Activation energy and the Boltzmann distribution

6 minAS Level8.2.18.2.2

AI-drafted, independently checked · not yet teacher-reviewed

By the end of this lesson

By the end you can define activation energy, sketch the Boltzmann distribution, and use it to explain why only a fraction of collisions lead to reaction.

Definition

Activation energy (Eₐ)

The minimum energy that colliding particles must have for the collision to be effective, so that a reaction occurs.

Most molecules are not energetic enough

Molecules in a gas or liquid do not all move with the same speed. They have a spread of kinetic energies, and the distribution changes constantly as they collide.

At any moment, many molecules are moving slowly, some are moving quickly, and a very small number are moving extremely quickly.

For a collision to be effective, the particles must arrive with at least the activation energy. Only the fastest-moving molecules in the mixture can manage that. Most collisions fail because the particles simply do not have enough energy.

That is why reaction rates are often much slower than collision frequencies would suggest. Particles collide billions of times per second, but only a tiny fraction of those collisions has enough energy to break the bonds that need to break.

The Boltzmann distribution. Only the shaded tail, beyond

E_a

, represents molecules with enough energy for an effective collision.

Reading the Boltzmann curve

The curve has three features to remember.

It starts near the origin: very few molecules have near-zero kinetic energy.
It peaks at a fairly low energy: most molecules have a modest amount of kinetic energy.
It has a long tail to the right: a small number have very high energies.

The area under the whole curve represents the total number of molecules.

The area under the curve to the right of $E_a$ represents the number of molecules with energy at least $E_a$ . Divide by the total area and you have the fraction of molecules that can react on collision.

A small change in $E_a$ can change that fraction a lot, because the tail is steep.

Activation energy is not the same as enthalpy change

The activation energy is an energy barrier on the way from reactants to products. The enthalpy change of reaction, $\Delta H$ , is the difference in energy between the reactants and the products.

A reaction can have a large activation energy and still be exothermic overall: the particles must climb a high hill before they can roll down the other side. The height of the hill and the net drop are separate quantities.

A catalyst provides an alternative route with a lower activation energy. More molecules then have enough energy to take that route, so the rate increases. The catalyst does not change the enthalpy change or the position of equilibrium.

Common mistakes

Activation energy is the energy released when the reaction happens.

That is the enthalpy change (or the energy released per mole). Activation energy is the minimum energy needed to start the reaction, not the energy given out.

All molecules have the same kinetic energy at a given temperature.

They have a distribution of energies. The Boltzmann curve shows how many have each energy; only a small fraction exceed $E_a$ .

In the exam

The definition of activation energy must include minimum energy and effective collision. "Energy needed to react" is too vague.
When sketching the Boltzmann curve, label both axes, start the curve near the origin, show a single peak and a long tail, and mark $E_a$ on the energy axis.
Shade the area beyond $E_a$ and say what it represents: the molecules with enough energy to react.
Do not draw the curve touching the energy axis at high energy; the tail approaches it but does not meet it.
For a catalyst, show a lower $E_a$ on the same axes and a larger shaded area. Do not shift the whole curve.

Key takeaways

Activation energy is the minimum energy for an effective collision.
Molecules have a distribution of kinetic energies.
The Boltzmann curve plots number of molecules against kinetic energy.
The area beyond Ea is the number of molecules that can react.
A catalyst lowers Ea, increasing the fraction of molecules that can react.

Definitions

Multiple choiceQuestion 1 · Recall

Multiple choiceQuestion 2 · Recall

Multiple choiceQuestion 3 · Apply

Answer the 3 questions above to continue.