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F3.3 · Explain gas behaviour using kinetic molecular theory

Learn to explain gas behaviour using kinetic molecular theory through clear examples and targeted practice.

Ontario Grade 11 Chemistry

Gases and Atmospheric Chemistry

How particle motion helps explain pressure, temperature, and volume

A sealed basketball can feel firmer when it is warm than when it is cold. A balloon may expand when warmed because it can stretch. These are observable changes in gases. The kinetic molecular theory (KMT) helps explain them by connecting the motion of gas particles to properties we can observe, such as pressure and volume.

What you will learn

Describe the main ideas of the kinetic molecular theory for gases.
Explain gas pressure and temperature using particle motion.
Use the particle model to explain how changing conditions can affect a gas.
Recognize that the kinetic molecular theory is a simplified model of real gases.

1. From familiar properties to a particle model

Matter is made of particles. Gas particles are much farther apart than particles in liquids and solids. A gas spreads out to fill its container and can be compressed, which means its volume can be reduced by pushing on it.

Volume is the space occupied by a sample. Pressure describes the effect of pushes on a surface. For a gas, those pushes come from particles colliding with the walls of its container. We cannot usually see individual gas particles, so a model helps us explain what we observe.

Kinetic energy is energy of motion. Temperature is related to the average kinetic energy of particles. When comparing average kinetic energy, use absolute temperature, measured in kelvins. Convert a Celsius temperature to kelvins using the relation below.

T(\mathrm{K})=t(^{\circ}\mathrm{C})+273.15

Gases fill the space available to them and can be compressed.
Gas pressure comes from particles colliding with container walls.
Kinetic energy is energy of motion.

2. The main ideas of kinetic molecular theory

Kinetic molecular theory, or KMT, explains gas behaviour using particle motion. In the model, gas particles move constantly and randomly. Random means their directions are not all the same. Between collisions, they move in straight lines.

The model treats particles as very small compared with the distances between them. Most of the space in a gas is therefore empty space in the model. It also assumes that particles do not pull strongly on one another as they move between collisions.

Gas particles collide with one another and with the walls of their container. In the ideal KMT model, collisions are elastic. This means the total kinetic energy is not lost during a collision. Particles can change direction or transfer energy, but the model does not treat a collision as a lasting loss of motion energy.

The average kinetic energy of gas particles increases as their absolute temperature increases. At a higher kelvin temperature, particles move faster on average. Individual particles can have different speeds; the model connects temperature to the average motion of the group.

\overline{E_{\mathrm{k}}}\propto T

Particles move constantly and randomly, traveling in straight lines between collisions.
The model treats gas particles as far apart, with little attraction between them.
In the ideal model, collisions are elastic.
Higher kelvin temperature means greater average kinetic energy.

3. Explaining pressure and changes in a gas

Each collision with a container wall pushes on it. Many particles make many collisions, and together these impacts produce the pressure we measure. If the same gas is squeezed into a smaller space, particles have less room to move. They reach the walls more often, so pressure can increase.

Imagine a sealed, rigid container. Rigid means its volume does not change easily. When the gas is warmed, its particles gain average kinetic energy and move faster. They collide with the walls more often and make harder impacts on average. The pressure therefore increases, provided the volume stays fixed.

A flexible balloon behaves differently because it can expand. When its gas is warmed, particles move faster and collide with the inside more often and more strongly. The balloon can expand, giving the gas more room. The balloon’s size reflects the balance between the gas pushing outward and the surroundings pushing inward. KMT explains how the gas particles contribute to that push.

Cooling has the opposite effect on average particle motion. At a lower kelvin temperature, particles have less average kinetic energy and move more slowly. In a rigid container, their impacts on the walls become less frequent and less forceful, so pressure decreases. In a flexible container, the gas may occupy less volume instead.

KMT is an idealization: a simplified picture that leaves out some details. Real particles have size, and their interactions are not always negligible. The model is useful when those effects are small enough for it to explain the gas behaviour.

Wall collisions produce gas pressure.
Less space available to a gas can mean more frequent wall collisions.
Warming increases average particle motion; the result depends on whether the container can expand.
KMT is a simplified model of real particles.

4. A reliable way to explain gas behaviour

First identify what is fixed and what can change. A sealed, rigid container keeps both the amount of gas and the volume fixed. A flexible container can change volume. This matters when predicting what happens after a temperature change.

Next connect the change in conditions to average particle motion, then connect that motion to collisions or spreading. For example, do not say that heat makes particles expand. In KMT, particles do not grow larger when warmed. Their average motion increases, and the gas may occupy more space if the container can expand.

Use kelvins when comparing average kinetic energy. A Celsius temperature of zero is not the point at which KMT describes particle motion as zero. Convert Celsius temperatures to kelvins before comparing average kinetic energy.

KMT does not show the exact path of every particle. It is a set of assumptions that explains large-scale behaviour using particle motion. A good explanation links an observation, such as a pressure change, to the model, such as more frequent or harder wall collisions.

Check whether the container is rigid or flexible before predicting what changes.
Warming changes average particle motion, not particle size.
Use kelvins to compare average kinetic energy.
Connect an observable change to a particle-level explanation.

Worked example

Comparing particle motion at two temperatures

A sealed, rigid container holds the same gas at

27.0\,^{\circ}\mathrm{C}

and later at

127.0\,^{\circ}\mathrm{C}

. Convert both temperatures to kelvins and compare the average kinetic energy of the particles. Then predict the pressure change using KMT.

Convert to kelvins
Convert each Celsius temperature because KMT relates average kinetic energy to absolute temperature. The Celsius values are given to the nearest $0.1\,^{\circ}\mathrm{C}$ , so report the converted values to the nearest $0.1\,\mathrm{K}$ .
$T_1=27.0+273.15=300.2\,\mathrm{K};\quad T_2=127.0+273.15=400.2\,\mathrm{K}$
Compare the temperatures
Divide the higher kelvin temperature by the lower one. Since average kinetic energy is proportional to kelvin temperature, this ratio compares the average kinetic energies.
$\frac{T_2}{T_1}=\frac{400.2\,\mathrm{K}}{300.2\,\mathrm{K}}\approx1.33$
Predict the pressure change
The sealed container keeps the amount of gas the same, and its rigid walls keep the volume fixed. Faster particles make more frequent and harder wall impacts on average. KMT therefore predicts an increase in pressure. The temperature comparison does not give a measured pressure value.

Answer: The temperatures are

300.2\,\mathrm{K}

and

400.2\,\mathrm{K}

. The average kinetic energy at the higher temperature is about

1.33

times the initial average. KMT predicts that pressure increases.

Check: The prediction follows from the stated conditions: the container is sealed and rigid. A flexible container could expand, so its pressure prediction would need to account for the volume change.

Common mistakes and how to avoid them

Saying that gas particles grow when a gas is warmed.

Correction: In KMT, warming increases average particle motion. The model does not treat particles as growing.

Explaining pressure without mentioning collisions.

Correction: KMT explains gas pressure through particles colliding with the container walls.

Using a Celsius temperature directly to compare average kinetic energy.

Correction: Convert the temperatures to kelvins before comparing average kinetic energy.

Predicting the same result for a rigid container and a flexible balloon.

Correction: A rigid container keeps its volume nearly fixed. A flexible container can expand, so different properties may change.

Lesson summary

KMT explains gas behaviour through particle motion and collisions.
Gas particles move constantly and randomly, in straight lines between collisions.
In the ideal model, particles are far apart, attractions are negligible, and collisions are elastic.
Gas pressure results from collisions with container walls.
Higher kelvin temperature means greater average kinetic energy. Whether pressure or volume changes depends on the container.

Check your understanding

Question 1

What produces the pressure of a gas on the walls of its container?

Gas particles colliding with the walls
Gas particles becoming larger
The empty space between particles pressing outward
Particles remaining still against the walls

Show answer and explanation

Gas particles colliding with the walls

KMT explains pressure through the impacts of moving gas particles on container walls.

Question 2

A sealed, rigid container of gas is warmed. Which explanation best matches KMT?

Particles gain average kinetic energy and make more frequent, harder impacts on the walls.
Particles become larger, so they take up more of the container.
Particles stop colliding, so pressure rises.
The container expands freely, so its volume must increase.

Show answer and explanation

Particles gain average kinetic energy and make more frequent, harder impacts on the walls.

Warming increases average particle motion. In a rigid container, volume stays fixed, so the increased wall impacts lead to higher pressure.

Question 3

Why should kelvins be used when comparing average kinetic energy at different temperatures?

Average kinetic energy is proportional to absolute temperature.
Kelvins measure the volume of a gas.
Celsius temperatures cannot be measured accurately.
Kelvins describe the number of particles in a sample.

Show answer and explanation

Average kinetic energy is proportional to absolute temperature.

KMT relates average kinetic energy to absolute temperature, which is measured in kelvins.

Key terms

Kinetic molecular theory: A model that explains gas behaviour using the motion and collisions of particles.
Kinetic energy: Energy an object or particle has because it is moving.
Pressure: A measure of the effect of pushes on a surface; gas pressure comes from particle collisions with container walls.
Elastic collision: A collision in which total kinetic energy is not lost in the ideal gas model.
Absolute temperature: Temperature measured on the kelvin scale.
Idealization: A simplified model that leaves out some details to help explain a pattern.

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Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Chemistry (SCH3U), expectation F3.3. It is a study resource, not an official curriculum publication.

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