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Concept
Arrhenius equation
Summary
In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1884 that the van 't Hoff equation for the temperature dependence of equilibrium constants suggests such a formula for the rates of both forward and reverse reactions. This equation has a vast and important application in determining the rate of chemical reactions and for calculation of energy of activation. Arrhenius provided a physical justification and interpretation for the formula. Currently, it is best seen as an empirical relationship. It can be used to model the temperature variation of diffusion coefficients, population of crystal vacancies, creep rates, and many other thermally-induced processes/reactions. The Eyring equation, developed in 1935, also expresses the relationship between rate and energy.
The Arrhenius equation gives the dependence of the rate constant of a chemical reaction on the absolute temperature as
where
k is the rate constant (frequency of collisions resulting in a reaction),
T is the absolute temperature (in Kelvin or degree Rankine),
A is the pre-exponential factor or Arrhenius factor or frequency factor. Arrhenius originally considered A to be a temperature-independent constant for each chemical reaction. However more recent treatments include some temperature dependence - see Modified Arrhenius equation below.
Ea is the activation energy for the reaction (in the same units as RT),
R is the universal gas constant.
Alternatively, the equation may be expressed as
where
Ea is the activation energy for the reaction (in the same units as kBT),
kB is the Boltzmann constant.
The only difference is the energy units of Ea: the former form uses energy per mole, which is common in chemistry, while the latter form uses energy per molecule directly, which is common in physics.
The different units are accounted for in using either the gas constant, R, or the Boltzmann constant, kB, as the multiplier of temperature T.
Official source
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