Eyring equation


The Eyring 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 empirical Arrhenius equation, despite the Arrhenius equation being empirical and the Eyring equation based on statistical mechanical justification.

General form

The general form of the Eyring–Polanyi equation somewhat resembles the Arrhenius equation:
where ΔG‡ is the Gibbs energy of activation, κ is the transmission coefficient, kB is Boltzmann's constant, and h is Planck's constant. The transmission coefficient is often assumed to be equal to one as it reflects what fraction of the flux through the transition state proceeds to the product without recrossing the transition state, so a transmission coefficient equal to one means that the fundamental no-recrossing assumption of transition state theory holds perfectly.
It can be rewritten as:
One can put this equation in the following form:
where:
If one assumes constant enthalpy of activation, constant entropy of activation, and constant transmission coefficient, this equation can be used as follows: A certain chemical reaction is performed at different temperatures and the reaction rate is determined. The plot of versus gives a straight line with slope from which the enthalpy of activation can be derived and with intercept from which the entropy of activation is derived.

Accuracy

requires a value of the transmission coefficient, called in that theory. This value is often taken to be unity. To avoid specifying a value of, the rate constant can be compared to the value of the rate constant at some fixed reference temperature which eliminates the factor in the resulting expression if one assumes that the transmission coefficient is independent of temperature.