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 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.
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: