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_BT/h) (1/cⁿ) 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_BT/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.

last changes: 11.11.2004, HZ
questions & comments to: zipse@cup.uni-muenchen.de