D24.2 Arrhenius Equation

The relationship between the activation energy (E_a), temperature, steric factor and the rate constant (k) for a given chemical reaction is summarized by the Arrhenius equation:

The constant A is called the frequency factor and it depends on the rate at which collisions occur and the fraction of collisions that have the correct orientation (steric factor). (In this course, we will generally assume that A is independent of temperature.) The exponential term, e^-E_a/RT, is the fraction of the total collisions that has sufficient energy to overcome the activation-energy barrier of the reaction. Here, R is the ideal gas constant (8.314 J/K·mol), T is absolute temperature in kelvin, and E_a is expressed in J/mol; hence units in the exponent cancel.

The Arrhenius equation describes quantitatively much of what we have already discussed about reaction rates. For example, for two similar reactions occurring at the same temperature, the reaction with the higher E_a has the smaller rate constant (k). Also, a change in conditions that increases the number of collisions with a favorable orientation results in an increase in A and, consequently, an increase in k.