Half-cell potentials standard-state reduction

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. 

The numerical values of cell potentials and half-cell potentials depend on various conditions, so tables of standard reduction potentials are true when ions and molecules are in their standard states. These standard states are the same as for tables of standard enthalpy changes. Aqueous molecules and ions have a standard concentration of 1 mol/L. Gases have a standard pressure of 101.3 kPa or 1 atm. The standard temperature... 

The numerical value of an electrode potential depends on the nature of the particular chemicals, the temperature, and on the concentrations of the various members of the couple. For the purposes of reference, half-cell potentials are taken at the standard states of all chemicals. Standard state is defined as 1 atm pressure of each gas (the difference between 1 bar and 1 atm is insignificant for the purposes of this chapter), the pure substance of each liquid or solid, and 1 molar concentrations for every nongaseous solute appearing in the balanced half-cell reaction. Reference potentials determined with these parameters are called standard electrode potentials and, since they are represented as reduction reactions (Table 19-1), they are more often than not referred to as standard reduction potentials (E°). E° is also used to represent the standard potential, calculated from the standard reduction potentials, for the whole cell. Some values in Table 19-1 may not be in complete agreement with some sources, but are used for the calculations in this book. 

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. 

The standard reduction potential (E°) provides a measure of the stability of a metal in a particular oxidation state. The E° value is the voltage generated in a half-cell coupled with the standard hydrogen electrode (SHE), which itself has a defined half-cell potential of 0.0 V. Put simply, the more positive is E0 the more difficult is it for metal oxidation to a hydrated metal ion to occur. Alternatively, we could express it by saying that the less positive is °, the more stable is the metal in the higher oxidation state of its couple... 

Table 4.1 Standard-State Reduction Half-Cell Potentials in Alphabetical Order...

The two half reactions of any redox reaction together make up an electrochemical cell. This cell has a standard potential difference, E , which is the voltage of the reaction at 25 °C when all substances involved are at unit activity. E refers to the potential difference when the substances are not in the standard state. E for a particular reaction can be found by subtracting one half cell reaction from the other and also subtracting the corresponding voltages. For example for reduction of Fe to Fe by H2, E° = 0.77 - 0 = 0.77 V. A further example is the oxidation of Fe " by solid Mn02 in acid solution. The half cell reactions are. 

Many half-reactions of interest to biochemists involve protons. As in the definition of AG °, biochemists define the standard state for oxidation-reduction reactions as pH 7 and express reduction potential as E °, the standard reduction potential at pH 7. The standard reduction potentials given in Table 13-7 and used throughout this book are values for E ° and are therefore valid only for systems at neutral pH Each value represents the potential difference when the conjugate redox pair, at 1 m concentrations and pH 7, is connected with the standard (pH 0) hydrogen electrode. Notice in Table 13-7 that when the conjugate pair 2ET/H2 at pH 7 is connected with the standard hydrogen electrode (pH 0), electrons tend to flow from the pH 7 cell to the standard (pH 0) cell the measured E ° for the 2ET/H2 pair is -0.414 V... 

The cell reaction for cells without liquid junction can be written as the sum of an oxidation reaction and a reduction reaction, the so-called half-cell reactions. If there are C oxidation reactions, and therefore C reduction reactions, there are C C — 1) possible cells. Not all such cells could be studied because of irreversible phenomena that would take place within the cell. Still, a large number of cells are possible. It is therefore convenient to consider half-cell reactions and to associate a potential with each such reaction or electrode. Because of Equation (12.88), there would be (C - 1) independent potentials. We can thus assign an arbitrary value to the potential associated with one half-cell reaction or electrode. By convention, and for aqueous solutions, the value of zero has been assigned to the hydrogen half-cell when the hydrogen gas and the hydrogen ion are in their standard states, independent both of the temperature and of the pressure on the solution. 

In these formulae / and Tin indicate the standard electrode potentials which are established, when all the half cell components arc in their standard state and have activities equalling unity. The relation between the standard oxidation and standard reduction potentials of the same element is exactly the same as those formed with other potentials, i. e. for example s) = — n. ... 

In voltaic cells, it is possible to carry out the oxidation and reduction halfreactions in different places when suitable provision is made for transporting the electrons over a wire from one half-reaction to the other and to transport ions from each half-reaction to the other in order to preserve electrical neutrality. The chemical reaction produces an electric current in the process. Voltaic cells, also called galvanic cells, are introduced in Section 17.1. The tendency for oxidizing agents and reducing agents to react with each other is measured by their standard cell potentials, presented in Section 17.2. In Section 17.3, the Nernst equation is introduced to allow calculation of potentials of cells that are not in their standard states. 

Many reactions that occur in living cells are oxidation-reduction reactions. Appendix IX lists several compounds of biological importance and shows their relative tendencies to gain electrons ai 25°C and pH 7 under standard conditions. The numerical values of Ho reflect the reduction potentials relative to the 2H + 2e" H2 half-reaction which is taken as — 0.414 volt at pH 7. The value for the hydrogen half-reaction at pH 7 was calculated from the arbitrarily assigned value (Ho) of 0.00 volt under true standard-state conditions (1 M H and 1 atm Hs). For those few halfreactions of biological importance that do not involve as a reactant, the Ho and Ho values are essentially identical. 

If the zinc and copper half-cells are combined, the copper half-cell will be the cathode because it has the more positive half-cell reduction potential. The galvanic cell voltage under standard-state conditions (Fig. 17.4) will be... 

Appendix E summarizes the standard reduction potentials for a large number of half-reactions. The table lists the reactions in order of decreasing reduction potentials—that is, with the most positive at the top and the most negative at the bottom. In any galvanic cell, the half-cell that is listed higher in the table will act as the cathode (if both half-cells are in the standard state). 

The standard state emf can be found from the cell diagram by subtracting the potential of the reduction half reaction on the left (the reaction at the anode) from the potential of the reduction half reaction on the right (the reaction at the cathode). 

This is arbitrarily assigned a standard reduction potential Eo= 0.0 V. At the biochemical standard state of pH 7, the hydrogen half-cell has an Eq = —0.421 V. 

We adopt the following convention the standard-state potential difference of a cell consisting of a hydrogen electrode on the left and any other electrode on the right is called the standard reduction potential of the right half-cell or the right electrode. It is also sometimes called the standard electrode potential. 

In addition, the Pt serves as the electrical conductor to the external circuit. Under standard state conditions, that is, when the H2 pressure equals 1 atm and the ideal concentration of the HCl is 1 M, and the system is at 25°C, the reduction potential for the reaction given in Eq. (15.8) is exactly 0 V. (The potential actually depends on the chemical activity of the HCl, not on its concentration. The relationship between activity and concentration is discussed subsequently. For an ideal solution, concentration and activity are equal.) The potential is symbolized by where the superscript zero means standard state conditions. The term standard reduction potential means that the ideal concentrations of all solutes are 1 M and all gases are at 1 atm other solids or liquids present are pure (e.g., pure Pt solid). By connecting the SHE half-cell with any other standard half-cell and measuring the voltage difference developed, we can determine the standard reduction potential developed by the second half-cell. 

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 ... 

Before we discuss standard electrode potential, we will talk about electromotive force (emf). The electromotive force of a cell is the potential difference between the two electrodes. This can be measured using a voltmeter. The maximum voltage of a cell can be calculated using experimentally determined values called standard electrode potentials. By convention, the standard electrode potentials are usually represented in terms of reduction half-reactions for 1 molar solute concentration. The standard electrode potential values are set under ideal and standard-state conditions (latm pressure and 25°C temperature). From the MCAT point of view, you can assume that the conditions are standard, unless stated otherwise. Table 12-1 shows a list of standard electrode potentials (in aqueous solution) at 25°C. 

Each half-cell reaction has a specific standard potential reported as the potential of the reduction reaction vs. the normal hydrogen electrode (NHE). In an elecdochemical cell, there is a half-cell corresponding to the working electrode (WE), where the reactions under study take place, and a reference half-cell. Experimentally the cell potential is measured as the difference between the potentials of the WE half-cell and the reference electrode/ref-erence half-cell (see Chapter 4). The archetypal reference electrode is the NHE, also known as the standard hydrogen electrode (SHE) and is defined, by convention, as 0.000 V for any temperature. Although the NHE is not typically encountered due to difficulty of operation, all conventional electrodes are in turn referenced to this standard to define their absolute potential (i.e., the Ag/AgCl, 3 M KCl reference has a potential of 203 mV vs. the NHE). In practice, experimental results are either stated as being obtained vs. a specific reference electrode, or converted to potentials vs. NHE. 

These potential values are those of reduction potentials. Hence, these values are those of zero-current cell potentials in which the hydrogen electrode is located on the left and that under study on the right (see Fig. 2.5 in Chap. 2). Moreover, all the species that participate in the half-reduction equilibria are in their standard states their activities are equal to unity. We have already seen that the hydrogen electrode necessarily plays the part of the anode and the electrode under study that of the cathode. Hence, the studied system suffers the electrodic reaction... 

Standard-state half-cell reduction potentials can be used to obtain the standard-state voltage for any cell that can be made from two half-cells in the table, using the relation... 

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