Undergraduate · 15 min

Reaction rate and collision theory

Watch A + B → 2C happen only when colliding particles carry enough energy; change temperature, Ea and catalyst.

Goal

See that the rate depends on the fraction of collisions with energy above $E_a$ , and why a higher temperature or a catalyst speeds a reaction up.

Apparatus and reagents

A simulation only: no reagents. The energies are scaled down (Ea ÷ 8) so that reactions are visible within seconds; the trends are the real ones.

Procedure

Run the default (300 K, Ea = 50 kJ/mol) and watch how fast C accumulates.
Raise the temperature to 350 K and compare.
Switch the catalyst on, then off again, and raise Ea to 80 kJ/mol.

What to observe

The share of collisions that react is about 2.5 % at 300 K, 3.8 % at 350 K, 15.7 % with the catalyst and only 0.5 % at Ea = 80 kJ/mol (theoretical values for this model).
Most collisions do nothing: the particles just bounce.
When A or B runs out the counts stop changing and the run restarts after a moment.

Explanation

A collision leads to reaction only if the energy along the line of centers exceeds $E_a$ . For thermal motion the fraction of such collisions is proportional to $e^{-E_a/RT}$ , which gives the Arrhenius equation $k = A\,e^{-E_a/RT}$ (the factor $A$ contains the collision frequency and geometry). Raising $T$ shifts more collisions above the threshold and also makes them more frequent. A catalyst offers a different pathway with lower $E_a$ ; it speeds up both directions and does not change the equilibrium constant or $\Delta H$ .

History and context

Wilhelmy's 1850 polarimeter study of sugar inversion was the first measured reaction rate; van 't Hoff's chemical dynamics (1884) then linked rates to equilibrium. In 1889 Arrhenius noticed that rate data of many kinds all bent the same way on a

1/T

plot and wrote

k = A\,e^{-E_a/RT}

— the equation this collision simulation animates particle by particle.

Related chemists

Svante Arrhenius Jacobus Henricus van ’t Hoff