Eyring equation

General form

The general form of the Eyring–Polanyi equation somewhat resembles the Arrhenius equation:

  k = k B T h e − Δ G ‡ R T

where ΔG^‡ is the Gibbs energy of activation, k_B is Boltzmann's constant, and h is Planck's constant.

It can be rewritten as:

k = k B T h e Δ S ‡ R e − Δ H ‡ R T

To find the linear form of the Eyring-Polanyi equation:

ln ⁡ k T = − Δ H ‡ R ⋅ 1 T + ln ⁡ k B h + Δ S ‡ R

where:

A certain chemical reaction is performed at different temperatures and the reaction rate is determined. The plot of   ln ⁡ ( k / T ) versus   1 / T gives a straight line with slope   − Δ H ‡ / R from which the enthalpy of activation can be derived and with intercept   ln ⁡ ( k B / h ) + Δ S ‡ / R from which the entropy of activation is derived.

Accuracy

Transition state theory requires a value of a certain transmission coefficient, called   κ in that theory, as an additional prefactor in the Eyring equation above. This value is usually taken to be unity (i.e., the transition state   A B ‡ always proceeds to products   A B and never reverts to reactants   A and   B ), and we have followed this convention above. Alternatively, to avoid specifying a value of   κ , the ratios of rate constants can be compared to the value of a rate constant at some fixed reference temperature (i.e.,   k ( T ) / k ( T R e f ) ) which eliminates the   κ term in the resulting expression.