Arrhenius plot

An Arrhenius plot displays the logarithm of kinetic constants (ln(k), ordinate axis) plotted against inverse temperature (1 / T, abscissa). 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.

Example: Nitrogen dioxide decay
2 NO2 → 2 NO + O2
Conventional plot: k against T
Arrhenius plot: ln(k) against 1/T

The Arrhenius equation can be given in the form:

$k = A e^{-E_a/RT}$

or alternatively

$k = A e^{-E_a/k_B T}$

The only difference is the energy units: the former form uses energy/mole, which is common in chemistry, while the latter form uses energy directly, which is common in physics. The different units are accounted for in using either R = Gas constant or Boltzmanns constant k_B.

The former form can be written equivalently as:

$\ln(k) = \ln(A) - \frac{E_a}{R}\left(\frac{1}{T}\right)$

Where:

k = Rate constant

A = Pre-exponential factor

E_a = Activation energy

R = Gas constant

T = Absolute temperature, K

When plotted in the manner described above, the value of the "y-intercept" will correspond to ln(A), and the gradient of the line will be equal to − E_a / R.

The pre-exponential factor, A, is a constant of proportionality that takes into account a number of factors such as the frequency of collision between and the orientation of the reacting particles.

The expression $e^{-E_a/RT}$ represents the fraction of the molecules present in a gas which have energies equal to or in excess of activation energy at a particular temperature.

See also

• Arrhenius equation
• Eyring equation