Cell potential half-reaction potentials

In any galvanic cell, the half-reaction with the more negative reduction potential occurs as oxidation at the anode, and the half-reaction with the more positive reduction potential occurs as reduction at the cathode. 

A "potential ladder" diagram models the potential difference. The rungs on the ladder correspond to the values of the reduction potentials. For a galvanic cell, the half-reaction at the cathode is always on the upper rung, and the subtraction... 

Because (like AG) refers to a difference in a state property, it can be evaluated in additive fashion along many alternative pathways. For this purpose, it is convenient to assign conventional ° values to each half-cell reaction [e.g., standard oxidation potentials as compiled in W. M. Latimer. Oxidation Potentials, 2nd edn (Prentice-Hall, New York, 1952)], such that the algebraic sum of the two half-reaction potentials equals the overall cell °. Such half-reaction ° values can in turn be obtained by choosing some standard electrode reaction as the conventional zero of the scale [such as the standard hydrogen electrode (SHE) for the l/2H(g) —> H+ aq) + e oxidation reaction, with she = 0]. Sidebar 8.2 illustrates a simple example of this procedure. 

Potentiometric measurements are based on the Nernst equation, which was developed from thermodynamic relationships and is therefore valid only under equilibrium (read thermodynamic) conditions. As mentioned above, the Nernst equation relates potential to the concentration of electroactive species. For electroanalytical purposes, it is most appropriate to consider the redox process that occurs at a single electrode, although two electrodes are always essential for an electrochemical cell. However, by considering each electrode individually, the two-electrode processes are easily combined to obtain the entire cell process. Half reactions of electrode processes should be written in a consistent manner. Here, they are always written as reduction processes, with the oxidised species, O, reduced by n electrons to give a reduced species, R ... 

Writing the chemical equation in the reverse direction requires changing the sign of the cell or half-cell potential. Note that all the equations in Table 17.2 refer to reduction half-reactions, but each complete cell requires one oxidation and one reduction. Thus one of the half-cell equations must be reversed (and the sign of its potential changed) to add to the other to make a complete cell equation. 

C is correct. The two half reaction potentials must be added after they have been rearranged to represent the galvanic cell. This means that the first half reaction is reversed. If this potential is applied, the cell can be recharged back to this potential which is the standard potential. 

See Skill 11.3 for information on cell potentials. The standard potential of an oxidation half-reaction E is equal in magnitude but has the opposite sign to the potential of the reverse reduction reaction. Standard half-cell potentials are tabulated as reduction potentials. These are sometimes referred to as standard electrode potentials E°. Therefore,... 

To determine the potential for the cell, the hydrogen electrode is by convention assigned a half-reaction potential E of 0.00 volt (V) under standard state conditions. This means that if the H ion activity and the H2 gas activity are both 1.00, for the hydrogen electrode is 0.00 volt. This convention can be symbolized as... 

The mineral particle is essentially a short-circuited electrochemical oell that assumes a mixed potential between the half-cell potentials of reactions [Eqs, (9.4-2) and (9.4-3)). The mixed potential depends on the properties of the electrode surface. Potentials more positive then the equilibrium potential drive the half-cell reaction in the net anodic direction and potentials more negative than the equilibrium potential drive tha reactions in the net cathodic direction. 

Before we discuss redox titration curves based on reduction-oxidation potentials, we need to learn how to calculate equilibrium constants for redox reactions from the half-reaction potentials. The reaction equilibrium constant is used in calculating equilibrium concentrations at the equivalence point, in order to calculate the equivalence point potential. Recall from Chapter 12 that since a cell voltage is zero at reaction equilibrium, the difference between the two half-reaction potentials is zero (or the two potentials are equal), and the Nemst equations for the halfreactions can be equated. When the equations are combined, the log term is that of the equilibrium constant expression for the reaction (see Equation 12.20), and a numerical value can be calculated for the equilibrium constant. This is a consequence of the relationship between the free energy and the equilibrium constant of a reaction. Recall from Equation 6.10 that AG° = —RT In K. Since AG° = —nFE° for the reaction, then... 

Construct a cell using a standard hydrogen electrode and an electrode designed around the redox couple of interest. The cel potential E is measured with a high impedance voltmeter under zero current conditions. When using SHE as a reference electrode, E is the desired half-reaction potential [7.13], Should the redox couple have one or more electroaclive species (i) that are solvated with concentration b, E must be measured over a range of b values. 

The standard potential of a cell or half-reaction is obtained under conditions where all species are in their standard states (10). For solids, like Ag in cell 2.1.32 or reaction 2.1.33, the standard state is the pure crystalline (bulk) metal. It is interesting to consider how many atoms or what particle size is needed to produce bulk metal and whether the standard potential is a function of particle size when one deals with metal clusters. These questions have been addressed (11-13) and for clusters containing n atoms (where n < 20), indeed turns out to be very different from the value for the bulk metal (n 20). Consider, for example, silver clusters, Agn- For a silver atom n = 1), the value of can be related to for the bulk metal through a thermodynamic cycle involving the ionization potential of Ag and the hydration energy of Ag and Ag. This process yields... 

Thus far we have confined our discussion to cells and half-reactions at standard state, that is, 25°C, 1 atm pressure, and unit activity for all species. To determine the effect of reactant and product concentrqtion, we need to draw further on our analogy between free energy change and electrode potential or cell emf. Using the free energy equation as developed in Chapter 3,... 

In general, only the reduction half-reaction potentials are listed in tables, as in Table 9.1. The potential of an oxidation half-reaction is the negative of the value of the reduction half-reaction. Moreover, it is convenient to standardise the concentrations of the components of the cells. If the ceU components are in their standard states, standard electrode potentials, E°, are recorded ... 

The scientific community has universally accepted the values for half-reaction potentials based on the assignment of 0 volts to the process 2H -r 2e H2 (under standard conditions where ideal behavior is assumed). However, before we can use these values, we need to understand several essential characteristics of half-cell potentials. 

Assuming that reaction in Eq. (2.52) proceeds from left to right, the half-cell potential for reaction in Eq. (2.53) written as oxidation is = —0.401 Vvs. SHE. According to... 

In order to simplify, the quantified concept half-cell potential or electrode potential has been introduced. This has been done by choosing a certain electrode reaction as reference, and defining the equilibrium potential of this electrode to be equal to zero. The numerical value of the equihbrium potential of any other electrode reaction X is given by the reversible cell voltage of the combination X-reference electrode, see Figure 3.7. 

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. 

The potential of these half-cell reactions can be determined by comparison with the hydrogen electrode all under standard conditions, which is unit concentration for ions in solution and 1 atm pressure for gases at 25°C. The value of these standard electrode reduction potentials is given in Table 9.4. The standard cell potential of reaction (9.15) is... 

Table 21-1 on page 667 of your textbook lists the standard reduction potentials ( ° values) of common half-cell reactions. These values apply to the standard conditions of a IM solution, 25°C, and 1 atm pressure. In any voltaic cell, the half-reaction with the lower reduction potential will proceed in the opposite direction, as an oxidation half-reaction. The half-reaction with the higher reduction potential will proceed as a reduction. The electrical potential of a voltaic cell, also called the cell potential, is found by subtracting the standard reduction potential of the oxidation halfreaction from the standard reduction potential of the reduction half-reaction. 

Standard Hydrogen Electrode The standard hydrogen electrode (SHE) is rarely used for routine analytical work, but is important because it is the reference electrode used to establish standard-state potentials for other half-reactions. The SHE consists of a Pt electrode immersed in a solution in which the hydrogen ion activity is 1.00 and in which H2 gas is bubbled at a pressure of 1 atm (Figure 11.7). A conventional salt bridge connects the SHE to the indicator half-cell. The shorthand notation for the standard hydrogen electrode is... 

Redox Electrodes Electrodes of the first and second kind develop a potential as the result of a redox reaction in which the metallic electrode undergoes a change in its oxidation state. Metallic electrodes also can serve simply as a source of, or a sink for, electrons in other redox reactions. Such electrodes are called redox electrodes. The Pt cathode in Example 11.1 is an example of a redox electrode because its potential is determined by the concentrations of Ee + and Ee + in the indicator half-cell. Note that the potential of a redox electrode generally responds to the concentration of more than one ion, limiting their usefulness for direct potentiometry. 

Figure 21.2a shows a sample/reference half-cell pair for measurement of the standard reduction potential of the acetaldehyde/ethanol couple. Because electrons flow toward the reference half-cell and away from the sample half-cell, the standard reduction potential is negative, specifically —0.197 V. In contrast, the fumarate/succinate couple and the Fe /Fe couple both cause electrons to flow from the reference half-cell to the sample half-cell that is, reduction occurs spontaneously in each system, and the reduction potentials of both are thus positive. The standard reduction potential for the Fe /Fe half-cell is much larger than that for the fumarate/ succinate half-cell, with values of + 0.771 V and +0.031 V, respectively. For each half-cell, a half-cell reaction describes the reaction taking place. For the fumarate/succinate half-cell coupled to a H Hg reference half-cell, the reaction occurring is indeed a reduction of fumarate. 

Equations 20.176 and 20.179 emphasise the essentially thermodynamic nature of the standard equilibrium e.m.f. of a cell or the standard equilibrium potential of a half-reaction E, which may be evaluated directly from e.m.f. meeisurements of a reversible cell or indirectly from AG , which in turn must be evaluated from the enthalpy of the reaction and the entropies of the species involved (see equation 20.147). Thus for the equilibrium Cu -)-2e Cu, the standard electrode potential u2+/cu> hence can be determined by an e.m.f. method by harnessing the reaction... 

Standard half-cell voltages are ordinarily obtained from a list of standard potentials such as those in Table 18.1 (page 487). The potentials listed are the standard voltages for reduction half-reactions, that is,... 

This shows that the voltage of a given cell may be thought of as being made up of two parts, one part characteristic of one of the half-reactions and one part characteristic of the other halfreaction. Chemists call these two parts half-cell potentials, a term that emphasizes the relation between voltage and potential energy. The halfcell potentials are symbolized °. 

We would like to measure the contribution each half-reaction makes to the voltage of a cell. Yet every cell involves two half-reactions and every cell voltage measures a difference between their half-cell potentials. We can never isolate one half-reaction to measure its E°. An easy escape is to assign an arbitrary value to the potential of some selected half-reaction. Then we can combine all other half-reactions in turn with this reference half-reaction and find values for them relative to our reference. The handiest arbitrary value to assign is zero and chemists have decided to give it to the half-reaction... 

Similarly, if we combine a Cu-Cu+2 half-cell in its standard state with a standard Hj-2H+ halfcell, the voltage (potential) we measure (0.34 volt) is the value assigned to the half-reaction ... 

Chemists have determined a large number of these half-cell potentials. The magnitude of the voltage is a quantitative measure of the tendency of that half-reaction to release electrons in comparison to the H2-2H+ half-reaction. If the sign is positive, the half-reaction has greater tendency to release electrons than does the H2-2H+ half-... 

The half-reactions, listed in order of decreasing half-cell potentials, are in the same order as in Table 12-1, which was dictated by laboratory experience. 

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