page_title: Arrhenius equation
section_title: Arrhenius plot
hierarchical_section_title: Arrhenius equation / Arrhenius plot
context_page_description: 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 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.
context_section_description: Taking the natural logarithm of Arrhenius equation yields:
  Rearranging yields:
  This has the same form as an equation for a straight line:
  where x is the reciprocal of T.
  So, when a reaction has a rate constant that obeys Arrhenius equation, a plot of ln k versus T⁻¹ gives a straight line, whose gradient and intercept can be used to determine Eₐ and A . This procedure has become so common in experimental chemical kinetics that practitioners have taken to using it to define the activation energy for a reaction. That is the activation energy is defined to be (−R) times the slope of a plot of ln k vs. (1/T):
caption: Arrhenius linear plot: ln k against 1/T.