Activation energy of electrochemical reaction measured at a constant value of electrode potential V.S. Protsenko ⇑ , F.I. Danilov Department of Physical Chemistry, Ukrainian State University of Chemical Engineering, Gagarin Av., 8, Dnepropetrovsk 49005, Ukraine article info Article history: Received 19 October 2010 Received in revised form 7 December 2010 Accepted 10 December 2010 Available online 15 December 2010 Keywords: Activation energy Electrode potential Temperature dependence Irreversible electrochemical reaction abstract Equations are derived and analyzed that interrelate the quantities of the ideal activation energy W (deter- mined at a constant Galvani potential value), the real activation energy A (measured at a constant over- potential value) and the so-called formal activation energy X (measured at a constant electrode potential vs. an arbitrarily chosen reference electrode). The mathematical forms of dependence of apparent formal activation energy on electrode potential are established. It is shown that using formal activation energy (measured at a constant electrode potential) is applicable for kinetics analysis of various electrode pro- cesses. The expressions obtained in this study may be used when processing temperature dependences of highly irreversible electrochemical reactions. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction A rate temperature dependence of any electrochemical reaction is well known to specify by its activation energy (along with the preexponential factor) according to the Arrhenius equation. Taking into account that the rate of electrode process depends among other things upon electric field intensity, there is a possibil- ity in principle to determine the activation energy at a constant va- lue of Galvani potential drop at the electrode/solution interface u, at a constant overpotential (deviation of the electrode potential from the equilibrium value) g and at a constant electrode potential measured vs. an arbitrary chosen reference electrode (at the same temperature, as the studied electrode) E, respectively, by the fol- lowing expressions: @ ln i @T   u;C ¼ W RT 2 ð1Þ @ ln i @T   g;C ¼ A RT 2 ð2Þ @ ln i @T   E;C ¼ X RT 2 ð3Þ where i is the current density, T is the thermodynamic temperature, R is the universal gas constant, C is the molar concentration of the reagents, W is the ideal activation energy, A is the real activation en- ergy and X is the parameter that we will further name the formal activation energy. The relationship between ideal and real activation energies was established by Temkin as follows [1]: A ¼ W  aq ð4Þ where a is the transfer coefficient of the electrode reaction, q is the hidden heat of the electrode process (inaccessible for experimental determination). Note that the signs of quantities in the latter equation are given for the cathodic direction of the electrode reaction under study. Since the value of Galvani potential drop cannot be measured (in contrast to overpotential and electrode potential), only the real and formal activation energies may be calculated on the base of experimental data. At the same time, it was repeatedly stressed that solely the W and A values have a physical meaning, as opposed to X due to the arbitrary character of choosing the reference electrode. There- fore, it is known that the activation energy is measured, as a gen- eral rule, at a constant overpotential [2–4]. However, in many cases (first of all, for highly irreversible elec- trochemical systems), measurement of the real activation energy by formula (2) is practically impossible because it is rather difficult to determine experimentally the equilibrium potential and overpo- tential values as well as to calculate them theoretically without lar- ger errors. In such cases, the value of the formal activation energy becomes practically the only accessible characteristics of the tem- perature dependence of the electrochemical reaction rate. The va- lue of X is used sometimes in electrochemical investigations 1572-6657/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jelechem.2010.12.014 ⇑ Corresponding author. E-mail address: vprotsenko@smtp.ru (V.S. Protsenko). Journal of Electroanalytical Chemistry 651 (2011) 105–110 Contents lists available at ScienceDirect Journal of Electroanalytical Chemistry journal homepage: www.elsevier.com/locate/jelechem