The Origin and Status of the Arrhenius Equation

The purpose of this article is to trace the origins of the Arrhenius equation and, in the light of the extensive data on the temperature dependence of reaction rates, assembled in just over a century of experimental endeavor, to assess in what ways its status has changed over the period since it was first proposed. The systematic study of the kinetics of chemical reactions commenced ( I ) mid-way through the nineteenth century. From the beginning it was realized that reaction rates showed an appreciable dependence on temperature, but for the next few decades, kinetic studies were directed more toward quantifying the effect of reactant concentrations (2) rather than that of temperature. Several sets of data on the latter effect were ohtained in the eighteen-eighties, and in 1889, Svaute Arrhenius showed that in each case temperature and rate constant could he correlated by one simple equation (3). I t still hears his name and is widely regarded as one of the most important equations in physical chemistry. Svante August Arrhenius, horn in 1859, was initially a student at Uppsala in Sweden. In Stockholm, he began in 1882 the series of measurements which led to his doctoral thesis, "Recherches sur la conductibilitt? galuanique des 6lectrolytes," in which he proposed his theory of the dissociation of electrolytes in solution. The conclusions of this young researcher were not highly regarded by his examiners and in 1884 the thesis was awarded only a grading of "non sine laude approbatur," though his defense of it was graded "cum laude approbatur" (4). As a consequence he strongly felt a need to vindicate his theory, and for some years his researches were devoted to this end, until eventually i t gained general acceptance. Thus, Arrhenius was primarily an electrochemist. His participation in rate measurements was derived from his desire to gain recognition for his theory of electrolytic dissociation and followed the production by Wilhelm Ostwald of kinetic evidence which supported it (5). The kinetic studies of Arrhenius were mostly of systems involving electrolytes and included measurements of the effects of neutral salts. However, even if he were not specially interested in reaction kinetics per se, in one paper (6 ) he put in a plea for the adoption of the term, "specific reaction rate," rather than "rate constant," on the grounds that this parameter was not invariant. Had his view prevailed it would have obviated the use of the apparently self-contradictory term, "time-dependent rate constant," which arises (7) in connection with the behavior of pairs of reactive entities produced in close proximity in solution. Over the period 1886-88, a travelling scholarship took Arrhenius to the laboratories of the leading ~hysical chemists in Europe, including Ostwald and van't Hoff. The classic paper (3) which is the main focus of attention here, appeared in 1889 under the title, "Uber die Reaktionsgeschwindigkeit bei der Inuersion uon Rohrzucker durch Sauren. " In the first section, Arrhenius considered eight sets of published data on the effect of temperature on reaction rates and showed (using more currently conventional symbols) that in each case he could choose a value of the constant C such that k ( T d , the rate constant at a temperature TI, was represented adequately by the equation,