In any gas some molecules crawl and a few race. The Boltzmann distribution shows how their energies are spread, and it explains why a ten-degree rise can roughly double a reaction rate.
The Boltzmann distribution shows the number of molecules with each energy. It starts at the origin (no molecule has zero energy), rises to a peak (the most probable energy) and then falls, approaching but never touching the energy axis, because there is no maximum energy. The area under the curve equals the total number of molecules. Only molecules to the right of Ea can react. At a higher temperature the curve is lower and broader, with its peak moved to the right and the same area; the area beyond Ea increases greatly, so a much larger proportion of collisions succeed.
Use the simulator to raise and lower the temperature and watch the distribution change shape. The shaded area to the right of Ea is the fraction of molecules that can react.
Raising the temperature by 10 K increases the average kinetic energy by only about 3%, yet many reactions go roughly twice as fast. Fig. 1 shows why.
| Effect of higher temperature | Consequence |
|---|---|
| molecules move faster | collisions slightly more frequent (a small effect) |
| curve flattens and shifts right | a much greater proportion of molecules have energy ≥ Ea |
| more successful collisions per second | rate increases a lot; often roughly doubles for 10 K |
On the higher-temperature curve the peak is lower and further right, and the area is the same, because the number of molecules has not changed. And temperature does not change Ea; it changes how many molecules have enough energy to overcome it. The main reason for the faster rate is the larger proportion of molecules with E ≥ Ea, not the increase in collision frequency.
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What does the area under a Boltzmann distribution curve represent?
Why does the Boltzmann curve start at the origin?
Why does the curve never meet the energy axis at high energy?
Which molecules on a Boltzmann distribution are able to react on collision?
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How does the Boltzmann distribution change when the temperature is increased?
The main reason a small rise in temperature greatly increases the rate is that:
On a Boltzmann distribution, where is the mean energy of the molecules compared with the peak?
Which change increases the proportion of molecules with energy above Ea without changing the temperature?
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