Arrhenius Equation

Molecules collide constantly, but only the small fraction carrying enough energy to climb the activation barrier actually react. The Boltzmann factor $e^{-E_a/RT}$ is that fraction, and A is roughly the collision frequency with the right geometry — so the rate constant is "how often they meet" times "how often the meeting is violent enough". Because $E_a$ sits in an exponent, the temperature dependence is ferocious: for a typical $E_a$ near 50 kJ/mol, a 10 K rise around room temperature roughly doubles the rate, the old rule of thumb behind refrigerating food and running reactions under reflux.

Svante Arrhenius proposed the form in 1889 after Jacobus van 't Hoff's thermodynamic argument suggested it. He was no stranger to sceptical committees: his 1884 Uppsala doctoral thesis on electrolytic dissociation — the claim that salts split into ions in water — so baffled his examiners that they awarded it the lowest passing grade, nearly ending his career. Nineteen years later the same work won him the 1903 Nobel Prize in Chemistry. A worked case: a reaction with A = 1.0 × 10¹³ s⁻¹ whose rate constant is 1.0 × 10⁻³ s⁻¹ at 300 K has $E_a$ = RT ln(A/k) = 8.314 × 300 × ln(10¹⁶) = 91.9 kJ/mol. Only the ratio A/k matters here, so any consistent pair of rate-constant units works.