AQA A-Level Chemistry (7405)

## Learning Outcomes

- Understand what the Maxwell-Boltzmann distribution shows about the energies of gas particles
- Identify the main features of a Maxwell-Boltzmann distribution curve and label its axes correctly
- Explain how activation energy links collision theory to the Maxwell-Boltzmann model
- Describe how increasing temperature changes the shape of the curve and increases reaction rate
- Distinguish clearly between the effect of temperature and the effect of a promoter
- Avoid common exam errors when sketching or interpreting Maxwell-Boltzmann graphs

## AQA A-Level Chemistry (7405) Syllabus

For the AQA A-Level Chemistry (7405), you are expected to understand the Maxwell-Boltzmann distribution in kinetics, with a focus on the following syllabus points:

- Know that gas particles at a given temperature have a distribution of kinetic energies rather than all having the same energy
- Identify the axes and key features of a Maxwell-Boltzmann distribution curve, including the peak, tail, and total area under the curve
- Understand that activation energy, **Ea**, is the minimum energy that colliding particles must have for a reaction to occur
- Explain that the area to the right of the activation energy line represents the fraction of particles with energy greater than or equal to **Ea**
- Describe how increasing temperature changes the distribution curve and increases the proportion of particles with sufficient energy to react
- Explain why a small increase in temperature can lead to a large increase in reaction rate
- Distinguish between the effect of temperature and the effect of a reaction pathway on a Maxwell-Boltzmann distribution
- Understand that a substance provides an alternative pathway with lower activation energy, without changing the energy distribution at constant temperature

## Test Your Knowledge

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, look more closely at that area during your revision._

1. What does a Maxwell-Boltzmann distribution show for a gas sample?
2. Why do only some collisions lead to reaction, even when particles are colliding all the time?
3. How does increasing temperature change a Maxwell-Boltzmann distribution curve?
4. What area on the graph represents particles able to react?
5. Why does a substance increase rate without changing the shape of the distribution curve?

## Introduction

In kinetics, one of the biggest ideas is that not all particles in a gas have the same energy. That matters because chemical reactions only happen when particles collide with enough energy and in a suitable orientation. The Maxwell-Boltzmann distribution helps you see this on a graph.

This topic is tested often because it links several parts of kinetics at once: collision theory, activation energy, temperature, and enzymess. AQA questions commonly ask you to label a distribution, compare two curves, or explain changes in rate using precise Maxwell-Boltzmann language.

> **Key Term: Maxwell-Boltzmann distribution**
> A theoretical model showing how the kinetic energies of particles are distributed in a gas at a given temperature.

### What the Maxwell-Boltzmann distribution actually shows

A Maxwell-Boltzmann distribution is not a graph of one particle moving over time. It is a graph for a whole sample of gas, showing how many particles have different energies at one moment.

The **x-axis** is energy. The **y-axis** is usually labelled as number of particles or fraction of particles. In AQA questions, both ideas may appear, so read the axis label carefully. The shape of the curve matters more than the exact wording.

The curve starts at the origin, rises to a peak, then falls and trails off to the right. This tells you several things at once:

- no particles have negative energy
- very few particles have very low energy
- most particles have intermediate energies
- a small fraction have very high energies

The long right-hand tail is especially important. Even at a moderate temperature, some particles have much higher energy than average. Those particles are often the ones that can take part in successful collisions.

> **Key Term: most probable energy**
> The energy possessed by the greatest number of particles in the sample; it is shown by the peak of the curve.

Students often confuse the peak with the average energy. The peak is the **most probable energy**, not the mean kinetic energy. Because the curve is skewed to the right, the mean kinetic energy is not exactly at the peak.

The area under the whole curve represents the total number of particles in the sample. If the sample size stays the same, that total area must stay the same even if the shape changes.

This explains why a higher-temperature curve becomes lower and broader. The number of particles has not changed, so the curve cannot simply get taller everywhere. Instead, the same total area is spread across a wider range of energies.

> **Key Term: area under the curve**
> The total area under a Maxwell-Boltzmann distribution represents the total number of particles in the sample.

A good mental picture is a class test score distribution. If more scores are spread out over a wider range, the graph becomes flatter, not taller. The same idea applies here, except the variable is particle energy rather than marks.

> **Test Tip:** If asked to sketch a higher-temperature Maxwell-Boltzmann curve, make it lower, broader, and shifted to the right. Keep the total area the same. A very common error is drawing the second curve taller.

### Activation energy and successful collisions

A reaction does not happen every time particles collide. Collision theory says two conditions are needed:

- the particles must collide
- the collision must have enough energy, and for many reactions the particles must also be correctly oriented

The minimum energy needed is the activation energy, **Ea**. On a Maxwell-Boltzmann graph, **Ea** is shown as a vertical line on the x-axis.

> **Key Term: activation energy (Ea)**
> The minimum energy that colliding particles must have for a reaction to occur.

Particles to the left of the **Ea** line do not have enough energy to react in that collision. Particles to the right have energy greater than or equal to **Ea**, so they can react if the orientation is suitable.

That means the area under the curve to the right of the **Ea** line represents the fraction of particles able to produce successful collisions.

> **Key Term: successful collision**
> A collision that leads to reaction because the particles collide with sufficient energy and suitable orientation.

This is the central link between the graph and reaction rate. The larger the fraction of particles with energy at least equal to **Ea**, the greater the number of successful collisions per unit time, so the faster the reaction.

Why is this useful? Because it explains why some reactions are slow at room temperature even though particles are colliding constantly. If the activation energy is high, only a small area of the curve lies to the right of **Ea**. So only a small fraction of collisions can succeed.

Consider two reactions at the same temperature:

- Reaction A has a low **Ea**
- Reaction B has a high **Ea**

On the same Maxwell-Boltzmann distribution, the **Ea** line for Reaction A would be further left. That means a larger area lies to the right of the line, so more particles can react. Reaction A is therefore faster, if other factors are similar.

This is why reactions with high activation energies may need heating before they proceed at a useful rate.

> **Test Tip:** In extended explanations, do not stop at “particles move faster”. To access full marks, link the graph to rate: “a greater proportion of particles have energy greater than or equal to the activation energy, so there are more successful collisions per second.”

### Effect of temperature on the distribution and reaction rate

Temperature is linked to the average kinetic energy of particles. When temperature increases, particles on average have more kinetic energy. But the Maxwell-Boltzmann model shows something more precise than just “particles move faster”.

At a higher temperature, the distribution curve:

- becomes lower
- becomes broader
- shifts to the right
- still has the same total area, if the number of particles is unchanged

The most important consequence is that the area to the right of the **Ea** line becomes much larger.

Why does this matter so much? Because reaction rate depends on successful collisions, not just total collisions. A temperature increase does increase collision frequency because particles move faster, but the larger effect is often that many more particles now have enough energy to overcome **Ea**.

This is why even a small temperature increase can produce a large increase in rate. The increase in the fraction above **Ea** is not proportional in a simple, gentle way. If the activation energy lies in the tail region of the curve, a small rightward shift can greatly enlarge the shaded area to the right.

A classic exam statement is that for reactions around room temperature, a rise of about **10 K** often roughly doubles the rate. You should treat this as a useful rule of thumb, not a fixed law for every reaction.

Here is the logic chain AQA wants:

1. temperature increases
2. particles have higher energies on average
3. the Maxwell-Boltzmann distribution becomes broader and lower, shifted right
4. a greater proportion of particles have energy greater than or equal to **Ea**
5. more collisions are successful
6. reaction rate increases

Worked-through comparison:

Suppose at temperature **T1**, only 5% of particles have energy greater than or equal to **Ea**. After a small increase to **T2**, perhaps 10% do. The total number of particles has not doubled, but the number able to react has doubled. That is why the rate can increase sharply.

Students often say “all particles have more energy at higher temperature”. This is too crude. The safer wording is:

- the particles have a higher average kinetic energy
- a greater proportion of particles have energy greater than or equal to **Ea**

That wording fits the graph and the mark scheme much better.

Another common mistake is saying temperature lowers activation energy. It does not. Temperature changes the distribution; **Ea** stays in the same position.

### Effect of a factor and how it differs from temperature

A substance increases reaction rate by providing an alternative pathway with lower activation energy.

> **Key Term: trigger**
> A substance that increases the rate of a reaction by providing an alternative pathway with lower activation energy and is chemically unchanged at the end.

On a Maxwell-Boltzmann diagram at constant temperature, the distribution curve does **not** change when a reaction profile is added. This point is heavily tested.

Instead, what changes is the position of the activation energy line. The catalysed **Ea** is lower, so its vertical line is drawn further to the left than the uncatalysed **Ea**.

That means the area to the right of the new, lower **Ea** line is larger. Therefore a greater fraction of particles can react, so there are more successful collisions per second.

Side-by-side comparison:

- **Increase temperature**
  - curve changes
  - **Ea** stays the same
  - more particles exceed **Ea**

- **Add trigger**
  - curve stays the same
  - **Ea** decreases
  - more particles exceed the new lower **Ea**

This distinction is one of the easiest places to lose marks.

Worked example of an exam explanation:

Question: Explain, using Maxwell-Boltzmann ideas, how a substance increases the rate of a gaseous reaction.

Model answer:
A substance provides an alternative pathway with lower activation energy. At constant temperature, the Maxwell-Boltzmann distribution is unchanged because the particles do not have more energy. However, the activation energy line moves to lower energy, so a greater proportion of particles have energy greater than or equal to **Ea**. Therefore there are more successful collisions per unit time and the reaction rate increases.

Common student errors:

- saying the idea that gives particles more energy
- drawing a different-shaped curve for the reaction rate enhancer
- saying a claiming increases collision frequency directly
- forgetting to mention lower activation energy

You may also get a question mixing temperature and pressure changes changes. In that case, keep the two effects separate. Do not merge them into one vague statement about “more collisions”.

> **Key Term: alternative pathway**
> A different reaction route provided by a substance, requiring a lower activation energy than the uncatalysed route.
>
> **Test Tip:** Use the memory line: temperature changes the curve; enzyme changes the **Ea** line. This short contrast is very useful in 2-mark and 3-mark questions.

## Key Point Checklist

_This article has covered the following key knowledge points:_

- A Maxwell-Boltzmann distribution shows how particle energies are distributed in a gas at a given temperature
- The x-axis is energy and the y-axis is number of particles or fraction of particles
- The curve starts at the origin, rises to a peak, then falls with a long tail to higher energies
- The peak shows the most probable energy, not the mean kinetic energy
- The total area under the curve represents the total number of particles in the sample
- Activation energy, **Ea**, is the minimum energy colliding particles must have for a reaction to occur
- The area to the right of the **Ea** line represents the fraction of particles with energy greater than or equal to **Ea**
- Increasing temperature makes the curve lower, broader, and shifted to the right
- At higher temperature, a greater proportion of particles have enough energy to react, so there are more successful collisions
- A small increase in temperature can cause a large increase in rate because the fraction above **Ea** increases strongly
- A reaction chemical substance does not change the shape of the Maxwell-Boltzmann distribution at constant temperature
- A substance lowers **Ea** by providing an alternative pathway, so a greater proportion of particles can react

## Key Terms and Concepts

- Maxwell-Boltzmann distribution
- most probable energy
- area under the curve
- activation energy (Ea)
- successful collision
- trigger
- alternative pathway


Kinetics - Maxwell-Boltzmann distribution