8.2 Temperature, rate and activation energy
- Syllabus
- 9701–2028–2029
- Topic
- 8.2
- Level
- AS
Learning objectives
8.2.1Activation energy, EA• Define activation energy, EA, as the minimum energy required for a collision to be effective8.2.2Sketch and use the Boltzmann distribution• Sketch and use the Boltzmann distribution to explain the significance of activation energy8.2.3In terms both of the Boltzmann distribution• Explain qualitatively, in terms both of the Boltzmann distribution and of frequency of effective collisions, the effect of temperature change on the rate of a reaction
Activation energy is the minimum energy for an effective collision
Activation energy, Eₐ, is the minimum energy required for a collision to be effective. Colliding particles with energy below Eₐ cannot follow that reaction pathway to products.
Meeting the energy threshold is necessary but does not remove the orientation requirement: particles must also collide in a suitable orientation for the required bonds to rearrange.
Eₐ is an energy barrier, not the reaction enthalpy ΔH and not the average kinetic energy of the particles. An exothermic reaction can still be slow if few collisions overcome a large Eₐ.
The area beyond Eₐ identifies collisions with sufficient energy
| Sketch feature | Required representation | Meaning |
|---|---|---|
| horizontal axis | particle energy, E | energy increases to the right |
| vertical axis | number or fraction of particles with energy E | population at each energy |
| distribution curve | begins at the origin, rises to one peak, then falls with a long tail approaching the axis | particles have a spread of energies, not one energy |
| total area under curve | fixed for a fixed number of particles | total particle population |
| vertical Eₐ line | placed to the right of the peak | minimum effective-collision energy |
| area to right of Eₐ | shade beneath the tail | fraction with energy at least Eₐ |
Only the shaded fraction has sufficient energy for an effective collision; a suitable collision orientation is still required. The area, not the height of the curve where it crosses Eₐ, represents the relevant fraction.
Do not make the curve touch the energy axis at a finite high energy, start above the origin, or label the peak as Eₐ. Eₐ is a threshold line and the high-energy tail approaches the axis asymptotically.
Higher temperature increases effective collisions in two linked ways
| On raising temperature for the same particle population | Boltzmann-distribution consequence |
|---|---|
| particles have greater average speed and kinetic energy | the curve becomes lower and broader and its peak moves to higher energy |
| total number of particles is unchanged | both curves enclose the same total area and cross |
| Eₐ for the unchanged pathway is unchanged | the area to the right of the same Eₐ line increases |
Faster particles collide slightly more frequently. More importantly, a much larger fraction of collisions now has energy at least Eₐ. Together these effects increase the frequency of effective collisions, so the reaction rate rises.
Lowering temperature reverses the comparison: collision frequency falls and the area beyond Eₐ becomes smaller, so there are fewer effective collisions per second and the rate decreases.
Temperature changes the distribution, not Eₐ. Do not shift the Eₐ line when comparing temperatures for the same mechanism, and do not claim that every collision in the high-energy area reacts because orientation can still be unsuitable.