Level: introductory+ (Note: #1 can be made introductory by specifying a gas. Introductory students will proceed by computing the typical speed at the requisite temperatures.)
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.
In his work on the temperature dependence of the reaction rate, Arrhenius was influenced by thermodynamic arguments. Comparing the Arrhenius equation to a later collisional theory of reaction rates interprets the temperature dependence in terms of the fraction of collisions that have an energy greater than or equal to the activation energy. For activation energies on the order of 100 kJ mol-1 and temperatures not far from ambient, the exponential term represents a small fraction of a Boltzmann distribution of molecules. That fraction can change significantly while still remaining small enough to affect the average energy only slightly.
Solutions: To download solutions, go to:
http://web.lemoyne.edu/giunta/classicalcs/arreqn.doc
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