Use a Boltzmann distribution to explain catalysis
Compare activation-energy thresholds to explain why a catalyst increases the effective-collision fraction at fixed temperature.
AS Level; Cambridge International Chemistry 9701, 2025–2027 syllabus. Rate data and diagrams are illustrative unless a question supplies measurements. A diagram is qualitative unless labelled values are provided. Written practice is self-checked
Before you begin
- Rearrange simple ratios and use consistent units for time, volume, mass and concentration.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
At the same temperature, what changes when a catalyst is introduced?
What you will learn
- Compare catalysed and uncatalysed Eₐ thresholds
- Interpret the area beyond each threshold
- Distinguish a lower barrier from a changed temperature distribution
A catalyst lowers the threshold, not the distribution
At the same temperature, the Boltzmann distribution for the particle sample is the same whether the catalyst is present or absent. The catalyst changes the reaction mechanism and lowers Eₐ; it does not shift the particles' distribution to higher energy.
On the same curve, draw the uncatalysed Eₐ farther to the right and the catalysed Eₐ to its left. The area to the right of the lower, catalysed threshold is larger.
More particles can cross the catalysed barrier
The larger area beyond the lower threshold means a greater fraction of particles has sufficient energy for an effective collision along the catalysed route. Effective collisions become more frequent, so the reaction is faster at the same temperature.
Do not say the catalyst gives every particle extra energy or changes the Boltzmann curve. It lowers the barrier that the existing distribution is compared with.
Pause and explain
On the same Boltzmann curve, which threshold gives a larger effective fraction?
Worked example
At a fixed temperature, a catalyst lowers Eₐ. Explain the effect on the fraction of particles able to react.
Show the worked solution
- Keep the same-temperature distribution fixed.
- The catalysed Eₐ threshold is lower.
- A larger area lies to its right, so a greater fraction can overcome the barrier.
Answer A greater fraction of the unchanged particle distribution lies above the lower catalysed Eₐ, so effective collisions become more frequent.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A catalyst lowers Eₐ without changing temperature. What stays the same and what changes on the Boltzmann sketch?
Give me a hint
Keep the particle distribution fixed and move only the threshold line.
Compare my reasoning
- The distribution curve and total area stay the same.
- The catalysed Eₐ line is at lower energy.
- The area beyond the new line is greater.
The distribution is unchanged; the lower catalysed Eₐ threshold leaves a larger fraction of particles beyond it.
Look for these in your work
- Curve unchanged
- Threshold lowered
- Effective fraction compared
Explain the increase in rate using the area beyond the catalysed activation-energy line.
Give me a hint
Connect the high-energy fraction to effective collisions per second.
Compare my reasoning
- More of the curve lies beyond the lower catalysed Eₐ.
- A greater fraction can overcome the barrier.
- Effective collisions are more frequent, so rate increases.
The catalyst lowers Eₐ, increasing the fraction of particles able to make effective collisions and thus the reaction rate.
Look for these in your work
- Area interpreted
- Barrier crossed
- Rate connected
A candidate draws a new higher-temperature Boltzmann curve after adding a catalyst at constant temperature. Correct the sketch.
Give me a hint
Catalyst and temperature change different parts of the model.
Compare my reasoning
- At the same temperature, keep the original particle-energy curve.
- Draw a lower Eₐ threshold for the catalysed pathway.
- Show the larger right-hand area beyond that lower threshold.
Keep the distribution unchanged and lower the Eₐ line; the catalysed reaction has a larger effective fraction without a temperature increase.
Look for these in your work
- Fixed-temperature curve retained
- Catalyst represented by lower Eₐ
- Larger effective fraction shown
Common mistakes
- Drawing the catalyst as a shift in temperature distribution
- Saying the catalyst raises all particle energies
- Claiming the lower threshold leaves fewer particles beyond it
- Forgetting to link the area to rate
What can you explain now?
At the same temperature, what changes when a catalyst is introduced?
Compare with the explanation
The mechanism and its activation-energy barrier
The catalyst offers a route with a lower Eₐ.
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Make it stick
For catalysis at fixed temperature, which changes: the energy distribution or the Eₐ threshold?
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