Temperature as Secondary X Axis in Arrhenius Plot

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.

Convert Temperature to 1/T and Rate Constant to ln(k)

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:

Plot Temperature to 1/T and Rate Constant to ln(k)

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).

Add Temperature (Celsius) as Top X axis

In Origin 2022 and later versions

Click the bottom X axis and choose Add Secondary Axis mini toolbar button.
In the dialog that opens, click > button next to Direct Formula and select Arrhenius to load the direct and inverse formula

Before Origin 2022

Need to use multiple dialogs to add secondary nonlinear axis.. 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:

Get Ea and A value

Make sure layer1 is active. Choose Analysis: Fitting: Linear Fit to get intercept and slope. Intercept corresponds to ln(A), and the slope corresponds to -Ea/R. So you can calculate Ea and A value based on intercept and slope. Add results as labels in graph, which you can find in Folder2 of the same project: 277_iamge_1

About S Z

Male, single, alive.

View all posts by S Z →

12 Comments on “Temperature as Secondary X Axis in Arrhenius Plot”

    1. Hi Taimoor, Please check under Project Explorer to see both Folder 1 and 2. This is a tab on the left side of the interface. I downloaded the project just now to check and was able to access Folder 2.

    1. Hello Dinislam,
      Thank you for your question.
      1000/T is used simply to not have so many zeros in the axis tick labels. As stated in the blog, it does not alter the actual data.

  1. Hello,

    I do not find ‘Scale / Type / Custom Fomula / Direct Formula and Inverse Formula’ in OriginPro 9.0 version according to the following instruction.
    Please support me. I do not make correct Arrhenius Plots using OriginPro 9.0.

    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:

    Thank you in advance and best regards.

    1. Hello, it’s said in the blog that the blog is based on Origin 2015 so the feature isn’t available in your Origin.

      We have released Origin 2020b yesterday and we provide temporary license for Origin users during coronavirus pandemic so please plot with it.
      https://www.originlab.com/covid19

  2. 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.

    1. 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.

Leave a Reply to CP Cancel reply

Your email address will not be published. Required fields are marked *