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I was taught (many years ago) the common misconception that fitting the linearized form of the Eyring equation overstates the error in the intercept because on a 1/T axis, the intercept is at infinite temperature, and the intercept is far from the real data. While researching various methods of data fitting, I stumbled across this great article from the New Journal of Chemistry (New J. Chem., 2005, 29, 759–760, doi: 10.1039/b501687h) which proves that in fact, the errors in ∆S‡ and ∆H‡ are the same no matter how you fit the data… but… you must be sure to appropriately weight the data in the non-linear fit. The supplemental information for the paper includes the real data so that you can examine it in more detail.
The attached Mathematica file was developed by my student Ryan Brewster (HMC, Chem 104, Spring 2010), and he deserves partial author credit for this learning object. I thank him for working with me and encouraging me to develop this LO.
| Attachment | Size |
|---|---|
| description of the activity | 71 KB |
| a zip file of a Mathematica notebook | 29.15 KB |
| a pdf file of the Mathematica notebook | 273.76 KB |
A student will learn to fit rate data to various forms of the Eyring equation.
A student will be able to explain when weighting of data is necessary.
If done as an in-class activity, computer workstations running Kaleidagraph, Mathematica or other curve-fitting programs would be required. If done as a discussion, the faculty member would need to have access to these programs in order to verify the data presented.
I have only done this as a lecture and problem set (see the related problem set) but I think it would work very well as an in-class activity. I look forward to seeing either comments or other implementations. Make sure to look at the supporting information for the article as it includes a dataset for use in class.
Here is a suggested procedure (and language) for implementing this activity as an in-class exercise. Take a kinetics data set (there is usually one in the chapter on ligand substitution reactions, or you could use the dataset in the article) and divide the class into several groups. Have one group of students fit the linearized data, one group fit to the Eyring equation using non-weighted data, and a third group fit to the equation while weighting the data appropriately.
Group 1: The following data (provided by the instructor) is a series of rate constants at different temperatures for a chemical reaction. Linearize the data by taking the natural log of each rate constant and plot it vs 1/T (Kelvin temperature!). Fit the linear data to the linearized form of the Eyring equation and extract the activation paramaters from the fit. Report your paramaters on the chalkboard and indicate your group number and how long it took you.
Group 2: The following data (provided by the instructor) is a series of rate constants at different temperatures for a chemical reaction. Fit the data to the Eyring equation and extract the activation paramaters from the fit. Do not weight the data. Report your paramaters on the chalkboard and indicate your group number and how long it took you.
Group 3: The following data (provided by the instructor) is a series of rate constants at different temperatures for a chemical reaction. Fit the data to the Eyring equation and extract the activation paramaters from the fit. Weight the data using the standard weighting scheme in Kaleidagraph (1/k2). Report your paramaters on the chalkboard and indicate your group number and how long it took you.
All groups: After you fit your data, be prepared to discuss the pros and cons of your approach. How easy was it to fit your data? How easy was it to extract the activation paramaters? Do your values match those from the other groups?
Evaluation
I would hope a discussion would ensue where different groups of students present the pros and cons of the various forms of data fitting.