Arrhenius & Collision Theory — Activation Energy
Raise the temperature and watch the Boltzmann tail past the activation energy fatten.
About this simulation
The Maxwell–Boltzmann energy distribution with the activation-energy threshold marked, and the reactive tail (E ≥ Ea) shaded. Students raise the temperature and see the distribution shift and broaden so far more molecules clear the barrier, or switch on a catalyst that lowers Ea to the same effect without heating. The reacting fraction, Ea/RT and the rate relative to a 300 K baseline update live, driving home why rate depends on the exponential tail (k = A·e^(−Ea/RT)) rather than the peak. The energy axis is deliberately schematic — as in every textbook Ea diagram — because a real Ea/RT ≈ 20 would hide the tail; every readout is computed self-consistently from the drawn distribution.
How to use it
- Start at 300 K and find the orange 'Eₐ' line: the shaded area to its right is the fraction of molecules with enough energy to react.
- Raise 'Temperature' and watch the curve flatten and spread right against the grey 300 K reference, while the shaded tail grows.
- Switch 'Catalyst' on and see the Eₐ line jump to the left, leaving the original barrier faintly dashed; the curve itself stays the same.
- Move the 'Activation energy' slider up and down and watch the shaded tail and the '% react' label at the foot of the Eₐ line.
- Compare the 'rate × … vs 300 K' line at the top in the 'Heat to 600 K' and 'Add a catalyst' presets: about ×2.2 and ×2.1, with Eₐ/RT beside it.
What to notice
- Only molecules in the tail of the distribution, with energy at least equal to Eₐ, can react on collision; most molecules near the peak cannot.
- Heating shifts the peak to higher energy and lowers it, keeping the total area the same, but the tail beyond Eₐ grows by a much larger factor.
- A catalyst does not change the distribution of energies; it gives an alternative path with a lower Eₐ, so more of the existing molecules can react.
- The rate depends on the size of the tail, not the position of the peak, which is why a modest rise in temperature can multiply the rate.
The formulas
- k = A · e^(−Eₐ / RT)
- Arrhenius equation: rate constant k from the frequency factor A, activation energy Eₐ, gas constant R and temperature T.
- log (k₂ / k₁) = (Eₐ / 2.303R) · (1/T₁ − 1/T₂)
- Compares rate constants k₁ and k₂ at two temperatures T₁ and T₂ to find Eₐ.
- fraction with E ≥ Eₐ ∝ e^(−Eₐ / RT)
- The Boltzmann factor: the share of molecules energetic enough to react falls steeply as Eₐ/RT grows.
Questions
What is activation energy?
Activation energy is the minimum extra energy that colliding molecules must have, above their average energy, to form the activated complex and go on to products. Collisions with less energy simply bounce apart. It is the height of the energy barrier between reactants and products. In the simulation it is the orange Eₐ line, and only the shaded molecules to its right can react.
Why does the rate of reaction increase with temperature?
At higher temperature molecules move faster, so they collide a little more often, but the main reason is that a much larger fraction of molecules have energy equal to or above the activation energy. The energy distribution spreads towards higher energies and the tail beyond Eₐ grows sharply. Raise the temperature in the simulation and compare the shaded tail with the grey 300 K curve.
How does a catalyst increase the rate of a reaction?
A catalyst provides an alternative reaction pathway with a lower activation energy. The energies of the molecules do not change, but because the barrier is lower, many more of them can now cross it. A catalyst does not change ΔH or the equilibrium constant; it speeds up the forward and backward reactions equally. Turn on Catalyst and watch the Eₐ line move left.
Why does a 10 °C rise in temperature nearly double the rate of many reactions?
Because the fraction of molecules above the activation energy depends exponentially on temperature, a small rise in T makes a large difference to the tail of the energy distribution. For many reactions near room temperature this roughly doubles the number of effective collisions for a 10 K rise, even though the average energy changes only slightly. The ratio of rates for a 10 K rise is the temperature coefficient.
What are effective collisions according to collision theory?
Collision theory says molecules must collide to react, but not every collision works. An effective collision needs two things: the colliding molecules must have energy at least equal to the activation energy, and they must be oriented correctly so the right bonds can break and form. The rate equals the collision frequency times the fraction of effective collisions, written as rate = P Z e^(−Eₐ/RT).
