Effect of temperature on reaction rates and the concept of activation energy

Activation energy ($E_a$) is the minimum energy required for a collision to be effective — i.e. the minimum energy colliding particles must have for a reaction to occur.

• Only molecules with energy ≥ $E_a$ can react when they collide.
• A high $E_a$ means few molecules have enough energy → slow reaction; a low $E_a$ means many do → fast reaction.

On a reaction pathway diagram (Topic 5.1), $E_a$ is the height of the energy barrier (hump) between reactants and the transition state.

In any sample, molecules have a range of energies. The Boltzmann distribution plots the number of molecules against energy.

Key features to draw correctly:

• The curve starts at the origin (no molecules with zero energy).
• It rises to a peak (the most probable energy), then falls with a long tail at high energy.
• It never touches the x-axis again (a few molecules always have very high energy).
• $E_a$ is marked as a vertical line; the shaded area to its right = the number (fraction) of molecules with energy ≥ $E_a$ that can react.

Increasing the temperature:

• shifts the Boltzmann curve to the right and makes it flatter (lower peak), keeping the total area the same;
• so a much larger fraction of molecules now have energy ≥ $E_a$;
• therefore there are more frequent effective collisions → the rate increases.

Two effects, but one dominates:

• Molecules also move faster, so collisions are slightly more frequent — a small contribution.
• The major effect is the large increase in the fraction of molecules with energy ≥ $E_a$.

This is why a modest temperature rise causes a large increase in rate (rule of thumb: rate roughly doubles for every ~10 °C rise).