3.6. Arrhenius Equation

It is easy to imagine, especially in the gas phase, that at higher temperature a given chemical reaction will proceed faster due to higher collision rate. This results in a higher kinetic energy, which has an effect on the activation energy of the reaction. The activation energy (Ea) is the amount of a minimal energy required to ensure that a reaction happens (Turányi, 2010).

Dependence of rate coefficient on temperature

Figure 3.2: Dependence of rate coefficient on thermodynamic temperature

The rate of the chemical reactions depends on the concentrations of reagents, which can vary during the reaction and the rate coefficient (Figure 3.2). Arrhenius equation describes the effect of a change of temperature on the rate coefficient and therefore on the rate of the reaction:

,

(3.13)

where A is the pre-exponential factor or the steric factor, which includes factors like the frequency of collisions and their orientation. It varies slightly with temperature, although not much. It is often taken as constant across small temperature ranges. Ea is the activation energy, R is universal gas constant, and T is the thermodynamic temperature, respectively. The former form (13) can be written equivalently as

.

(3.14)

This is the so-called Arrhenius plot, where there is a linear correlation between ln k and 1/T (Figure 1.3). The slope and the intercept of (14) provide activation energy and pre-exponential factor, respectively.

Arrhenius plot

Figure 3.3: Arrhenius plot