Electrochemical conversion

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Electrochemical energy conversion is the direct conversion of chemical energy, i.e. free energy of the form (4.8) into electrical power or vice versa. A device that converts chemical energy into electric energy is called a fuel cell (if the free energy-containing substance is stored within the device rather than flowing into the device, the name "primary battery" is sometimes used). A device that accomplishes the inverse conversion (e.g. electrolysis of water into hydrogen and oxygen) may be called a driven cell. The energy input for a driven cell need not be electricity, but could be solar radiation, for example, in which case the process would be photochemical rather than electrochemical. If the same device can be used for conversion in both directions, or if the free energy-containing substance is regenerated outside the cell (energy addition required) and recycled through the cell, it may be called a regenerative or reversible fuel cell and, if the free energy-containing substance is stored inside the device, a regenerative or secondary battery.

The basic ingredients of an electrochemical device are two electrodes (sometimes called anode and cathode) and an intermediate electrolyte layer capable of transferring positive ions from the negative to the positive electrode (or negative ions in the opposite direction), while a corresponding flow of electrons in an external circuit from the negative to the positive electrode provides the desired power. Use has been made of solid electrodes and fluid electrolytes (solutions), as well as fluid electrodes (e.g. in high-temperature batteries) and solid electrolytes (such as ion-conducting semiconductors). A more detailed treatise of fuel cells may be found in Serensen (2004a).

Fuel cells

The difference in electric potential, AQext, between the electrodes (cf. the schematic illustration in Fig. 4.10) corresponds to an energy difference eA$ext for each electron. The total number of electrons which could traverse the external circuit may be expressed as the product of the number of moles of electrons, ne, and Avogadro's constant NA, so the maximum amount of energy emerging as electrical work is

where F = NAe = 96 400 C mol-1 (Faraday's constant) is sometimes introduced. This energy must correspond to a loss (conversion) of free energy,

which constitutes the total loss of free energy from the "fuel" for an ideal fuel cell. This expression may also be derived from (4.8), using (4.2) and AQ = T AS, because the ideal process is reversible, and AW = —P AV + AWekc>.

Figure 4.10. Schematic picture of a hydrogen-oxygen fuel cell. The electrodes are in this case porous, so that the fuel gases may diffuse through them.

Figure 4.10 shows an example of a fuel cell, based on the free energy change AG = - 7.9 x 10-19 J for the reaction

[cf. (3.42)]. Hydrogen gas is led to the negative electrode, which may consist of a porous material, allowing H+ ions to diffuse into the electrolyte, while the electrons enter the electrode material and may flow through the external circuit. If a catalyst (e.g. a platinum film on the electrode surface) is present, the reaction at the negative electrode

may proceed at a much enhanced rate (see e.g. Bockris and Shrinivasan, 1969). Gaseous oxygen (or oxygen-containing air) is similarly led to the positive electrode, where a more complex reaction takes place, the net result of which is

This reaction may be built up by simpler reactions with only two components, such as oxygen first picking up electrons or first associating with a hydrogen ion. Also, at the positive electrode the reaction rate can be stimulated by a catalyst. Instead of the porous material electrodes, which allow direct contact between the input gases and the electrolyte, membranes can be used (cf. also Bockris and Shrinivasan, 1969) like those found in biological material, i.e. membranes which allow H+ to diffuse through but not H2, etc.

The drop in free energy (4.71) is usually considered to be mainly associated with the reaction (4.73), expressing G in terms of a chemical potential

(3.49), e.g. of the H+ ions dissolved in the electrolyte. Writing the chemical potential p as Faraday's constant times a potential 0, the free energy for n moles of hydrogen ions is

When the hydrogen ions "disappear" at the positive electrode according to the reaction (4.73), this chemical free energy is converted into the electrical energy (4.70) or (4.71), and since the numbers of electrons and hydrogen ions in (4.73) are equal, n — ne, the chemical potential p is given by p— F 0— F A0ext. (4.75)

Here 0 is the quantity usually referred to as the electromotive force (e.m.f.) of the cell, or "standard reversible potential" of the cell, if taken at standard atmospheric pressure and temperature. From the value of AG quoted above, corresponding to -2.37 x 105 J per mole of H2O formed, the cell e.m.f. becomes

with n — 2 since there are two H+ ions for each molecule of H2O formed. The chemical potential (4.75) may be parametrised in the form (3.50), and the cell e.m.f. may thus be expressed in terms of the properties of the reactants and the electrolyte [including the empirical activity coefficients appearing in

(3.50) as a result of generalising the expression obtained from the definition of the free energy, (4.6), assuming P, V and T to be related by the ideal gas law, PV — RT, valid for one mole of an ideal gas (cf. e.g. Angrist, 1976)].

The efficiency of a fuel cell is the ratio between the electrical power output (4.70) and the total energy lost from the fuel. However, it is possible to exchange heat with the surroundings, and the energy lost from the fuel may thus be different from AG. For an ideal (reversible) process, the heat added to the system is

AQ — T AS — AH - AG, and the efficiency of the ideal process thus becomes nideal — - AG / (- AG - AQ> — AG / AH. (4.77)

For the hydrogen-oxygen fuel cell considered above, the enthalpy change during the two processes (4.72) and (4.73) is AH = -9.5 x 10-19 J or -2.86 x 105 J per mole of H2O formed, and the ideal efficiency is

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