Chemical Kinetics · Collision Theory

Activation Energy & the Boltzmann Tail

Molecules carry a spread of energies — the Maxwell–Boltzmann distribution. Only those past the activation energy Ea collide hard enough to react (the shaded tail). Raising the temperature shifts the spread right and fattens that tail; a catalyst lowers Ea instead. Both send more molecules over the barrier — and rate follows the tail, not the peak. (Energy axis is schematic, as in every textbook Ea diagram — real Ea/RT ≈ 20 would hide the tail entirely.)

■ distribution at T ■ baseline (300 K) ▮ Ea · shaded = able to react

Conditions

Temperature T 300 K
Activation energy Ea 18

Catalyst

A catalyst opens a lower-Ea path (here ≈ 40% lower). It doesn't heat the mixture — it moves the barrier, so the same molecules clear it.

0.0
fraction of molecules with E ≥ Ea
18
effective Ea (units)
2.3
Ea / RT
1.0×
rate vs 300 K baseline
4.0
most-probable E
k = A·e−Ea/RT

Try this

Watch the tail, not the peak. Raise T and the reacting fraction climbs far faster than the curve seems to move — because rate depends exponentially on the tail (the real ~10 °C rule can double a rate). Then, at fixed T, flip on the catalyst: lowering Ea grows the same shaded fraction, no heating needed.