The Maxwell–Boltzmann Distribution
Raise the temperature and watch the energy distribution spread and flatten. The shaded fraction of molecules that can react climbs — and a catalyst moves the goalposts.
In any gas, molecules are not all moving at the same speed — some crawl, some race, most are in between. The Maxwell–Boltzmann distribution captures that spread, and it quietly explains one of the biggest ideas in chemistry: why a small rise in temperature can double a reaction rate. Heat it up below and watch the reactive fraction surge.
Molecules do not all move alike
Collisions constantly shuffle energy between molecules, so at any instant there is a whole range of kinetic energies. Plot the fraction of molecules against energy and you get the Maxwell–Boltzmann curve: it starts at zero (no molecule has zero energy), rises to a peak at the most probable energy, then tails off to the right, because a few molecules always have very high energy.
Only the fastest molecules — those out in the right-hand tail — carry enough energy to react. Everything about rate comes down to how big that tail is.
Heat it up
Raise the temperature and watch the curve spread and flatten, its peak sliding right and lower. The shaded area beyond the activation-energy line is the fraction of molecules that can actually react — and it grows dramatically. Then add a catalyst and see the same molecules suddenly qualify.
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An interactive Maxwell–Boltzmann distribution: fraction of molecules (vertical) against kinetic energy (horizontal). The curve starts at the origin, rises to a peak at the most probable energy, and tails off to the right. A temperature slider reshapes it: raising the temperature lowers and broadens the peak and shifts it to higher energy, while the total area under the curve (the number of molecules) is held constant. A dashed vertical line marks the activation energy Eₐ, and the area under the curve to its right — the fraction of molecules with enough energy to react — is shaded and rises steeply as temperature increases. A catalyst checkbox moves the Eₐ line to the left (a lower activation energy) without changing the curve, increasing the shaded reactive fraction at the same temperature.
Reading the curve
Why heating speeds reactions
For a reaction to happen, colliding molecules need at least the activation energy, Ea. Only the molecules in the shaded tail beyond Ea qualify.
Raising the temperature shifts the whole distribution to higher energies and flattens it, so a much larger fraction of molecules now sit beyond Ea. Because that fraction rises roughly exponentially, even a modest temperature increase — around 10 °C for many reactions — can approximately double the rate. A faster average speed contributes a little; the dramatic effect comes from the swelling tail.
What a catalyst really does
A catalyst does not change the distribution and does not give molecules more energy. Instead it provides an alternative reaction pathway with a lower activation energy. On the graph the Ea line moves left, so a larger fraction of the same molecules — at the sametemperature — now have enough energy to react. Toggle the catalyst in the simulator and watch the shaded area jump without the curve moving at all.
Worked example
A student heats a reaction from 25 °C to 35 °C and the rate roughly doubles, even though the average molecular speed rises only a few percent. Explain the mismatch.
The average speed barely changes, but rate depends on the fraction of molecules past Ea, not the average. Because that fraction lies in the steep exponential tail, a small shift of the whole distribution to higher energy moves a disproportionately large number of molecules over the barrier — so the rate rises far more than the average speed does.
Your turn
On a Maxwell–Boltzmann diagram, how do you show the effect of a catalyst — and what stays exactly the same?
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Move the Ea line to the left (lower activation energy), enlarging the shaded area to its right. The distribution curve itself, the temperature and the total area under the curve are all unchanged.
Common mistakes
Frequently asked questions
What does the Maxwell–Boltzmann distribution show?+
Why does increasing temperature increase the rate of reaction?+
How does a catalyst affect the Maxwell–Boltzmann distribution?+
What is activation energy?+
The ScholarsGate Chemistry Team
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Written and reviewed by ScholarsGate tutors who teach A-Level and undergraduate chemistry. Every explainer is checked against the AQA, Edexcel, OCR and CIE specifications.
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