Electrode potentials of half-reactions

Eq. (4.154) describes the (oxidation) reaction (4.146a) therefore, and the reverse (reduction) process (4.146b) is expressed by Eq. (4.155) when substance B is replaced by A. Because E A) = Eied( ) it also follows then that E% = Ef. This explains why only reduction standard potentials are listed in the literature, almost termed the electrode potentials of half-reactions (Table 4.7). 

If you select any two half-reactions from the chart of standard electrode potentials, the half-reaction higher on the list will proceed as a reduction, and the one lower on the list will proceed in the reverse direction, as an oxidation. Beware Some references give standard electrode potentials for oxidation half-reactions, so you have to switch higher and lower in the rule stated in the preceding sentence, though this is not common. 

Standard electrode potentials for half-reactions and overall reactions are quoted with units of volts (V). However many electrons are transferred in... 

The standard electrode potential of the reaction is considered to be equal to the difference between the values of the standard reduction potentials of the two half-reactions, (4.3) and (4.4) ... 

As we have seen, acidity and basicity are intimately connected with electron transfer. When the electron transfer involves an integral number of electrons it is customary to refer to the process as a redox reaction. This is not the place for a thorough discussion of the thermodynamics of electrochemistry that may be found in any good textbook of physical chemistry. Rather, we shall investigate the applications of electromotive force (emf) of interest to the inorganic chemist. Nevertheless, a very brief review of the conventions and thermodynamics of electrode potentials and half-reactions will be presented. 

Electrode potentials for half-reactions are most easily obtained from a table of standard electrode potentials (Table 17-1, p 275) they may be modified for concentrations appreciably different from unit activity (p 276). A list of features characteristic of electron-transfer reactions is given on p 300. 

Inspection shows that the reduction potential has the same sign as the potential of the actual electrode. For this reason we adopt the IUPAC recommendation that only reduction potentials should be called electrode potentials. Every half-reaction is therefore written in the form... 

The electromotive series is a list of the elements in accordance with their electrode potentials. The measurement of what is commonly known as the "single electrode potential", the "half-reaction potential" or the "half-cell electromotive force" by means of a potentiometer requires a second electrode, a reference electrode, to complete the circuit. If the potential of the reference electrode is taken as zero, the measured E.M.P. will be equal to the potential of the unknown electrode on this scale. W. Ostwald prepared the first table of electrode potentials in 1887 with the dropping mercury electrode as a reference electrode. W. Nernst selected in 1889 the Normal Hydrogen Electrode as a reference electrode. G.N. Lewis and M. Randall published in 1923 their table of single electrode potentials with the Standard Hydrogen Electrode (SHE) as the reference electrode. The Commission of Electrochemistry of the I.U.P.A.C. meeting at Stockholm in 1953 defined the "electrode potential" of a half-cell with the SHE as the reference electrode. 

Another way to predict the spontaneity of a redox reaction is to note the relative positions of the two half-reactions in Table 18.1. Since the table lists half-reactions in order of decreasing electrode potential, the half-reactions near the top of the table— those having large positive electrode potentials— attract electrons and therefore tend to occur in the forward direction. Half-reactions near the bottom of the table— those having large negative electrode potentials—repel electrons and therefore tend to occur in the reverse direction. In other words, as you move down Table 18.1, the half-reactions become less likely to occur in the forward direction and more likely to occur in the reverse direction. As a result, any reduction half-reaction listed is spontaneous when paired with the reverse of a half-reaction that appears below it in Table 18.1. 

At equilibrium at 298 K the electrode potential of the half-reaction for copper, given approximately by... 

When the two electrodes are connected, current flows from M to X in the external circuit. When the electrode corresponding to half-reaction 1 is connected to the standard hydrogen electrode (SHE), current flows from M to SHE. (a) What are the signs of ° of the two half-reactions (b) What is the standard cell potential for the cell constructed from these two electrodes ... 

In addition to defined standard conditions and a reference potential, tabulated half-reactions have a defined reference direction. As the double arrow in the previous equation indicates, E ° values for half-reactions refer to electrode equilibria. Just as the value of an equilibrium constant depends on the direction in which the equilibrium reaction is written, the values of S ° depend on whether electrons are reactants or products. For half-reactions, the conventional reference direction is reduction, with electrons always appearing as reactants. Thus, each tabulated E ° value for a half-reaction is a standard reduction potential. 

Figure 16.3 A potential waveform in cyclic voltammetry. F°(R/R ) is the standard electrode potential of the half-reaction under examination.

In this section, you learned that you can calculate cell potentials by using tables of half-cell potentials. The half-cell potential for a reduction half-reaction is called a reduction potential. The half-cell potential for an oxidation half-reaction is called an oxidation potential. Standard half-cell potentials are written as reduction potentials. The values of standard reduction potentials for half-reactions are relative to the reduction potential of the standard hydrogen electrode. You used standard reduction potentials to calculate standard cell potentials for galvanic cells. You learned two methods of calculating standard cell potentials. One method is to subtract the standard reduction potential of the anode from the standard reduction potential of the cathode. The other method is to add the standard reduction potential of the cathode and the standard oxidation potential of the anode. In the next section, you will learn about a different type of cell, called an electrolytic cell. 

SHE, standard hydrogen electrode The electrode used as a standard against which aU other half-cell potentials are measured. The following reaction occurs at the platinum electrode when immersed in an acidic solution and cormected to the other half of an electrochemical cell 2H (aq) -H 2e —> H2(g). The half- cell potential of this reaction at 25°C, 1 atm and 1 m concentrations of aU solutes is agreed, by convention, to be OV... 

Measnrements of Ea are usually made with a platinum electrode placed in the soil solntion together with a reference half cell electrode of known potential. The platinnm electrode transfers electrons to and from the soil solution withont reacting with it. Reducing half reactions in the soil tend to transfer electrons to the platinum electrode and oxidizing half reactions to remove them. At eqnilibrinm no electrons flow and the electric potential difference between the half cell comprising the platinnm electrode and the soil solntion and the half cell comprising the reference electrode is recorded. 

To calculate the E°, the voltage, of an electrochemical cell, the voltage for the oxidation half reaction at the anode is added to the voltage for the reduction half reaction at the cathode E°a ll = E°oxid react + E°red react. For an electrochemical cell with zinc and copper electrodes, E° = 0.76 + 0.34 = 1.10 V, voltage equals 0.76 + 0.34, which equals 1.10 volts. The sign for the zinc reduction potential half reaction is changed because the half reaction is reversed to show that oxidation occurs at the zinc electrode. The two half reactions can also be added to show the overall reaction in the electrochemical cell ... 

The free energies in (18) are illustrated in Fig. 10. It can be seen that GA is that part of AG ° available for driving the actual reaction. The importance of this relation is that it allows AGXX Y to be calculated from the properties of the X and Y systems. In thermodynamics, from a list of n standard electrode potentials for half cells, one can calculate j (m — 1) different equilibrium constants. Equation (18) allows one to do the same for the %n(n— 1) rate constants for the cross reactions, providing that the thermodynamics and the free energies of activation for the symmetrical reactions are known. Using the... 

Although potentials of half-cell electrode reactions cannot be measured, their consideration is extremely useful. For example, consider the two cells in series, as indicated in reaction (X),... 

The hydrogen electrode. The hydrogen electrode is discussed first because it is the primary reference electrode used to define an internationally accepted scale of standard potentials in aqueous solution. By convention, the potential of an electrode half-reaction that is measured with respect to the normal hydrogen electrode (NHE also written as SHE, standard hydrogen electrode) is defined as the electrode potential of the half reaction. This convention amounts to an arbitrary assignment for the standard potential of the hydrogen electrode as zero at all temperatures. Thus, there is in effect a separate scale of electrode potentials at each temperature level. 

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