Everything about The Arrhenius Equation totally explained
The
Arrhenius equation is a simple, but remarkably accurate, formula for the temperature dependence of the
rate constant, and therefore rate, of a chemical reaction. The equation was first proposed by the Dutch chemist
J. H. van 't Hoff in 1884; five years later in 1889, the Swedish chemist
Svante Arrhenius provided a physical justification and interpretation for it. Nowadays it's best seen as an empirical relationship. It can be used to model the temperature-variance of diffusion coefficients, population of crystal vacancies, creep rates, and many other thermally-induced processes/reactions.
The general rule of thumb, without solving the equation, is that for every 10°C increase in temperature the rate of reaction doubles. As with any rule of thumb, it doesn't always work.
Overview
In short, the Arrhenius equation gives "the dependence of the
rate constant k of
chemical reactions on the
temperature T (in
Kelvin) and
activation energy Ea", as shown below: that makes explicit the temperature dependence of the pre-exponential factor. If one allows
arbitrary temperature dependence of the prefactor, the Arrhenius description becomes overcomplete, and the inverse problem (for example determining the prefactor and activation energy from experimental data) becomes singular. The modified equation is usually of the form
»
where Δ
G‡ is the
Gibbs free energy of activation,
kB is
Boltzmann's constant, and
h is
Planck's constant.
At first sight this looks like an exponential multiplied by a factor that's
linear in temperature. However, one must remember that free energy is itself a temperature dependent quantity. The free energy of activation includes an entropy term, which is multiplied by the absolute temperature, as well as an enthalpy term. Both of them depend on temperature, and when all of the details are worked out one ends up with an expression that again takes the form of an Arrhenius exponential multiplied by a slowly varying function of
T. The precise form of the temperature dependence depends upon the reaction, and can be calculated using formulas from
statistical mechanics involving the partition functions of the reactants and of the activated complex.
Further Information
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