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=Ae^{-E_{a}/RT}

or alternatively

k=Ae^{-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