Maxwell-Boltzmann Distribution

Specification Reference Physical Chemistry, Kinetics 3.1.5.1

Quick Notes

The Maxwell-Boltzmann distribution curve describes the distribution of molecular energies in a gas.
Key features of the curve:
- Starts at the origin (0,0) → No particles have zero energy.
- Peaks at the most probable energy → The energy that most particles have.
- Has a long tail to the right → Some particles have very high energy.
Only particles with energy ≥ activation energy (E_a) can react.
Increasing temperature: Shifts the curve to the right and lowers the peak. More particles have energy ≥ E_a → Faster reaction rate.
Adding a catalyst: Lowers the activation energy (E_a), increasing the fraction of particles that can react.

Full Notes

Maxwell-Boltzmann Distribution Curves have been outlined with more background theory here.

This page is just what you need to know for AQA A-level Chemistry :)

Understanding the Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann distribution is a graph that shows how available energy is spread out and shared amongst molecules of a gas.
It helps explain why:

Not all molecules have the same energy.
Only a small fraction of molecules have enough energy to react.
Increasing temperature increases reaction rate.

Features of the Maxwell-Boltzmann Distribution Curve

AQA A-Level Chemistry Maxwell–Boltzmann distribution curve showing origin at zero, peak at most probable energy, and long right-hand tail.

Starts at the origin (0,0) because no particles have zero energy.
Peak at the most probable energy represents the energy that most particles have.
Has a long tail to the right – a few molecules have very high energy (never crosses the x axis again).
Area under the curve = Total number of molecules.
Only molecules with energy ≥ activation energy (E_a) can react.

Effect of Temperature on the Distribution

Increasing temperature shifts the curve right and lowers the peak.

AQA A-Level Chemistry comparison of Maxwell–Boltzmann curves at T1 and higher T2 showing rightward shift and lower peak; shaded region above E a increases.

More molecules have energy ≥ E_a, increasing the rate of successful collisions.
The total number of molecules stays the same (area under the curve is unchanged).

Effect of a Catalyst on the Distribution

A catalyst lowers the activation energy (E_a).

AQA A-Level Chemistry Maxwell–Boltzmann style schematic highlighting that only molecules with energy beyond E a can react; a catalyst effectively lowers E a threshold.

This means more molecules now have energy ≥ E_a, so frequency of successful collisions increases.

The Maxwell-Boltzmann curve shape does not change, but the activation energy shifts left.

Key Comparisons: Temperature vs. Catalyst Effects

Factor	Effect on Curve	Effect on Reaction Rate
Increasing Temperature	Shifts curve right, peak lowers	More molecules have E ≥ E_a, faster reaction
Adding Catalyst	No shift in curve, but E_a is lower	More molecules can react, faster reaction

Summary

Maxwell–Boltzmann curve: origin at zero, most probable energy peak, long tail to the right.
Only particles with E ≥ E_a can react; area under the curve is constant.
Higher temperature increases the fraction above E_a; catalysts lower E_a.