Transition State Theory — The Eyring Equation

Activation Parameters

Activation enthalpy ΔH‡ 60 kJ/mol

Activation entropy ΔS‡ -20 J/mol·K

Temperature T 298 K

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Gibbs energy of activation ΔG‡

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Eyring rate constant k

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Half-life t₁⁄₂

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Crossings so far

How it works

Transition state theory treats a reaction as a molecular ensemble crossing an energy saddle point (the activated complex, ‡) that sits between reactant and product wells. The rate constant is given by the Eyring equation:

k = (k_B·T / h) · exp(−ΔG‡ / R·T)
ΔG‡ = ΔH‡ − T·ΔS‡

k_B is Boltzmann's constant, h is Planck's constant, R is the gas constant. Unlike the empirical Arrhenius equation, ΔG‡ splits into an enthalpy term (bond reorganisation energy at the barrier) and an entropy term (loss of freedom — translational, rotational, conformational — on forming the rigid activated complex).

ΔH‡ — raising it exponentially suppresses the crossing rate: a higher, "taller" barrier.
ΔS‡ — a more negative activation entropy (a tightly ordered transition state, typical of bimolecular association) slows the reaction even at fixed ΔH‡; a positive ΔS‡ (e.g. a ring-opening) speeds it up.
T — appears both linearly in the k_BT/h prefactor and, far more powerfully, inside the exponential — this is why reaction rates roughly double every ~10 °C near room temperature.

The particles below sit in the reactant well and periodically "attempt" the barrier at a pace set by the k_BT/h prefactor; each attempt succeeds with the Boltzmann probability exp(−ΔG‡/RT) — exactly the physics behind the k value shown above, just slowed down so you can watch it.

Reactant (unreacted) Crossing barrier Product (reacted)

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