R. Porsons University of Bristol Bristol 8, England
Electrochemical Dynamics
The kinetics of electrode reactions is a subject which is neglected by many physical chemists, being pushed to the back of physical chemistry textbooks. Although there is some justification for this in the fact that a good deal of knowledge of chemical kinetics, thermodynamics, etc., is required to appreciate the subject fully, this relegation does not give a proper idea of its importance. Together with catalysis, electrochemical dynamics is of enormous practical importance already in analytical chemistry, storage batteries, fuel cells, plating, and corrosion. There are signs that only the fringes of vast fields of electrosynthesis and biological applications have so far been explored. The fundamental problem of charge transfer processes is also of great interest and is likely to be the key to understanding many biochemical reactions. Thebrief survey by LaiteneninMChemicalDynamics" (publication 1292-B NAS and NRC) gives an excellent account of the present position of electrode processes. The foundations of the subject were laid in the 1930's particularly by Butler ( I ) , Gurney (2), Frumkin (S), Volmer (4), and Horiuti and Polanyi (6). However, it was not until after the second world war that a genera1 development of understanding of electrode kinetics on a broad front occurred. In the prewar period there was a strong emphasis on the reaction of hydrogen evolution, but more recent development of electronic techniques among others, especially relaxation techniques (6, 7) has facilitated the study of a much wider variety of reactions. Most important, fast reactions which tend to be simpler in mechanism have become accessible and this has led to the development of theories of electron transfer reactions (8). One of the main reasons for the neglect of the subject has certainly been the absence of a readable elementary textbook in English. This situation has improved by the recent publication of a revised edition (9) of Kortiim's textbook although this is not a freshman text. Various other books are in preparation and it is to be hoped that some will be useful for this purpose. The difficulty arises because new concepts are required just as when we go from gas kinetics to solution kinetics. In going from solution kinetics to the kinetics of surface reactions we need to introduce the ideas of catalysis and for electrochemical reactions, in addition we have to introduce the ideas of charge transfer across interfaces. Of course it helps if the student has a previous acquaintance with such subjects as ionic equilibrium, conductance, surface chemistry, etc., all of which previous speakers have urged should be turned out to make room for the elegant new ideas in chemical dynamics. Nevertheless, I think that the great and increasing importance of electrode reactions makes it essential that the princi390
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Journal of Chemical Education
pal concepts of these processes should be given to the student a t an early stage. They must, of course, be preceded by a description of the ideas of homogeneous and non-electrochemical heterogeneous kinetics. The most important concept which must be introduced to explain electrode processes arises from the fact that these reactions occur with the net transfer of charge from one phase (usually electrolyte) to another (usually metal). This leads directly to the fact that the free energy change (AG) in the overall reaction is a linear function of the potential of the electrode with r e spect to some standard electrode (e.g., standard hydrogen or saturated calomel).
(a
n is the number of charges transferred and F, the Faraday. In other words the free energy of the electrode reaction can be controlled by controlling the electrode potential. Then by an argument similar to the elementary derivation of the Arrhenius equation i t follows that the free energy of actiuation of the forward and reverse processes is also potential dependent. This may be expressed for the forward (cathodic) reaction dAG4
=
anFdE
(28)
and for the reverse (anodic) reaction dAGJ
= -(1
- ahFdE
(2b)
where a is a number, less than unity, known as the transfer coefficient, which expresses the way in which the effect of potential is divided between the free energy of activation of forward and reverse reactions. The transfer coefficientmay be determined experimentally as shown below and is frequently found to be independent or nearly independent of E, hence it is usually valid to write AGrf AGJ
=
=
AGd
+ anFE
AGO,*- (1 - a)nFE
(3s) (3b)
Using the exponential relation between rate constant and free energy of activation (10) we can see at once that we have a rate constant which can be varied a t will by the experimenter by turning the knob on a potentiometer. In some cases the rate constant of a single reaction can be varied over very wide limits, e.g., hydrogen evolution on mercury electrodes bas been studied with the rate constant varying by eleven powers of ten. Again in many cases, this adjustable rate constant means that a given reaction can be studied over the full range from completely reversible to completely irreversible conditions, that is, from the equilibrium potential (E.) where the rates of forward (if) and reverse reactions (i3 are equal to potentials far from this value
where the rate of either forward (cathodic) (E > E.) becomes negligible. In the region where E is very close to the reversible potential and the rates of both reactions are significant it is found experimentally that the current is directly proportional to the deviation of E from E. (cj., eqn. (19) below). Thus electrode reactions provide the best, if not the only, chemical example of a process whose rate near to equilibrium is proportional to the overall free energy change. In most discussions of this relationship and of the related Onsager reciprocal relations, phy,sical processes are used as examples. In view of the varlable rate of electrode reactions, the quantity used to characterize the rate a t a given electrode is the exchange current (io) or the current carried by either forward or reverse reaction a t equilibrium. The other important features of electrode reactions are more or less common to catalytic reactions: h t , that the reaction is confined to the interface and consequently involves a small number of molecules, roughly IO-g/cmz of interface, in contact with a much larger amount of bulk phase. This means that the kinetics of the reactions are extremely sensitive to the state of the interface and particularly to contamination. This is a real problem in doing experiments in electrode reactions, especially for undergraduates. Second, because of the interfacial nature of the reaction, the reactants must be transported to and from the interface. This process may have a rate which is comparable to the rate of the faster electrode reactions (those having a large exchange current). Especially in the case of the mechanistically simpler fast reactions, the process under steady state conditions becomes entirely diffusion controlled. For the study of such reactions it is essential to use the relaxation techniques developed in the last twenty years. It was suggested earlier that diffusion processes have been neglected in chemical kinetics; this is certainly not true of electrochemical kinetics. Recent progress in the study of electrochemical reactions would have been impossible without thorough study of mass transport phenomena and accurate solution of the relevant equations (11). Now, as to the way in which this subject should be presented to freshmen: I think that the concepts described above should be discussed and that these should be applied to a simple electron exchange reaction; probably
is the best example. This can be studied at mercury electrodes in acid solution with the minimum of complications (19). It is first order in either direction so that we may write the rate of the forward (reduction) reaction per cm2as
and that of the reverse (oxidation) reaction as
and [ P + ] are the concentrations of the two where [P+] species a t the electrode surface. Since each elementary reaction involves the transfer of unit charge across the interface (this is Farday's law of electrolysis), the rate can be expressed in terms of the current:
it =
Fut
i.
Fv.
=
the observed current being of course the difference if i,. Thus measurement of the current density flowing through the electrode i
=
if -
