The Eyring equation (occasionally also known as Eyring–Polanyi equation) is an equation used in chemical kinetics to describe changes in the rate of a chemical reaction against temperature. It was developed almost simultaneously in 1935 by Henry Eyring, Meredith Gwynne Evans and Michael Polanyi. The equation follows from the transition state theory, also known as activated-complex theory. If one assumes a constant enthalpy of activation and constant entropy of activation, the Eyring equation is similar to the Arrhenius equation, despite the Arrhenius equation being phenomenological and the Eyring equation based on statistical mechanical justification.

General form

The general form of the Eyring–Polanyi equation somewhat resembles the Arrhenius equation is the Gibbs energy is the transmission coefficient is the Boltzmann constant is the absolute temperature (Kelvin is the Planck constant.

is typically not one because (i) the reaction coordinate chosen for the process at hand is usually not perfect and (ii) many barrier-crossing processes are somewhat or even strongly diffusive in nature. For example, the transmission coefficient of methane hopping in a gas hydrate from one site to an adjacent empty site is between 0.25 and 0.5. from the resulting plateau in the RFCF. This approach is also referred to as the Bennett-Chandler approach, which yields a dynamical correction to the standard transition state theory-based rate constant.

It can be rewritten as:

where:

• = reaction rate constant

• = absolute temperature

• = enthalpy of activation

• = gas constant

• = transmission coefficient

• = Boltzmann constant = R/NA, NA = Avogadro constant

• = Planck constant

• = entropy of activation

from which the enthalpy from which the entropy of activation is derived.

Accuracy

Transition state theory requires a value of the transmission coefficient always proceed directly to products and never revert to reactants and factor in the resulting expression if one assumes that the transmission coefficient is independent of temperature.

Error propagation formulas

Error propagation have been published.

Notes

References

• Chapman, S. and Cowling, T.G. (1991). "The Mathematical Theory of Non-uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases" (3rd Edition). Cambridge University Press,

External links

• Eyring equation at the University of Regensburg (archived from the original)

• Online-tool to calculate the reaction rate from an energy barrier (in kJ/mol) using the Eyring equation

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