Temperature as Secondary X Axis in Arrhenius Plot

posted in: Graphing | 3

 

Arrhenius plots are often used to determine the activation energy (Ea) and A factor (A) by a linear fit of the logarithm of Arrhenius’ equation.

The Arrhenius equation can be given in the form:

k = Ae-Ea/RT

Where k=Rate constant, R=Gas constant, T=Absolute temperature(K).

Taking the natural logarithm of Arrhenius’ equation yields:

ln(k) = ln(A) – (Ea/R) * (1/T)

An Arrhenius plot is to plot ln(k) versus 1/T. A linear regression on Arrhenius plot will solve intercept which corresponds to ln(A), and the slope which corresponds to -Ea/R.

Here we will show you how to make an Arrhenius plot from raw data, and add a linked secondary top axis as experimental temperature (0C).

The following discussions/screenshots are all based on Origin2015, but some features involved are also available in earlier versions.

Feel free to download the sample project: Arrhenius plot Sample.zip. The data is obtained from NIST.

Go to Folder1 Book1. The raw data is a set of measured rate constants (M-1s-1) at different temperatures (K) for reaction 2ClO(g)–>Cl2(g)+O2(g).

 

Lets now add two new columns C and D. Enter formula in F(X) cells to convert Temperature data to 1/T, and Rate Constant data to ln(k). Also enter Long Name, and Comments and set Column C as X:

 

 

Select col(C) and col(D) to make a scatter plot.

Usually x axis will be plotted as 1000/T. We can add a Divide by Factor in Axis dialog to show as 1000/T. This will not alter the actual data.

Update axis title as well to be 1000/T(K-1).

To add a secondary top X axis to display temperature at unit of Celsius, click on Add Top-X Layer button 277_iamge_9 on Graph toolbar to add a layer with top X axis only.

The formula to convert Kelvin to Celsius is oC = K – 273.15. Since our original X data are in 1/T unit, the equation become Xtop = (1 / Xbot) – 273.15. In Plot Details dialog. Select TopX node on the left and go to Link Axes Scales tab to set the formula between bottom axis of layer 1 and top axis in layer2 as follows. X1 and X2 in formula refer to the Start and End value of bottom X axis.

post277_05

 

By default, the newly added axis will be linear scale. We will need to correct the scale from the formula. Double click on the top axis to open Axis Dialog. In Scale tab for X axis, choose Custom Formula option in Type drag-down list, and type in following formula:

You can further add a linear fit to get Ea and A value, and customize the graph to get the graph the final graph, which you can find in Folder2 of the same project:

277_iamge_1

3 Responses

  1. Robert Nelson

    The growth rate (y-axis) should be a log scale, not a ln scale! Almost no one will accept or be able to interpret an axis label in powers of “e”. The rate data cover a range of only 6 to 1 so a log scale would be much better anyway.

    • Thanks for the comment. We have modified the blog now to use new data.

    • Aurélien R

      I do not know about the usual representation of growth rates, but a ln scale is the only valid option for an Arrhenius plot (which is discussed here) if one wants to be able to – correctly – linear fit an Arrhenius law.
      Sadly, Arrhenius plots are often represented in log scales which makes no difference to the eye, but in my opinion trying to linear fit for an Arrhenius law and measure an activation energy in such a scale is erroneous.

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