IB Chemistry SLTopic 5 — The Rate of ReactionPaper 1 & 2Core idea~13 min read
Maxwell–Boltzmann Distributions
Every explanation in this sub-topic has leaned on the phrase “a greater proportion of particles with enough energy”. This is the graph that phrase refers to — and once you can read it, those explanations stop being something to memorise.
📚 What you need to know
A Maxwell–Boltzmann distribution shows how the kinetic energies of particles are spread at a given temperature.
It starts at the origin (no particle has zero energy) and approaches but never touches the energy axis (no maximum energy).
The peak is the most probable energy, Emp — not the average, which lies slightly to the right.
The total area under the curve is the total number of particles.
The area beyond Ea is the proportion of particles able to react.
Raising the temperature makes the peak lower and further right, with a higher tail and the same total area.
Reading the curve
The tail is what matters. It looks negligible, but the particles in it are the only ones doing any chemistry.
Four features are worth being able to justify rather than just recall:
It starts at the origin because a particle with literally zero kinetic energy would be stationary, which collisions make effectively impossible.
It has a peak because most particles cluster around a typical energy, with fewer at the extremes.
It never touches the axis on the right because there is no upper limit to how fast a particle can be moving — only a vanishing probability.
The area under the curve is a count of particles, so shading a region means “this many particles have energies in this range”.
Note where Ea sits: well to the right of the peak, in the thin part of the tail. That is the visual statement of something from the collision theory page — only a tiny fraction of particles can react at any moment, which is why reactions take time at all.
What temperature does
The shaded region beyond Ea is roughly twice as large for the hotter sample, even though the curve has barely moved.
Everything about the shape follows from one constraint: the number of particles has not changed, so the area under both curves must be the same. Heating spreads the particles over a wider range of energies, and if the curve gets wider it must also get lower to keep the area constant.
🧩 Sketching two temperatures
Both curves start at the origin.
The hotter curve’s peak is lower and further right.
The two curves cross exactly once.
Beyond the crossing point, the hotter curve’s tail stays above the colder one.
Mark Ea on the energy axis with a vertical line, and shade to the right of it.
Examiners now tend to ask about lowering the temperature rather than raising it, which catches out anyone reciting a memorised answer. Same theory, reversed: the peak becomes higher and moves left, the tail drops, and far fewer particles lie beyond Ea.
WORKED EXAMPLE
Use a Maxwell–Boltzmann distribution to explain why cooling a reaction mixture from 40 °C to 20 °C slows it down considerably.
Step 1 — what happens to the curveAt the lower temperature the peak becomes higher and shifts to the LEFT, and the tail falls.Step 2 — the area beyond EₐEₐ stays exactly where it is — cooling does not change the barrier. But the area to the right of it is now much smaller.Step 3 — link to collisionssmaller proportion with E ≥ Eₐ → fewer successful collisions per secondStep 4 — the secondary effectParticles also move more slowly, so they collide slightly less often. This matters far less than the change in proportion.the rate falls sharply
What a catalyst does
Nothing about the particles has changed. The line marking Ea has moved left, and the shaded area grows because of where the line now sits.
This is the crucial contrast with temperature and it is drawn very differently. Temperature redraws the curve and leaves Ea alone. A catalyst leaves the curve exactly where it was and moves Ea. Both end up increasing the shaded area, for completely different reasons.
If a question asks you to shade the particles that can react when a catalyst is present, shade everything to the right of the catalysed Ea — the whole region, not just the extra strip the catalyst gained you. The extra strip is the increase; the total is the answer.
WORKED EXAMPLE
A student sketches two Maxwell–Boltzmann curves for the same sample at two temperatures. Their sketch shows (i) both curves starting a little way up the y-axis, (ii) the two curves crossing twice, and (iii) the hotter curve with a higher peak shifted right. Identify each error.
(i) starting above the originWrong — the curve must begin at (0, 0), because no particles have zero kinetic energy.(ii) crossing twiceWrong — two curves for the same number of particles cross exactly ONCE.(iii) higher peakWrong — shifting right is correct, but the hotter peak must be LOWER, or the area would exceed the number of particles present.only the rightward shift was rightEvery one of these errors traces back to the same rule: the area under the curve cannot change.
WORKED EXAMPLE
Explain, using the distribution, why a 10 °C rise can roughly double a reaction rate even though the average particle energy rises by only a few percent.
Step 1 — where Eₐ sitsEₐ lies far out in the tail, where the curve is falling away steeply.Step 2 — what a small shift does thereA small rightward shift of the whole curve moves a disproportionately large slice of area past Eₐ, because the tail is so steep at that point.Step 3 — the numbersaverage energy +3%, but the area beyond Eₐ roughly doublesrate roughly doublesThe rate follows the AREA BEYOND the barrier, not the average energy. That is the whole reason temperature is such a powerful lever.
💡 Exam tip
Label both axes: number of particles against kinetic energy. Unlabelled axes lose easy marks.
Start at the origin, never touch the axis on the right, and cross any second curve once.
Say “a greater proportion of particles have energy ≥ Ea“ — the proportion, not just “more particles”.
Temperature moves the curve; a catalyst moves Ea. Never draw it the other way round.
When shading for a catalyst, shade the whole region beyond the new Ea.
⚠️ Common mix-up
Drawing the hotter curve with a higher peak. Wider means lower, because the area is fixed.
Letting the curve touch the x-axis at high energy.
Moving Ea when the temperature changes. The barrier is a property of the reaction.
Moving the curve when a catalyst is added. The particles’ energies are unaffected.
Calling the peak the average energy. It is the most probable energy; the mean is a little higher.
That completes How Fast? The Rate of Reaction. You can measure a rate, take it off a graph with a tangent, explain every factor that changes it in terms of collisions, and draw the distribution that underpins the lot. Up next in Topic 5: How Far? — reactions that stop before they finish, and why.
Want this explained one-to-one?
Book a free session with an experienced IB Chemistry tutor and get your trickiest topics made simple.
