Maxwell-Boltzmann distributionsEdexcel A-Level Chemistry: Revision notes

Section 1

The Maxwell–Boltzmann distribution

In a sample of gas, the molecules do not all have the same energy. They constantly collide and exchange energy, giving a distribution of molecular energies: the Maxwell–Boltzmann distribution, a graph of the number of molecules (vertical axis) against energy (horizontal axis).

Key features of the curve:

It starts at the origin: no molecules have zero energy.
It rises to a peak (the most probable energy) and then falls away in a long tail.
It never touches the energy axis at high energy: there is no maximum energy.
The area under the curve is the total number of molecules, so it is the same at any temperature.

Key termsMaxwell–Boltzmann distributionmost probable energy

Common mistake

Drawing the curve so that it touches the energy axis at high energy, or does not start at the origin.

Section 2

Activation energy on the distribution

Mark the activation energy, $E_a$ , on the energy axis. Only molecules with energy equal to or greater than $E_a$ can react when they collide. These are the molecules in the area under the curve to the right of $E_a$ . For most reactions this is a small fraction of the molecules, which is why most collisions fail.

The rate of reaction depends on the frequency of successful collisions, so it increases whenever this area (the proportion of molecules with energy ≥ $E_a$ ) increases.

Key termsactivation energy

Section 3

Effect of temperature

When the temperature increases:

The curve flattens: the peak is lower and moves to a higher energy.
The area under the curve is unchanged, because the number of molecules is the same.
The tail is higher, so the area to the right of $E_a$ is much greater.
$E_a$ itself is unchanged.

A greater proportion of molecules have energy ≥ $E_a$ , so there are more successful collisions per second and the rate increases. Molecules also collide a little more often, but the change in proportion with enough energy is the main reason. Lowering the temperature has the opposite effect.

Key termsflatter curveproportion of molecules

Exam tip

When drawing two temperature curves, draw the higher temperature curve below the lower one at the peak and above it in the tail, so they cross once. Label them T₁ and T₂ and mark Ea.

Section 4

Effect of a catalyst

A catalyst provides an alternative reaction route with a lower activation energy. On the distribution:

The curve is unchanged (same temperature).
The $E_a$ line moves to the left.
The area to the right of the new $E_a$ is greater.

A greater proportion of molecules have enough energy to react, so successful collisions are more frequent and the rate increases, without raising the temperature. For the same reason a catalyst allows a reaction to run at a lower temperature.

Key termscatalystalternative route

Common mistake

Saying a catalyst 'gives the molecules more energy' or 'shifts the curve'. It changes the activation energy, not the energy of the molecules.

Must Know

The curve starts at the origin and never touches the axis
Area under the curve = number of molecules (same at any temperature)
Reaction needs energy ≥ Ea: the area to the right of Ea
Higher T: peak lower and to the right, area to the right of Ea greater, Ea unchanged
Catalyst: curve unchanged, Ea moves left
Both increase the proportion of molecules with energy ≥ Ea

That's the notes covered.

Carry on to the next subtopic.

Exam questions on Maxwell-Boltzmann distributions

A student sketches the Maxwell–Boltzmann distribution of molecular energies for a gas at a fixed temperature, with the number of molecules on the vertical axis and energy on the horizontal axis, and marks the activation energy of a reaction on the energy axis.
Explain why the curve starts at the origin and why it never touches the energy axis at high energy.2 marks
A reaction mixture of gases is heated from 300 K to 310 K, and the rate of the reaction approximately doubles. The student sketches the distribution of molecular energies at the two temperatures on the same axes.
Explain, using the distributions, why the reaction is faster at 310 K.2 marks
A car's catalytic converter contains platinum and rhodium on a solid support. At the temperature of the exhaust gases it converts carbon monoxide and nitrogen monoxide into carbon dioxide and nitrogen: 2CO(g) + 2NO(g) → 2CO₂(g) + N₂(g). Without the catalyst the reaction is far too slow at this temperature.
Explain, with reference to the Maxwell–Boltzmann distribution, how the catalyst increases the rate of the reaction at the same temperature.3 marks

See the full worksheet

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).