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# Arrhenius plot

An Arrhenius plot displays the logarithm of a rate (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.

The Arrhenius equation given in the form:

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

can be written equivalently as:

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

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