page_title: Arrhenius plot
section_title: Worked example
hierarchical_section_title: Arrhenius plot / Worked example
caption_attribution_description: English: Plot of k = e^23.1 * e^(-12,667/T)
context_page_description: In chemical kinetics, an Arrhenius plot displays the logarithm of a reaction rate constant, plotted against reciprocal of the temperature. Arrhenius plots are often used to analyze the effect of temperature on the rates of chemical reactions. For a single rate-limited thermally activated process, an Arrhenius plot gives a straight line, from which the activation energy and the pre-exponential factor can both be determined.
  The Arrhenius equation can be given in the form: that
  Where:
  = Rate constant
  = Pre-exponential factor
  = Activation energy
  = Boltzmann constant
  = Gas constant, equivalent to times Avogadro's constant.
  = Absolute temperature, K
  The only difference is the energy units: the former form uses energy/mole, which is common
  in chemistry, while the latter form uses energy on the scale of individual particles directly, which is common in physics.
  The different units are accounted for in using either the gas constant
  or the Boltzmann constant.
  Taking the natural logarithm of the former equation gives.
  When plotted in the manner described above, the value of the y-intercept will correspond to, and the slope of the line will be equal to.
context_section_description: This example uses the decay of nitrogen dioxide: 2 NO₂ → 2 NO + O₂
  Based on the red "line of best fit" plotted in the graph given above:
  Let y = ln(k[10⁻⁴ cm³ mol⁻¹ s⁻¹])
  Let x = 1/T[K]
  Points read from graph:
  y = 4.1 at x = 0.0015
  y = 2.2 at x = 0.00165
  Slope of red line = (4.1 - 2.2) / (0.0015 - 0.00165) = -12,667
  Intercept [y-value at x=0] of red line = 4.1 + (0.0015 x 12667) = 23.1
  Inserting these values into the form above:
  yields:
  as shown in the plot at the right.
  for:
  k in 10⁻⁴ cm³ mol⁻¹ s⁻¹
  T in K
  Substituting for the quotient in the exponent of :
  -Eₐ / R = -12,667 K
  approximate value for R = 8.31446 J K⁻¹  mol⁻¹
  The activation energy of this reaction from these data is then:
  Eₐ =  R x 12,667 K = 105,300 J mol⁻¹ = 105.3 kJ mol⁻¹.
caption: Plot of k = e^23.1 * e^(-12,667/T)
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