Innumerable experiments have been performed on both inner- and outer-sphere electron-transfer reactions. We do not review them here, but present a few results that are directly relevant to the theoretical issues raised in the preceding chapters. The Butler-Volmer equation (5.10) predicts that for |η| > kT/e0 a plot of the logarithm of the current versus the applied potential (Tafel plot) should result in a straight line, whose slope is determined by the transfer coefficient α. Because of the dual role of the transfer coefficient (see Section 5.2), it is important to verify that the transfer coefficient obtained from a Tafel plot is independent of temperature. We shall see later that proton- and ion-transfer reactions often give straight lines in Tafel plots, too, but the apparent transfer coefficient obtained from these plots can depend on the temperature, indicating that these reactions do not obey the Butler-Volmer law. In order to test the temperature independence of the transfer coefficient, Curtiss et al. investigated the kinetics of the Fe2+/Fe3+ reaction on gold in a pressurized aqueous solution of perchloric acid over a temperature range from 25° to 75°C. In the absence of trace impurities of chloride ions, this reaction proceeds via an outer sphere mechanism with a low rate constant (k0 ≈ 10-5 cm s-1 at room temperature). Figure 8.1 shows the slope of their Tafel plots, d(lni)/dη, as a function of the inverse temperature 1/T. The Butler-Volmer equation predicts a straight line of slope αe0/k, which is indeed observed. Over the investigated temperature range both the transfer coefficient and the energy of activation are constant: α = 0.425 ± 0.01 and Eact = 0.59± 0.01 eV at equilibrium, confirming the validity of the Butler-Volmer equation in the region of low overpotentials, from which the Tafel slopes were obtained. The phenomenological derivation of the Butler-Volmer equation is based on a linear expansion of the Gibbs energy of activation with respect to the applied overpotential. At large overpotentials higher-order terms are expected to contribute, and a Tafel plot should no longer be linear.
Relationship between the Energy of Activation and the Overall Free Energy of Bridge-assisted Electron Transfer Reactions in Polar Media.
