Rate constants for chemical reactions are known to depend strongly on the reaction temperature. One well known empirical relationship expressing this dependence is the Arrhenius equation (1):
k = A exp(-E_{a}/RT) (1)
The important parameters in this relationship are the activation energy E_{a} (in units of kJ/mol or kcal/mol) and the preexponential factor A. The latter is given in the same units as the rate constant itself ([s^{-1}] for a first order reaction and [l mol^{-1} s^{-1}] for a second order reaction).
A second expression used to describe the temperature dependence of reaction rate constants is the Eyring equation (2) that results from transition state theory :
k = (k_{B}T/h) (1/c^{n}) exp(-dG**/RT) (2)
Here the first part of the equation contains only Boltzmann's constant k_{B} and Planck's constant h as well as the absolute temperature T (in [K]). The second part accounts for the concentration dependence of the rate constant, c being the reference concentration of the reaction. The exponent n assumes a value of 0 for a first order reaction and of 1 for a second order reaction. The third part of equation (2) contains the activation free enthalpy dG** of the reaction which, according to equ. (3) is directly related to the activation enthalpies and activation entropies:
dG** = dH** - TdS** (3)
The activation parameters of the Arrhenius and Eyring equations of a first order reaction are related as follows:
E_{a} = dH** + RT (4)
A = (c k_{B}T/h) exp(dS**/R) (5)
In particular the difference between Arrhenius activation energy E_{a} and the activation enthalpy dH** are quite small and numerically close to the accuracy attained in most experiments (RT = 2.5 kJ/mol at 298.15K). These two energies are therefore frequently used interchangeably in the literatur to define the activation barrier of a reaction.