Reaction Rates

How the model works

The model reaction is elementary and second order:

A + B → C, rate = k [A][B], k = A_f · e^(−Ea / RT)

Two things set the rate. Collision frequency grows with concentration (more particles per volume). The fraction of collisions with enough energy grows steeply with temperature: only collisions with energy above the activation energy Ea react, and the Boltzmann factor e^(−Ea/RT) gives that fraction.

The right-hand graph integrates the rate law exactly (it shows the expected concentrations). The particle box is a stochastic illustration with a fixed random seed, so Reset replays the same run. The rule of thumb that “every 10 °C doubles the rate” holds only for Ea ≈ 50 kJ/mol near room temperature.

Model reaction with a stated pre-exponential factor A_f = 1.0×10⁹ L/(mol·s). It is not a specific real reaction; real mechanisms can have several steps.

Guided experiments

1. Heat it up by 10 °C. Ea = 50 kJ/mol, compare 298 K with 308 K. Prediction: k rises by a factor e^(Ea/R × (1/298 − 1/308)) ≈ 1.93, so the rate nearly doubles. Run at 308 K
2. Double [A]. Keep T fixed and double the starting [A]. Prediction: the initial rate doubles (first order in A). The reaction stops when B runs out, because B is now limiting. Double [A]
3. A catalyst. Lower Ea from 50 to 40 kJ/mol at 298 K. Prediction: k rises by e^(10000/(8.314 × 298)) ≈ 57 times, from a modest change in Ea. Lower Ea (catalyst)

Challenge

A reaction's rate triples when heated from 25 °C to 45 °C. Estimate its activation energy.

References

• OpenStax, Chemistry 2e, §12.3 “Rate Laws” and §12.5 “Collision Theory”.