# Activation energy and the Arrhenius equation

Activation energy (Ea) is the minimum energy needed for a collision to react. The Arrhenius equation, k = Ae^(−Ea/RT), shows k grows with temperature and falls as Ea rises. A is the frequency factor.

Chemistry (university) · Part 06: Chemical kinetics · Card 7 of 9 · Last updated 2026-10-19

## Analogy

A hill between two valleys: molecules need enough energy to climb over the top before rolling down.

## Example

**Ea = 50 kJ/mol, 298 K to 308 K**

ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂)
= (50000/8.314)(1.09×10⁻⁴)
= 0.655
k₂/k₁ ≈ 1.9 (about double)

## In practice

A high Ea is why petrol does not ignite by itself in the tank but burns fast once a spark gives the first push.

## Practice

### Flashcards

- **What is activation energy?** The minimum energy needed for a collision to lead to reaction.
- **How do you get Ea from a graph?** Plot ln k against 1/T. Slope = −Ea/R.

## Questions people ask

### How do I find Ea from experimental data?

Measure k at several temperatures. Plot ln k against 1/T (in kelvin). The graph is a straight line with slope −Ea/R. Multiply the slope by −R, where R = 8.314 J/(mol·K), to get Ea in joules per mole. Divide by 1000 if you want kilojoules per mole.

### Is activation energy the same as ΔH?

No. Ea is the height of the energy barrier from reactants to the peak. ΔH is the difference in energy between reactants and products. A reaction can be strongly exothermic yet have a large Ea, which is why it needs a spark to start.

## Related concepts

- [Collision theory](https://studyvisually.com/learn/science/chemistry-university/chemistry-university-part-6/chemistry-university-part-6-concept-6)

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