CHEM-E4106 - Electrochemistry D, Lecture, 10.1.2022-22.2.2022

An electrochemical reaction involves always electron transfer between species. Such a reaction is called a redox reaction. It is defined:

A substance capable of oxidizing another substance is knows as an oxidant. Accordingly, a reducing substance is a reductant. If we write down a reaction

where n electrons are transferred from B to A, A is the oxidant of B and B is the reductant of A. Hereinafter in this book, the subscripts ’ox’ and ’red’ refer to the oxidized and reduced species, respectively.

The ability of a substance to oxidize or reduce another substance depends on their electron structure and, to a lesser extent, on the medium. This ability is reflected in the values of the standard reduction potentials that are tabulated for several elements and molecules. Standard potentials are discussed in Chapter 4, and a selection of the most common redox couples is given in Appendix 6. From the standard potentials it is possible to deduce which reactions would occur spontaneously or how much energy must be fed in to the system to force a reaction to take place.*

If an electron transfers from a species in the solution to another species without a mediating electrode, electron transfer is homogeneous. For example, if an aqueous solution of CeCl₄ and FeCl₂ are shaken for a while, Ce⁴⁺ oxidizes Fe²⁺ to Fe³⁺ reducing to Ce³⁺. In biology, redox reactions are mostly homogeneous. Metals can also be reduced from aqueous solutions with strong reductants without an external circuit. One of the best known processes is the deposition of nickel from a hypophosphate solution. This kind of processes are known as electroless plating. They do not, however, represent true homogeneous electron transfer because a solid surface mediates electrons and other simultaneous reactions compensate the transferred charges.

A redox reaction is electrochemical if electron transfer takes place heterogeneously, most commonly on solid electrodes.

An alternative definition would be

Electrodes traditionally used in electrochemistry are made of solid materials that have sufficient electrical conductivity, such as metals, graphite or indium-titan oxide glass (ITO). An electrode exchanges an electron with a reacting species, and receives an electron from an external circuit or donates an electron to it. The surface of an electrode can be modified with functional groups in order to enhance its selectivity towards a particular reacting species.

As a result of a redox reaction, an imbalance of charges is created in the solution, and another electrode must be inserted in the system to maintain electroneutrality in the solution. The electrodes must be connected via an external circuit. Reaction (1.1) can now be written in terms of electrode reactions as follows:

Summing reactions (1.2a) and (1.2b) gives reaction (1.1). In reaction (1.2a) the electrode donates n electrons to A_ox: it is a cathode. In reaction (1.2b) the other electrode receives the same number of electrons: it is an anode.

Reactions (1.2) and (1.2b) are the half-reactions of reaction (1.1). If we want to study, say, the rate of the half-reaction (1.2a), the cathode is called the working electrode, and the anode that only balances the number of charges in the solution the counter electrode or the reference electrode. In modern electrochemical measurement, the counter and reference electrodes are separate – this will be discussed in Chapter 4.7.

Electron transfer is a fundamental reaction which is very difficult to describe with quantum mechanics. Theories of electron transfer have traditionally been based on the famous Arrhenius equation or the absolute rate theory (aka theory of activated complexes) by Eyring. The rate of electron transfer, in other words electric current, is, however, easily measured and controlled in situ, making electrolysis a widely used chemical process.

1.2.1 Cell voltage due to an electrochemical reaction

Let’s write down a very simple and familiar reaction:

It is found from thermodynamic tables that the standard Gibbs free energy of the reaction is $\Delta$G⁰ = –237 kJ mol^–1. The reaction does not appear electrochemical but it is the net reaction of the hydrogen fuel cell in acidic conditions. At the anode of the fuel cell, hydrogen decomposes by means of a catalyst (oxidizes):

Protons are transported to the cathode through the electrolyte and electrons via the external circuit. At the cathode, oxygen is reduced:

Two electrons are transported per water molecule. Hence, the standard cell voltage (or potential) is

          $\displaystyle E^0=\frac{237000\text{ J/mol}}{2 \cdot 96485 \text{ As/mol} }$

the thermodynamic (= equilibrium) potential of the hydrogen fuel cell**.

Thus, in electrochemistry, a homogeneous reaction is split into two heterogeneous reactions and the Gibbs free energy of the reaction, $\Delta$G, is harnessed as electrical energy. In a reverse process, electrical energy can be used to run reactions against their natural affinity. The question of how $\Delta$G of the total reaction is split between the half-reactions remains still unanswered. As will be seen in Chapter 4, thermodynamics is incapable of answering this question, but it is resolved with an IUPAC resolution. This does not actually matter because measuring a single electrode potential, i.e. its energy, is not possible, only the potential difference between two electrodes can be measured.

1.2.2 Electric current due to an electrochemical reaction

where i is electric current density (A cm^–2), n the number of electrons exchanged in the reaction, F the Faraday constant (96485 As mol^–1) and r the reaction rate (mol cm^–2 s^–1). The direction of electric current is defined as the direction of positive current, i.e. opposite to the direction of electrons. In a solution, the current flows in the direction of the positively charged species. When representing current-voltage curves in x-y coordinates, it is still necessary to agree if an oxidation or reduction current is positive: according to the IUPAC resolution, an oxidation current is positive. Many text books, however, especially ones about polarography, show cathodic current (reduction current) as positive. Great care must therefore be taken when reading literature and noticing the sign convention used by authors.

It is necessary to emphasize that an electrochemical reaction is the only reaction, the rate of which can be measured in situ. With modern current amplifiers, the measurement of pA (10^–12 A) currents is rather easy. Applying the Faraday law it is simple to calculate that this corresponds to the transfer of the order of 10⁶ electrons per second.

Since electric current is a property of a closed circuit, its magnitude depends on the rate of the slower reaction. Let’s assume that the reduction reaction (1.2a) is faster than the oxidation reaction (1.2b). If the electrodes in Fig. 1.1 are short-circuited, electric current density is i = nFr_ox because the rate of the oxidation reaction limits the rate of electron flow. Superficially thinking, this observation may seem self-evident but it has a huge impact in the production of metals via electrolysis where oxygen evolution is the anode reaction. The rate of oxygen evolution (inverse of reaction (1.5)) is limited by reaction kinetics, increasing the cell voltage by several hundred millivolts which, in turn, increases the energy cost of the process significantly.