas laws in the next section we will only deal with ideal gases.

Ideal gas

An ideal gas has identical particles of zero volume, with no intermolecular forces between them. The atoms or molecules in an ideal gas move at the same speed.

Almost all gases obey the gas laws within a limited range of pressures and temperatures. So we can use the gas laws to predict how real gases will behave.

Real gas

Real gases behave more or less like ideal gases except at high pressures and low temperatures.

Before we go on to look at the gas laws we will first see what happens to gases at high pressures and low temperatures.

When we defined an ideal gas, we said that an ideal gas has identical particles of zero volume and that there are no intermolecular forces between the particles in the gas. We need to look more closely at these statements because they affect how gases behave at high pressures or at low temperatures.

1. Molecules do occupy volume

When pressures are very high and the molecules are compressed, the volume of the molecules becomes significant. This means that the total volume available for the gas molecules to move is reduced and collisions become more frequent. This causes the pressure of the gas to be higher than what would be expected for an ideal gas (Figure 7.1).

2. Forces of attraction do exist between molecules

At low temperatures, when the speed of the molecules decreases and they move closer together, the intermolecular forces become more apparent. As the attraction between molecules increases, their movement decreases and there are fewer collisions between them. The pressure of the gas at low temperatures is therefore lower than what would have been expected for an ideal gas (Figure 7.2). If the temperature is low enough or the pressure high enough, a real gas will liquefy.

Exercise 7.1

Summarise the difference between a real gas and an ideal gas in the following table:

 Property Ideal gas Real gas Size of particles Attractive forces Speed of molecules
 Property Ideal gas Real gas Size of particles No volume and can be ignored Non-negligible volume Attractive forces No attractive forces Attractive forces Speed of molecules All molecules at the same speed. Molecules move at different speeds and we use the average speed.