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Arrhenius: Activated Rate Theory

Reaction rates, energy barriers, and the log-linear Arrhenius plot

PARAMETERS

k (Arrhenius):
k (Kramers):
k (Eyring):
Half-life t₁/₂:

Arrhenius (1889): k = A·exp(−Eₐ/RT). The pre-exponential A encodes attempt frequency; the exponential is the Boltzmann probability of surmounting the barrier.

ln k = ln A − Eₐ/(RT)

Kramers (1940) derives the rate from the Fokker-Planck equation — valid for overdamped or underdamped limits.

Eyring / TST (1935): k = (k_BT/h)·exp(−ΔG‡/RT) — uses partition functions at the transition state.

The slope of the Arrhenius plot (ln k vs 1/T) is −Eₐ/R — a straight line reveals the activation energy directly.