Redox reactions standard state

The standard-state electrochemical potential, E°, provides an alternative way of expressing the equilibrium constant for a redox reaction. Since a reaction at equilibrium has a AG of zero, the electrochemical potential, E, also must be zero. Substituting into equation 6.24 and rearranging shows that... 

Balance the following redox reactions, and calculate the standard-state potential and the equilibrium constant for each. Assume that the [H3O+] is 1 M for acidic solutions, and that the [OH ] is 1 M for basic solutions. 

The ladder diagram for this system is shown in Figure 11.24a. Initially the potential of the working electrode remains nearly constant at a level near the standard-state potential for the Fe UFe redox couple. As the concentration of Fe + decreases, however, the potential of the working electrode shifts toward more positive values until another oxidation reaction can provide the necessary current. Thus, in this case the potential eventually increases to a level at which the oxidation of H2O occurs. 

Earlier we described a voltammogram as the electrochemical equivalent of a spectrum in spectroscopy. In this section we consider how quantitative and qualitative information may be extracted from a voltammogram. Quantitative information is obtained by relating current to the concentration of analyte in the bulk solution. Qualitative information is obtained from the voltammogram by extracting the standard-state potential for the redox reaction. For simplicity we only consider voltammograms similar to that shown in Figure 11.33a. 

Electrochemical Reversibility and Determination of m In deriving a relationship between 1/2 and the standard-state potential for a redox couple (11.41), we noted that the redox reaction must be reversible. How can we tell if a redox reaction is reversible from its voltammogram For a reversible reaction, equation 11.40 describes the voltammogram. 

We have already noted that the standard free energy change for a reaction, AG°, does not reflect the actual conditions in a ceil, where reactants and products are not at standard-state concentrations (1 M). Equation 3.12 was introduced to permit calculations of actual free energy changes under non-standard-state conditions. Similarly, standard reduction potentials for redox couples must be modified to account for the actual concentrations of the oxidized and reduced species. For any redox couple. 

Redox reactions, like all reactions, eventually reach a state of equilibrium. It is possible to calculate the equilibrium constant for a redox reaction from the standard voltage. To do that, we start with the relation obtained in Chapter 17 ... 

It is clear from what has already been stated that standard reduction potentials may be employed to determine whether redox reactions are sufficiently complete... 

The above important relationship now allows evaluation of the thermodynamic driving force of a redox reaction in terms of a measurable cell emf. Moreover, it is possible to utilize the relationship between the standard state potential and the standard state free energy to arrive at an expression for the equilibrium constant of a redox reaction in terms of the emf. Thus... 

Metal/metal oxides are the materials of choice for construction of all-solid-state pH microelectrodes. A further understanding of pH sensing mechanisms for metal/metal oxide electrodes will have a significant impact on sensor development. This will help in understanding which factors control Nemstian responses and how to reduce interference of the potentiometric detection of pH by redox reactions at the metal-metal oxide interface. While glass pH electrodes will remain as a gold standard for many applications, all-solid-state pH sensors, especially those that are metal/metal oxide-based microelectrodes, will continue to make potentiometric in-vivo pH determination an attractive analytical method in the future. 

Figure 6. Summary of ranges in isotopic compositions for natural terrestrial samples as discussed in this volume. Isotopic variability in extraterrestrial samples is often greater. Isotopic compositions reported as 5 values in units of per mil (%o), based on isotopic ratios and reference standards as used in this volume (Table 1). Note that the range of isotopic compositions for Li is much greater than the scale used in the diagram, where 5 Li values vary from -21 to +54. In many cases, relatively large isotopic fractionations occur during redox reactions (see Chapter 3), and the common oxidation states in near-surface natural environments are listed on the left.

The redox reaction is illustrated with gaseous iron ions Fef , - Fe > + Cjsto) ", where eism) is the gaseous electron in the standard state. The occupied... 

L OX , + eligand coordinated with redox particles and ejsTD, is the electron in the gaseous standard state at the outer potential of the aqueous solution (Refer to Chap. 4.). The following reaction cycle may be used to obtain the energy relationship between the two redox reactions ... 

Aquatic chemists have defined their own electrochemical standard state to fecilitate calculation of redox speciation in aqueous solutions. In this standard state, all reactions are conducted at pH 7.0, 25°C, and 1 atm. The concentrations of all other solutes are 1 molal (unless otherwise specifically noted). Values so obtained are designated with the subscript w. The pe s for the most important redox couples in seawater are given in Table 7.4. 

Jnst as free protons do not exist in solution in acid-base reactions, there are no free electrons in redox reactions. However it is possible to define the activity of electrons relative to a specified standard state and thereby treat electrons as discrete species in equilibrinm calcnlations in the same way as ions and molecules. The standard state of electron activity for this pnrpose is by convention defined with respect to the redox conple made by hydrogen ions and hydrogen gas ... 

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... 

Values of E° by definition refer to conditions under which all species are in their standard states at 298 K. For non-standard conditions the electrode potential, E, of a redox reaction is given by the familiar Nernst expression (equation 24), where... 

Triarylamine is a purely organic molecule which is interesting as a chro-mophore in e.g. display technology. The molecule can be switched between a reduced colourless, and an oxidized blue state. The sensitization to nanos-tructured TiC>2 electrodes provides the substantial surface area required for a strong coloration. It is, however, believed that the electron transfer involved in the redox reaction takes place mainly within the sensitizer layer, and does not involve the substrate. Instead, there is an eventual electrical contact between the back-contact and the sensitizer layer [98]. For a quantum chemical modelling of the system, the inclusion of the substrate is in this case not likely to be essential. For a molecule of this size, it is possible to apply standard quantum... 

The standard electrode potential E° of a redox reaction is a measure of the potential that would be developed if both reductants and oxidants were in their standard states at equal concentrations and with unit activities. The units of E° are volts and ° can be calculated from the Gibbs free energy change (AG ) of the redox reaction from the relationships... 

In soil solutions the most important chemical elements that undergo redox reactions are C, N, O, S, Mn, and Fe. For contaminated soils the elements As, Se, Cr, Hg, and Pb could be added. Table 2.4 lists reduction half-reactions (most of which are heterogeneous) and their equilibrium constants at 298.15 K under 1 atm pressure for the six principal elements involved in soil redox phenomena. Although the reactions listed in the table are not full redox reactions, their equilibrium constants have thermodynamic significance and may he calculated with the help of Standard-State chemical potentials in the manner... 

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