IB Chemistry SL & HLTopic 5 — The Rate of Chemical ChangePaper 1 & 2Core skill~12 min read
Maxwell-Boltzmann Distributions
This one graph explains temperature and catalysts better than any amount of writing. It shows that particles at a single temperature have wildly different energies — and once you can see that spread, you can see exactly which particles are able to react and which are not.
📘 What you need to know
The curve shows how kinetic energy is spread among the particles at one temperature.
A few particles have very low energy, a few have very high energy, and most are in between.
The peak is the most probable energy. It is not the average, which sits slightly to the right.
The curve starts at the origin and never touches the x-axis on the right.
The area under the curve is the total number of particles, so it cannot change when you heat the mixture.
Heating makes the curve flatter, wider, and shifted right, with a higher tail. The two curves cross exactly once.
A catalyst does not change the curve at all — it moves the Ea line to the left.
Reading the graph
Both axes matter. Across the bottom is kinetic energy. Up the side is how many particles have that energy. So the height of the curve at any point tells you how common that energy is.
The shaded strip goes all the way to the right-hand edge, because there is no upper limit on how much energy a particle can have. The curve gets very low but never actually reaches the axis.
🧩 Drawing the curve so it earns full marks
Start at the origin. No particle has zero energy, so the curve begins at (0, 0).
Rise steeply to a peak quite far to the left, then fall away more gently.
Never let the tail touch the axis. It should approach it and keep going to the edge of your graph.
Label both axes — “number of particles” up, “kinetic energy” across.
Add the Ea line as a vertical line well to the right of the peak, and shade to the right of it.
The peak is the most probable energy, not the mean. Because the curve has a long tail stretching to the right and nothing to the left of zero, it is lopsided, and that drags the average slightly above the peak.
Raising the temperature
Here is the thing that makes the area rule so useful: heating the mixture does not create any new particles. You still have exactly the same number of them, just arranged differently across the energy range. So the area under the curve has to stay the same — which is precisely why the curve has to get flatter as it spreads out.
The temperature gap here is exaggerated so you can actually see the effect. In this diagram the shaded tail nearly triples — for a real 10 °C rise the increase is closer to double, but the mechanism is identical.
The three things to say every time
The peak becomes lower and moves to the right.
The curves cross once, and the area underneath is unchanged.
Beyond Ea the higher-temperature curve is above the lower one, so a greater proportion of particles can react.
Why the peak has to drop. Students often draw the hot curve higher and wider, which would mean more particles appeared out of nowhere. Since the area is fixed, spreading out sideways forces the curve down. Wider means flatter — there is no way around it.
Lowering the temperature
Examiners have taken to asking about cooling rather than heating, which catches people who have only memorised one direction. The physics is identical, just reversed:
The peak becomes higher and moves left.
The tail beyond Ea gets lower.
A smaller proportion of particles has enough energy, so the rate falls.
If you get a cooling question, sketch the heating version in the margin first and then read your own diagram backwards. It takes ten seconds and stops you talking yourself into the wrong direction.
Adding a catalyst
A catalyst is different in a really important way. It does not touch the particles’ energies at all, so the curve does not move. What moves is the Ea line, which slides to the left because the new pathway needs less energy.
Read the shading carefully. The particles that can react with the catalyst present are both bands added together, not just the pale one. That distinction is a favourite exam trap.
The trap, spelled out. If a question says “shade the area representing particles able to react in the presence of a catalyst”, you shade everything to the right of the catalysed Ea line — the pale band and the dark band. Shading only the pale band gives just the extra particles, which is a different question.
Worked examples
WORKED EXAMPLE
Describing the effect of heating
A reaction mixture is heated from 25 °C to 45 °C. Describe how the Maxwell-Boltzmann distribution changes, and explain why the rate increases. (3 marks)
Mark 1: shape of the new curve
The peak is lower and shifted to the right, and the curve is flatter and broader.
Mark 2: the area stays fixed
The total area is unchanged, because the number of particles has not changed.
Mark 3: link to rateThe area to the right of Ea is larger, so a greater proportion of particles has energy of at least Ea and the rate increases.“greater proportion” plus “at least Ea” is what the mark scheme is hunting for
WORKED EXAMPLE
The same idea in reverse
A student cools a reaction mixture in an ice bath. Sketch what happens to the distribution curve and explain the effect on the rate.
Step 1: reverse everything
The peak becomes higher and moves to the left; the curve is narrower and taller.
Step 2: the tail
The tail beyond Ea drops, so the shaded area shrinks.
Step 3: concludeA smaller proportion of particles reaches Ea, so fewer successful collisions occur per second and the rate falls.the curves still cross exactly once, and the area is still the same
WORKED EXAMPLE
Telling temperature and catalyst apart
A student claims that adding a catalyst shifts the Maxwell-Boltzmann curve to the right, in the same way heating does. Explain what is wrong with this, and describe what a catalyst really changes on the graph.
Step 1: what is wrong
The shape of the curve depends only on temperature. A catalyst does not change the temperature, so it cannot change the distribution of energies.
Step 2: what does change
The catalyst offers a pathway with a lower Ea, so the vertical Ea line moves to the left.
Step 3: the consequenceMore of the unchanged curve now lies to the right of the line, so a greater proportion of particles can react.heating moves the curve; a catalyst moves the line — never both
💡 Exam tip
Start at the origin and never touch the axis. Both errors are marked, and both are easy to avoid.
When you draw two temperature curves, make sure they cross exactly once and the hot tail sits clearly above the cold one on the right.
Use “proportion” or “fraction”, not just “more particles”. The number of particles never changes.
Write “energy greater than or equal to Ea“ rather than “greater than Ea“.
For a catalyst, move the line, not the curve. Draw one curve and two vertical lines.
If asked to shade for a catalysed reaction, shade the total area right of the new line, not just the extra sliver.
Label the peak as most probable energy if asked, not as the mean.
⚠ Common mix-up
Drawing the hot curve both taller and wider. That invents extra particles. Wider forces flatter.
Letting the tail meet the x-axis. There is no maximum possible energy, so the curve keeps going.
Starting the curve above the origin. It must begin at (0, 0).
Moving the curve when a catalyst is added. Only temperature changes the curve.
Moving the Ea line when the temperature changes. Ea is fixed for a given pathway.
Shading only the extra band in a catalyst question.
Saying the peak is the average energy. The mean sits a little to the right of the peak.
Having the two curves cross twice. They meet at exactly one point.
Up next: The Rate Equation (HL) — from here on the course stops describing rate in words and starts putting it in an equation, with orders of reaction and the rate constant.
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