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Inorganic Electrochemistry
Theory, Practice and Application
By P. Zanello The Royal Society of Chemistry
Copyright © 2003 The Royal Society of Chemistry
All rights reserved.
ISBN: 978-1-84755-114-6
CHAPTER 1
Fundamentals of Electrode Reactions
Electrochemistry is essentially based on the relationships between chemical changes and flows of electrons (i.e. the passage of electricity). In this connection it is well known that electron transfer processes play an essential role in many physical, chemical and biological mechanisms and a number of such examples will be illustrated in the text. Perhaps in no other field of chemical reactivity has one looked for and found so many relationships between theory and experimental measurements.
Two disciplines cover the majority of the theoretical and practical aspects of the mechanisms through which electron transfers proceed: electrochemistry and photochemistry. In this book only mechanisms relating to electrochemistry will be considered.
1 ELECTRON TRANSFER REACTIONS
In a purely formal manner the description of an electron transfer event, such as the reduction in solution of Fe(III) ion, can be written in two ways, depending on whether the reduction is operated by a chemical agent or by an electrode:
• through a reducing agent (redox reaction in a homogeneous phase):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
• through an electrode (redox reaction in a heterogeneous phase):
[Fe(H2O6]3+ + e- [right arrow] [Fe(H2O)6]2+
In both cases, the adopted symbolism only gives a picture of the overall process. In fact, from a mechanistic viewpoint, the redox reactions (as with any other type of reaction) proceed by a series of intermediate steps involving phenomena such as:
• diffusion of the species through the solution;
• interaction between reagents, in the case of reactions in a homogenous phase, or interactions between reagents and electrode, in the case of reactions in a heterogenous phase;
• formmation of short- or long-live intermediates due to variations in electronic configurations, to the eventual substitution of ligands, etc.
Commonly, oxidation-reduction reactions in a homogenous phase are classified as:
• outer-sphere reactions;
• inner-sphere reactions.
In the inner-sphere reactions, the process involves a 'transition state' in which a mutual strong penetration of the coordination spheres of the reagents occurs (and, therefore, strong interaction between reagents), whereas in the outer-sphere reactions there is no overlap of the coordination spheres of the reagents (and, therefore, there is weak interaction between reagents).
The classical example of inner-sphere mechanism is the reduction of the Co(III) salt [Co(NH3)5 Cl]2+ by Cr(II) ions ([Cr(H2O)6] 2+):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
The fact that from a chloro-cobalt complex a chloro-chromium complex is formed, suggests that the reaction must proceed through an intermediate state that enables the transfer of a chlorine atom from cobalt to chromium. The proposed mechanism for this reaction is:
[FORMULA NOT REPRODUCIBLE IN ASCII]
It is assumed that the intermediate product is [(NH3) 5CoIII-Cl-CrII(H2O) 5)]4+:
[FORMULA NOT REPRODUCIBLE IN ASCII]
in which there is a clear overlap of the coordination spheres of the two reagents. It follows that the electron-transfer can take place only after such an intermediate has formed.
As an example of a reaction which involves an outer-sphere mechanism the following reaction can be considered:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
In this case one may assume that the charge transfer takes place as soon as the two reagents collide, without the occurrence of any exchange of ligands (which would imply breaking of old or formation of new bonds in the reaction intermediate).
As a consequence, the mechanism with which a homogeneous reaction proceeds is conditioned by the rate of either the ligand exchange or the electron transfer. An outer-sphere mechanism is certainly active when the exchange of ligands between reagents is slower than the exchange of electrons between reagents.
In this picture, the electron transfer processes mediated by metallic electrodes (redox reactions in a heterogeneous phase) can also be classified to proceed according to outer-sphere or inner-sphere mechanisms (obviously, considering the electrode surface as a reagent).
One can define as outer-sphere electrode processes those in which the electron transfer between the electrode and the active site occurs through the layer of solvent directly in contact with the electrode surface. The electrode and electroactive species are, therefore, separated such that the chemical interaction between them can be considered practically nil (obviously, apart from their electrostatic interaction), see Figure 1.
Inner-sphere electrode processes are defined as those in which the electron exchange occurs between the electrode and the electroactive species (the metal core or its ligand) that are in direct contact with the electrode surface, see Figure 2.
It should be emphasized that the majority of electrochemically induced redox processes in inorganic chemistry proceed (or are assumed to proceed) through outer-sphere mechanisms.
2 FUNDAMENTALS OF ELECTRON TRANSFERS AT AN ELECTRODE
As we shall be considering the electrochemical characterization of chemical systems, it is useful at this point to make clear a few fundamental concepts inherent in electrochemical processes.
2.1 The Electrode/Solution System
An electrode reaction is always a heterogeneous chemical process, in that it involves the passage of an electron from an electrode (metal or semiconductor) to a chemical species in solution, or vice versa.
As illustrated in Figure 3, one can depict the electrode/solution system as being partitioned roughly into four regions:
• the electrode
• the double layer
• the diffusion layer
• the mass (or bulk) of the solution
The electrode/solution interface represents a discontinuous plane with respect to the distribution of the electrical charge. This is the result of electrode possessing an excess of charge of a given sign (for example, negative in the figure) in immediate contact with an excess of charge of opposite sign, due to the electrostatic attraction. This situation generates the so-called double layer, which, as we shall see, has important consequences on the electrochemical events.
The so-called diffusion layer is still a region dominated by an unequal charge distribution (i.e. in such a zone the principle of electro-neutrality is not valid) due to the electron transfer processes occurring at the electrode surface. In fact, the electrode acts as an electrostatic pump for species of a certain charge, resulting in a flow of these charged systems from the mass of the solution (i.e. the bulk of the solution where the principle of electro-neutrality is fully valid) towards the electrode, or vice versa.
2.2 The Nature of Electrode Reactions
Let us consider a chemical species which possesses two different oxidation states, oxidized (Ox) and reduced (Red), both stable and soluble in the electrolytic medium (solvent + inert electrolyte). The simplest formulation of the electrode reaction which converts Ox to Red:
Ox + ne- [right arrow] Red (1)
in reality hides a sequence of elementary processes. In fact, in order to maintain a continuous flow of electrons:
• first, the electrode surface must be continually supplied with reagent (Ox);
• then, the heterogeneous electron transfer process from the solid electrode to the species Ox must takes place (through an inner- or outer-sphere mechanism);
• finally, the reaction product (Red) must be removed from the electrode surface, in order to allow the access of further amounts of Ox to the electrode surface.
Consequently, we can rationalize the process represented by Equation (1) as involving at least the following three elementary steps:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
Clearly, the overall rate of the reduction process will be conditioned by the slowest elementary step, which can be associated either with the mass transport (from the bulk of the solution to the electrode surface, and vice versa) or with the heterogeneous electron transfer (from the electrode to the electroactive species, or vice versa).
As pointed out, the electrode process (1) can be described by the mentioned sequence of 'at least' three elementary stages. In reality, quite often other phenomena complicate the electrode reactions. These consist of fundamentally three types:
• coupled chemical reactions
It is possible that the species Red generated at the electrode surface may be unstable and tend to decompose. It may also be involved in chemical reactions with other species present in solution while it is moving towards the mass of the solution (homogeneous chemical reactions) or while it is still adsorbed on the electrode surface (heterogeneous chemical reactions). Furthermore, the new species formed during such reactions may be electroactive. These kind of reactions are called following chemical reactions (following, obviously, the electron transfer).
In addition, though less common, there are cases of preceding chemical reactions (preceding, naturally, the electron transfer). In this case, the reagent Ox is the product of a preliminary chemical reaction of a species that is not itself electroactive. For example, the reduction of acetic acid proceeds through the two microscopic stages:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
H+ + e- [right arrow] (ELECTRON TRANSFER)
• adsorption
In the sequence of reactions (2)–(3)–(4) it was assumed that electron exchange takes place without the interaction of the species Ox and Red with the electrode surface. However, it is possible that the exchange of electrons does not occur unless the reagent Ox, or the product Red, is weakly or strongly adsorbed on the electrode surface. It is also possible that the adsorption of the species Ox or Red might cause poisoning of the electrode surface, thus preventing any electron transfer process.
• formation of phases
The electrode reaction can involve the formation of a new phase (e.g. electro-deposition processes used in galvanizing metals). The formation of a new phase is a multi-stage process since it requires a first nucleation step followed by crystal growth (in which atoms must diffuse through the solid phase to then become located in the appropriate site of the crystal lattice).
2.3 The Current as a Measurement of the Rate of an Electrode Reaction
An electrode reaction always implies a transfer of electrons. If we consider again the reaction:
Ox + ne- [right arrow] Red
it is easily deduced that for each mole of species Ox which is reduced, n mol of electrons must be released from the electrode (the working electrode, WE) and supplied to the species. As illustrated in Figure 4, these electrons are supplied, through an external circuit, by an electrode reaction that occurs at a second electrode (the counter electrode, CE) at the expense of any other redox-active species Red present in the same electrolytic solution (solvent itself included).
It is clear that if, as in this case, the process occurring at the working electrode is a reduction half-reaction then there will be an oxidation half-reaction at the counter-electrode.
Faraday's law states that if M mol of reagent Ox are reduced, the total charge spent is given by:
Q = n·F·M
where F is the Faraday constant (96 485 C mol-1).
The variation of charge with time, i.e. the current, i, will be equal to:
dQ/dt = i = n·F· dM/dt
The variation of the mol number with time, dM/dt, reflects the variation of concentration per unit time, or the reaction rate, v (in mol s-1).
Since we are considering heterogeneous processes, the rate of which is commonly proportional to the area of the electrode, one can normalize with respect to the electrode area, A, so that:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
This expression shows that the current flowing in the external circuit of Figure 4 is proportional to the rate of the electrode reaction:
i = n·F·A·v
the proportionality constant being the factor n·F·A.
This type of current, which originates from chemical processes which obey Faraday's law, is called a faradaic current, to distinguish it from non-faradaic currents which, as we shall see in Section 5, arise from processes of a strictly physical nature.
In the course of an electrochemical experiment the experimental conditions are carefully controlled to minimize the onset of non-faradaic currents as much as possible.
2.4 The Potential as a Measurement of the Energy of the Electrons Inside the Electrode
According to band theory, the electrons inside a metal populate the valence band up to the highest occupied molecular orbital, which is called the Fermi level. The potential applied to a metallic electrode governs the energy of its electrons according to Figure 5.
If the electrode potential is made more negative with respect to the zero-current value, the energy of the Fermi level is raised to a level at which the electrons of the metal (or, the electrode) flow into the empty orbitals (LUMO) of the electroactive species S present in solution, Figure 5a. Thus, a reduction process takes place, written as: S + e- [right arrow] S-
In an analogous way, the energy of the Fermi level can be decreased by imposing an electrode potential more positive than the zero-current value. A situation is now reached in which it is energetically more favourable that the electroactive species donates electrons from its occupied molecular orbital (HOMO) to the electrode, see Figure 5b. An oxidation process has been activated, which can be depicted as: S [right arrow] + S+ e-
The critical potential at which these electron-transfer processes occur identifies the standard potential, Eº of the couples S/S- and S+/S, respectively.
Let us consider the case of the reduction process:
S + e- [right arrow] S-
By raising the electrode potential towards more and more negative values a threshold value will be reached: above this value the reduced form S- is stabilized at the electrode surface, whereas below this value the oxidized form S is stabilized at the electrode surface. This threshold value is just defined as the standard potential of the S/S- couple.
2.5 The Biunique Relationship Between Current and Potential
Since the potential regulates the energy of the electron exchanges, it also controls the rate of such exchanges and, hence, the current. This biunique correspondence between current and potential implies that if one of the two parameters is fixed the other, consequently, also becomes fixed.
3 POTENTIAL AND ELECTROCHEMICAL CELLS
As discussed in Section 2.3, for an electrode reaction to take place one needs two electrodes: a working electrode, at which the electron transfer process of interest occurs, and a counter electrode, that operates to maintain the electro-neutrality of the solution through a half-reaction of opposite sign, see Figure 4. Unfortunately, it is not possible to measure rigorously the absolute potential of each of the two electrodes (i.e. the energy of the electrons inside each electrode). The difference of potential set up between the two electrodes is, instead, easily experimentally measured and is defined as cell voltage, V. However, as illustrated in Figure 6, this cell voltage is the sum of a series of differences of potential.
(Continues...)
Excerpted from Inorganic Electrochemistry by P. Zanello. Copyright © 2003 The Royal Society of Chemistry. Excerpted by permission of The Royal Society of Chemistry.
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