Undergraduate · 15 min

Activation energy and the Arrhenius law

Vary temperature, activation energy, catalyst and concentration in a collision model and extract the exponential sensitivity of rate to temperature.

Goal

Estimate the activation energy by comparing rates at two temperatures via $\ln k = \ln A - E_a/RT$ and see how a catalyst lowers the effective barrier.

Apparatus and reagents

Virtual collision chamber with sliders for temperature T, activation energy Ea, catalyst and relative concentration.

Procedure

Fix Ea = 60 kJ/mol and conc = 50; count effective collisions at T = 300 K, then at 350 K.
Compute k₂/k₁ and solve for Ea from $\ln(k_2/k_1)=-\frac{E_a}{R}\left(\frac1{T_2}-\frac1{T_1}\right)$ ; compare with the set value.
Double the concentration and verify the rate scales with the collision frequency.
Toggle the catalyst and describe how the rate rises without changing T or concentrations.

What to observe

Raising T by tens of kelvin multiplies the fraction of collisions above the barrier far more than proportionally — the exponential Boltzmann factor.
The catalyst increases the rate by offering a lower-barrier pathway: the number of reactive collisions rises although temperature and concentration are unchanged.

Explanation

Only collisions with energy above $E_a$ react; the Maxwell–Boltzmann distribution makes that fraction proportional to $e^{-E_a/RT}$ , hence $k = A e^{-E_a/RT}$ . This is why a ~10 K rise often doubles rates near ambient temperature and why high- $E_a$ reactions are more temperature-sensitive.

History of the experiment

Svante Arrhenius gave the rate law its exponential form in 1889, generalising van ’t Hoff’s earlier work; Henry Eyring’s transition-state theory later grounded

E_a

in the potential-energy surface.

Chemists behind it

Svante Arrhenius Jacobus Henricus van ’t Hoff