Level: introductory+ (exercises 1 & 2), advanced (exercise 3)
Reference: Svante Arrhenius, "On the Reaction Velocity of the Inversion of Cane Sugar by Acids," Zeitschrift für physikalische Chemie 4, 226ff (1889)
Notes: Svante Arrhenius (1859-1927) is best known to chemists for his work on electrolyte solutions and kinetics. He also attempted to model the influence of atmospheric carbon dioxide on climate (a phenomenon now known as the greenhouse effect). He was awarded the Nobel Prize in chemistry in 1903.
The Arrhenius equation was first proposed as a general relationship for the temperature dependence of rates of reaction by Arrhenius in 1889. (Actually, Arrhenius proposed a mathematically equivalent relationship. He was not the first to propose that particular relationship; van't Hoff had proposed it for a particular set of kinetic data and had used other relationships for other sets of data.) Exercise 1 in this set carries out a set of calculations similar to those done by Arrhenius, showing that eight published sets of kinetic data obey the Arrhenius equation. Exercise 2 has the student correct an error in one of the data sets Arrhenius published and (more importantly) raises the question of when it may be appropriate to make such a correction.
Exercise 3 returns to the same sets of data as exercise 1, and has students determine that the Arrhenius plot was far from unique in its ability to fit the data. Indeed, most of the investigators who originally published the kinetic data used other relationships to fit the temperature dependence. (Two articles from J. Chem. Educ. discuss the origins of the Arrhenius equation and the work of Arrhenius' contemporaries: S. R. Logan, "The Origin and Status of the Arrhenius Equation," 59, 279-81 (1982) and Keith J. Laidler, "The Development of the Arrhenius Equation," 61, 494-8 (1984).) Laidler points out that T, 1/T, and ln T are linear functions of each other over relatively small temperature ranges (as can be seen from power series expansions), and all of these temperature ranges are fairly small compared to the absolute temperatures themselves. So a quantity (ln rate, in this case) that can be fit to a linear function of one can be fit to a linear function of any of them. The eventual emergence of the Arrhenius equation can be attributed to its theoretical fruitfulness rather than an empirically objective superiority.
Pedagogical note: There is not much point in having a student carry out all of the computations in this set of exercises. A suitable exercise for introducing students to chemistry computations with spreadsheets would involve assigning different data sets to different students.
Solutions: To download solutions, go to:
http://web.lemoyne.edu/giunta/classicalcs/arrkin.doc
To download a worked spreadsheet, go to:
http://web.lemoyne.edu/giunta/classicalcs/arrkinans.xls
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