Maxwell-Boltzmann Distribution

Full Notes

Maxwell-Boltzmann distributions are graphs that show how available energy is spread out and shared amongst molecules of a gas. They help explain why:

• Not all molecules have the same energy.
• Only a small fraction of molecules have enough energy to react.
• Increasing temperature increases reaction rate.

Features of the Maxwell-Boltzmann Curve

• Starts at the origin (0,0) → no particles have zero energy.
• Peaks at the most probable energy → the energy most particles have.
• Has a long tail to the right → a few molecules have very high energy (never crosses x-axis again).
• Area under the curve = total number of molecules.
• Only molecules with energy ≥ activation energy (E_a) can react.

Temperature and Catalysts

How changing temperature and using a catalyst affect the rate of a reaction can be explained visually using Maxwell-Boltzmann distribution curves.

Effect of Temperature:

Increasing temperature causes the curve to shift right and flatten slightly.

• More particles exceed activation energy (E_a).
• Frequency of successful collisions increases.
• Reaction rate increases sharply, even with small temperature rise.

Effect of a Catalyst:

Using a catalyst lowers the activation energy barrier, moving the E_a line left on the curve.

More particles now have sufficient energy (≥ E_a) meaning the reaction is faster.

Matt’s exam tip

Increasing the temperature or using a catalyst increases the area under the curve beyond E_a. This represents the proportion of particles that can react. It explains why reactions don’t happen instantly – only a fraction of particles have enough energy at any time.

Summary

• Maxwell-Boltzmann distribution shows how particle energies are spread in gases.
• Only particles with energy ≥ activation energy can react.
• Temperature increases shift the curve right and flatten it, giving more particles above E_a.
• Catalysts lower the activation energy barrier, increasing successful collisions.