8.2 Effect of Temperature
🎯 Learning outcomes
After completing this lesson, you should be able to:
- define activation energy, EA, as the minimum energy required for a collision to be effective
- sketch and use the Boltzmann distribution to explain the significance of activation energy
- explain qualitatively, in terms both of the Boltzmann distribution and of the frequency of effective collisions, the effect of temperature change on the rate of a reaction
1🔁Recap: activation energy
In the previous lesson on collision theory, you met the idea that only effective collisions — those with the correct orientation and enough energy — lead to a reaction.
The activation energy, EA, is the minimum energy required for a collision between reacting particles to be effective.
But not all particles in a sample move at the same speed, or carry the same amount of kinetic energy — some move slowly, some move very fast, and most are somewhere in between. This spread of energies turns out to be the key to understanding why temperature has such a dramatic effect on rate.
An effective collision needs both correct orientation and energy ≥ EA. Temperature changes don’t affect orientation — they affect how many particles have enough energy. That’s what this lesson explores.
2📈The Boltzmann distribution
The Boltzmann distribution is a graph showing the number of molecules with a particular kinetic energy, plotted against kinetic energy. Its shape changes with temperature.
This curve tells us how the total kinetic energy of a sample is shared out among its particles at a given moment. Three features of the shape matter enormously at A level:
- The curve starts at the origin — no molecules have zero kinetic energy.
- It rises to a peak, showing the energy that the largest number of molecules possess (the most probable energy) — this is not the same as the average energy, which lies slightly to the right of the peak.
- It falls away into a long tail that gets closer and closer to the energy axis but never quite touches it — meaning a small number of molecules always have very high energies, however far along the axis you look.
When sketching the curve, examiners look for: (1) the curve starting at the origin, (2) a single asymmetric peak (steep rise, gentle fall), and (3) the tail approaching — but not touching — the x-axis. Missing any of these loses easy marks.
3🌡️Effect of temperature on the distribution
Raising the temperature increases the average kinetic energy of the molecules — this reshapes the whole Boltzmann distribution in a very specific way.
Key changes when temperature increases from T₁ to T₂:
- the peak moves to the right (higher most-probable energy) and becomes lower and broader
- the area under the curve stays the same — the sample still contains the same number of molecules, just redistributed across a wider energy range
- the proportion of molecules with energy ≥ EA (the shaded area) increases substantially — this is the single most important feature to point out in an exam answer
Comparing the two shaded regions on the diagram: even though the T₂ curve is lower overall, its tail sits well above the T₁ curve everywhere beyond EA — so the shaded (reacting) region for T₂ is far bigger, despite a relatively modest rise in temperature.
4🚀Why rate increases with temperature
Increasing temperature speeds up a reaction for two combined reasons:
- The frequency of effective collisions is greater, simply because the molecules move faster and collide more often.
- A greater proportion of molecules have kinetic energy greater than the activation energy, EA.
The second reason has a far greater effect. A small rise in temperature only slightly increases how often molecules collide, but it dramatically increases the proportion of molecules with enough energy to react — because that proportion depends on the shrinking tail beyond EA, which grows very quickly as the distribution shifts.
As a rough guide often quoted for many reactions, the rate of reaction roughly doubles for every 10 °C rise in temperature — a striking result given how small a fraction of molecules actually gain enough energy to cross EA. This is only an approximation, not a fixed law, and varies between reactions.
A full-mark answer must reference both ideas — collision frequency and the Boltzmann distribution — and should make clear that the increase in the proportion of molecules with E ≥ EA is the dominant reason, not simply “particles move faster and collide more.” Answers that only mention collision frequency are incomplete.
5📝Exam-style practice
Try reasoning through these typical exam-style questions before revealing each model answer.
Show model answer
Raising the temperature shifts the Boltzmann distribution so that a much greater proportion of molecules now have kinetic energy ≥ EA (shown by the larger shaded area beyond EA). Because this proportion increases sharply even for a small temperature rise, the frequency of effective collisions — and hence the rate — increases far more than the modest rise in overall collision frequency would suggest.
Show model answer
There is always a (very small) probability that a molecule, through repeated collisions, ends up with an extremely high kinetic energy. However far along the energy axis you look, the number of molecules never becomes exactly zero — it just becomes vanishingly small. This is why the curve approaches, but never meets, the x-axis.
Show model answer
Differences: the 40 °C curve has its peak shifted to the right (higher most probable energy) and is lower/more spread out (broader) than the 20 °C curve.
Stays the same: the area under both curves is equal, since the total number of molecules in the sample has not changed.
📌 Exam tips & quick summary
✅ Do remember
- EA = minimum energy needed for an effective collision
- Boltzmann curve: starts at origin, one asymmetric peak, long tail that never touches the x-axis
- area under the curve = total number of molecules (constant at fixed sample size)
- ↑ T → peak shifts right, becomes lower & broader; area beyond EA grows a lot
- two reasons rate ↑ with T: collision frequency ↑, AND proportion with E ≥ EA ↑ (this second one dominates)
🚫 Do not confuse
- the most probable energy (the peak) is not the same as the average energy (slightly to the right of the peak)
- increasing T does not change the value of EA itself — only the proportion of molecules that can reach it
- don’t rely on “faster collisions” alone as your explanation — always link back to the Boltzmann distribution
🔁 Quick recap
- EA: minimum energy for an effective collision
- Boltzmann distribution: number of molecules vs. kinetic energy
- ↑ Temperature: peak shifts right & flattens, area beyond EA increases sharply
- Dominant reason rate ↑: proportion of molecules with E ≥ EA