Standard Half-Reaction Potentials at

Potentiometry has found extensive application over the past half-century as a means to evaluate various thermodynamic parameters. Although this is not the major application of the technique today, it still provides one of the most convenient and reliable approaches to the evaluation of thermodynamic quantities. In particular, the activity coefficients of electroactive species can be evaluated directly through the use of the Nemst equation (for species that give a reversible electrochemical response). Thus, if an electrochemical system is used without a junction potential and with a reference electrode that has a well-established potential, then potentiometric measurement of the constituent species at a known concentration provides a direct measure of its activity. This provides a direct means for evaluation of the activity coefficient (assuming that the standard potential is known accurately for the constituent half-reaction). If the standard half-reaction potential is not available, it must be evaluated under conditions where the activity coefficient can be determined by the Debye-Hiickel equation. 

At 25°C the standard half reaction potential for the process 2H20 + 2e - H2 + 20H is -0.8277 V determine the dissociation constant for water at that temperature. 

In the discussion of the Daniell cell, we indicated that this cell produces a voltage of 1.10 V. This voltage is really the difference in potential between the two half-cells. The cell potential (really the half-cell potentials) is dependent upon concentration and temperature, but initially we ll simply look at the half-cell potentials at the standard state of 298 K (25°C) and all components in their standard states (1M concentration of all solutions, 1 atm pressure for any gases and pure solid electrodes). Half-cell potentials appear in tables as the reduction potentials, that is, the potentials associated with the reduction reaction. We define the hydrogen half-reaction (2H+(aq) + 2e - H2(g)) as the standard and has been given a value of exactly 0.00 V. We measure all the other half-reactions relative to it some are positive and some are negative. Find the table of standard reduction potentials in your textbook. 

In section 11.1, you learned that a cell potential is the difference between the potential energies at the anode and the cathode of a cell. In other words, a cell potential is the difference between the potentials of two half-cells. You cannot measure the potential of one half-cell, because a single half-reaction cannot occur alone. However, you can use measured cell potentials to construct tables of half-cell potentials. A table of standard half-cell potentials allows you to calculate cell potentials, rather than building the cells and measuring their potentials. Table 11.1 includes a few standard half-cell potentials. A larger table of standard half-cell potentials is given in Appendix E. 

Step 1 The oxidation and reduction half-reactions are as follows. Oxidation half-reaction (occurs at the anode) 2r(aq) l2(s) + 2e Reduction half-reaction (occurs at the cathode) Br2( ) -i- 2e 2Br (aq) Step 2 The relevant reduction potentials in the table of standard reduction potentials are ... 

Where Ox, Ox, Red, and Red are reactants (sums of species). The subscripts are abbreviations for right and left, but the two half-reactions could be distinguished in other ways. The half-reactions and their standard apparent reduction potentials at a specified pH are represented by... 

Figure 9.2 The pH dependence of the standard apparent reduction potentials at 298.15 K and 0.25 M ionic strength of the following biochemical half reactions, starting at the top of the ordinate [With permission from R. A. Alberty, Biophys. Chem. 389, 94-109 (2001). Copyright Academic Press.] ...

Therefore for a given reaction to take place, the cell potential must be positive. The cell potential is taken as the difference between the two half-cell reactions, the one at the cathode minus the one at the anode. The half-cell potential exists because of the difference in the neutral state compared to the oxidized state, such as Fe/Fe + or, at the cathode, the difference between the neutral state and the reduced state, as in These reduction-oxidation (redox) potentials are measured relative to a standard half-cell potential. The chart shown in Table 2 lists potentials relative to the which is set as zero. 

Equations 2.72 and 2.73 are Nemst half-cell equations. For example, with Eq 2.73, when aMm+= 1, E m Mn,+ = E m+ Hence, E Mm+ is the half-cell potential at unit activity of the ions (i.e., the standard electrode half-cell potential). Values of the standard potentials of many electrode reactions are available in the literature, some of which are given in Table 2.1 (Ref 2, 7, 8). All values are given in sign and magnitude relative to the standard hydrogen electrode as previously discussed. 

For some electrochemical cells, like those in Figure 1.1.1, it is possible to calculate the open-circuit potential from thermodynamic data, that is, from the standard potentials of the half-reactions involved at both electrodes via the Nemst equation (see Chapter 2). The key point is that a true equilibrium is established, because a pair of redox forms linked by a given half-reaction (i.e., a redox couple) is present at each electrode. In Figure... 

The emf of a cell can be calculated from the standard electrode potentials of the half-reactions. In order to find the emf, we have to look at the two halfreactions involved in the reaction. Then, set up the two half-reactions so that when they are added we will get the net reaction. Once we have set the equations properly and assigned the prpper potentials to those half-reactions, we can add the standard electrode potentials. A common mistake that students make is that they forget the fact that the standard electrode potentials are given in terms of reduction reactions. Redox reactions involve both oxidation and reduction. If one half-reaction is reduction, the other should be oxidation. So we must be careful about the signs of the half-reaction potentials, before we add the two half-reaction potentials to get the emf value. Do the next example. 

The saturated calomel electrodes are convenient for corrosion measurements because the diffusion potential initiated at the interface of the saturated potassium chloride solution and the electrolyte is insignificant and can be ignored. The electrode potential of the saturated calomel electrode of 0.241 V is lower than the potential of the standard half reaction of e° = 0.268 V because of the higher chloride activity. 

The standard cell potential of a voltaic cell, depends on the particular cathode and anode half-cells. We could, in principle, tabulate the standard cell potentials for all possible cathode/anode combinations. However, it is not necessary to undertake this arduous task. Rather, we can assign a standard potential to each half-cell and then use these half-cell potentials to determine Etea- The cell potential is the difference between two half-cell potentials. By convention, the potential associated with each electrode is chosen to be the potential for reduction at that electrode. Thus, standard half-cell potentials are tabulated for reduction reactions, which means they are standard reduction potentials, denoted Ered- The standard cell potential, ceU> is the standard reduction potential of the cathode reaction, (cathode), minus the standard reduction potential of the anode reaction, (anode) ... 

Use data in Appendix E to determine (a) which half-reaction occurs at the cathode and which occurs at the anode and (b) the standard ceU potential... 

The potential difference is closely related to the difference of the electrochemical potential based on the electrochemical affinity. If we could measure A(p directly, we could organize the table of electromotive forces based on the Galvani potential difference. However, A

reference electrode to measure the half cell potential at an electrode. When a certain electrcxle is coupled with a reference electrode, then the electromotive force can be measured. Since we usually use some reference electrodes as standards, the electromotive force is defined as the equilibrium potential of the reaction. The table was made in such a way and the hydrogen reference electrode was used to measure and calculate potentials for the half cell reactions. 

All of these half-reaction potentials are shown for standard state conditions where all concentrations are 1 molar and all pressures are 1 atm. (These conditions are rare in the lab.) The Nernst equation must be used to determine reduction potentials at nonstandard state conditions. 

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. 

Eo = the specific standard half-cell potential for the reaction cited at unity activity for dissolved species and 1 atmosphere fugacity for gaseous substances at 25°C. The standard half cell potential for the reaction 2H + 2e" = H2 is defined as 0.0 V versus the normal hydrogen electrode (NHE) at 25°C. 

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