Hard

The Maxwell–Boltzmann Distribution

Simple Explanation

The Maxwell–Boltzmann distribution is a graph showing the range of kinetic energies that particles in a gas or liquid have at a given temperature — most particles have a moderate energy, while a smaller number have very low or very high energy.

Why Do We Need It?

This distribution explains, visually and quantitatively, why only a fraction of particles can react at any moment — only particles in the high-energy tail of the distribution, beyond the activation energy, are capable of reacting when they collide.

Why Does This Work?

Particles in a sample are constantly colliding and exchanging energy randomly, which naturally spreads their kinetic energies into this characteristic asymmetric curve (a long, thin tail toward high energies) — a statistical consequence of huge numbers of random particle collisions, not something imposed on the system from outside.

Real-Life Example

Why raising the temperature speeds up a reaction so much

A relatively small increase in temperature (say, 10°C) can roughly double a reaction's rate.

On the Maxwell–Boltzmann distribution, raising the temperature shifts and widens the whole curve toward higher energies — even a modest shift can dramatically increase the area under the curve beyond the activation energy, meaning far more particles now have enough energy to react.

Practice

On a Maxwell–Boltzmann distribution graph, what does the area under the curve to the right of the activation energy (Ea) represent?

Hard

Common mistake

Assuming raising the temperature simply shifts the WHOLE distribution to the right by a fixed amount — in reality, the curve also flattens and widens, and the fraction of particles beyond Ea grows disproportionately faster than the average energy itself, which is why rate increases so sharply with temperature.

Quick Review

The distribution shows the spread of particle kinetic energies at a given temperature.
Only particles beyond Ea (the shaded area under the tail) can react on collision.
Raising temperature widens the curve, sharply increasing the fraction beyond Ea.