Electrode potentials, standard defined

First of all, the important role of platinum as the metal part of the standard hydrogen electrode (SHE), which is the primary standard in electrochemistry should be mentioned. The standard potential of an electrode reaction (standard electrode potential) is defined as the value of the standard potential of a cell reaction when that involves the oxidation of molecular hydrogen to solvated (hydrated) protons (hydrogen ions) ... 

Because electrode potentials are defined with reference to the H+/H2 electrode under standard conditions, E° values apply implicitly to (hypothetically ideal) acidic solutions in which the hydrogen ion concentration is 1 mol kg-1. Such E° values are therefore tabulated in Appendix D under the heading Acidic Solutions. Appendix D also lists electrode potentials for basic solutions, meaning solutions in which the hydroxide ion concentration is 1.0 mol kg-1. The conversion of E° values to those appropriate for basic solutions is effected with the Nernst equation (Eq. 15.15), in which the hydrogen ion concentration (if it appears) is set to 1.0 x 10-14 mol kg-1 and the identity and concentrations of other solute species are adjusted for pH 14. For example, for the Fc3+/2+ couple in a basic medium, the relevant forms of iron(III) and iron(II) are the solid hydroxides, and the concentrations of Fe3+ (aq) and Fe2+ (aq) to be inserted into the Nernst equation are those determined for pH 14 by the solubility products of Fe(OH)3(s) and Fe(OH)2(s), respectively. Examples of calculations of electrode potentials for nonstandard pH values are given in Sections 15.2 and 15.3. 

The electrode potential is defined as the potential difference between the terminals of a cell constructed of the half-cell in question and a standard hydrogen electrode (or its equivalent) and assuming that the terminal of the latter is at zero volts. Note therefore that the electrode potential is an observable physical quantity and is unaffected by the conventions used for writing cells. The statement. . . the electrode potential of zinc is —0.76 volts. . . implies only that a voltmeter placed across the terminals of a cell consisting of standard hydrogen electrode and the zinc electrode would show this value of potential difference, with the zinc terminal negative with respect to that of the hydrogen electrode. An electrode potential is never a metal/solution potential difference , not even on some arbitrary scale. 

The standard potential of an -> electrode reaction (standard electrode potential) is defined as the value of the standard potential of a cell reaction (E ) when that... 

The power of an oxidant or a reductant is measured by the electrode potential of the substance. Under standard conditions, the electrode potential is defined as the standard electrode potential, E°. Standard conditions are the cases at 25° C, 1 atm pressure, and unit activity of all species. Table 1 lists the values of E° for some chemical oxidants used in water and wastewater treatment processes. 

In electrochemistry, the electrode potential is defined by the electronic energy level in a solid electrode referred to the energy level of the standard gaseous electron just outside the surface of an electrolyte (aqueous solution) in which the electrode is immersed [6] ... 

For unknown activities the measurement of the standard electrode potential is more complicated. The standard electrode potential is defined at /ra = 1 mol kg with the hypothetical activity coefficient of y = 1 (ideal diluted solution). First principal experimental determinations of standard potentials may only be made by extrapolation to this hypothetical value. For measurements, selected cell arrangements are used with complete elimination of the diffusion potential and with diluted electrolytes. For the correction of the activity the Debye-Hiickel approximation (Eq. (1.15)) may be used, for example, for the Hamed cell Ag/AgCl, HCl (m+)/Pt(H2). A concentration corrected potential value is plotted versus the square root of the molaUty. The extrapolation to 7ra+ = 0 gives the standard potential of the Ag/AgCl electrode (Figure 3.5). Using this electrode as reference electrode other standard potentials can be determined. 

For biological electron-transfer processes, the pH of the system is around 7.0, and a biological standard electrode potential, ", is defined instead of E°. We discuss this further in Section 29.4 when we consider the mitochondrial electron-transfer chain. 

For the study of electrochemistry and corrosion one must be able to compare the equilibrium potentials of different electrode reactions. To these ends, by convention, a scale of standard electrode potentials is defined by arbitrarily assigning the value of zero to the equilibrium potential of the electrode (2.42), under standard conditions (Pfj2 = 1 bar =1.013 atm, T = 298 K, au+ = 1) ... 

Standard anode electrode potential Standard cathode electrode potential Defined in Eq. (5.3) = nLI2d Effectiveness factor for the uniformity of current distribution in parallel plate cells... 

The standard electrode potential is defined as the potential difference between a standard hydrogen electrode and a metal (the electrode) which is immersed in a solution containing metal ions at 1 moldm concentration at 298 K (25 °C) and 100 kPa. 

If a check is needed on the correctness of the measured value for an experimental cell, a standard cell, such as the Weston cadmium cell, may be used as a calibration, since the value of its emf is accurately known over a range of temperatures. The electrode potential is defined using the standard hydrogen electrode as reference, as described in Topic C2. 

Shortcomings of the choice of the equilibrium state as the electrical reference point in the evaluation of the temperature effect on the rate of electrode reactions, and consequently of the overpotential as an experimental substitute for A(A0) in the WE-RE cell at various temperatures, have been discussed in the previous section. Hence, another reference point should be sought. From a theoretical point of view, the choice is unambiguous—it is the zero point on the relative electrode potential scale, defined by the SHE convention. Basically, this is also an equilibrium state, but of a single reaction selected by convention, namely, the reduction of two hydrogen ions to molecular hydrogen. The value of A0 at the interface when this reaction is held at equilibrium, assuming all species involved are in standard thermodynamic states, is fixed by the SHE convention as zero. The same convention associates additional properties with this reference state temperature, solvent, and solute Independence. Formally, the properties of the SHE satisfy the principal theoretical requirements for the electrical reference point in the evaluation of the effect of temperature on the rate of electrode reactions. 

It should be kept in mind, that these rate constants are defined based on the volume concentrations of the reacting species. Another standard rate constant hP can be defined with regard to the rate of the reaction at the standard electrode potential of the electrode reaction. This rate constant refers consequently to standard activities instead of concentrations. 

Equation (3.3) gives the potential dependence of the reaction free energy of Reaction (3.2). Since this reaction equilibrium defines the standard hydrogen electrode potential, we now have a direct fink between quite simple DFT calculations and the electrode potential. In a similar way, we can now calculate potential-dependent reaction free energies for other reactions, such as O - - H" " + e OH or OH - -+ e HzO. 

This last equation contains the two essential activation terms met in electrocatalysis an exponential function of the electrode potential E and an exponential function of the chemical activation energy AGj (defined as the activation energy at the standard equilibrium potential). By modifying the nature and structure of the electrode material (the catalyst), one may decrease AGq, thus increasing jo, as a result of the catalytic properties of the electrode. This leads to an increase in the reaction rate j. 

If a cell is to be used as a potential standard, then it must be prepared as simply as possible from chemicals readily available in the required purity and, in the absence of current passage, it must have a known, defined, constant EMF that is practically independent of temperature. In this case the efficiency, power, etc., required for cells used as electrochemical power sources is of no importance. The electrodes of the standard cell must not be polarizable by the currents passing through them when the measuring circuit is not exactly compensated. 

AGq is the standard activation free energy, also termed the intrinsic barrier, which may be defined as the common value of the forward and backward activation free energies when the driving force is zero (i.e., when the electrode potential equals the standard potential of the A/B couple). Expression of the forward and backward rate constants ensues ... 

The standard electrode potential of an element is defined as its electrical potential when it is in contact with a molar solution of its ions. For redox systems, the standard redox potential is that developed by a solution containing molar concentrations of both ionic forms. Any half-cell will be able to oxidize (i.e. accept electrons from) any other half-cell which has a lower electrode potential (Table 4.1). 

By raising the electrode potential towards more and more negative values a threshold value will be reached above this value the reduced form S- is stabilized at the electrode surface, whereas below this value the oxidized form S is stabilized at the electrode surface. This threshold value is just defined as the standard potential of the S/S- couple. 

The electrode potential in the equilibrium of redox electron transfer may also be defined by the free enthalpy change in the reaction of the hydrated redox particles with the standard gaseous electron eisro) as shown in Eqn. 4—20 ... 

While this potential cannot he determined for a single electrode, a potential can be derived if the potential of the other electrode in a cell is defined, i.e. the potential of the standard hydrogen electrode (SHE) is arbitrarily taken as 0.(XXX)V. In this way. a potential scale can then be devised for single electrode potentials - see Section 3.2. t The abbreviation emf , in upright script, is often used in other lextNmks as a direct , i.e. non-variable, acronym for the electromotive force. Note, however, that in this present text it is used to represent a variable (cell potential) and is therefore. shown in italic script. 

Figure 2.1 Simplified schematic plots showing the exponential relationship between the current density i and the potential of the electrode, E. (The latter is represented here as being relative to the standard electrode potential of the couple undergoing electromodification for now, the abscissa ( — ) can be thought of as deviation from equilibrium.) Three examples of electron-transfer rate (/feei) are shown (a) (coincident with the y-axis) representing a very fast rate of electron transfer of 10 A cm" (b) representing an average rate of electron transfer of 10 A cm (c) representing a slow rate of electron transfer of 10 A cm . For each trace, T = 298 K and the reaction was symmetrical , i.e. a = 0.5, as defined later in Section 7.5.

The SHE. The H" " H2 couple is the basis of the primary standard around which the whole edifice of electrode potentials rests. We call the H H2 couple, under standard conditions, the standard hydrogen electrode (SHE). More precisely, we say that hydrogen gas at standard pressure, in equilibrium with an aqueous solution of the proton at unity activity at 298 K has a defined value of of 0 at all temperatures. Note that all other standard electrode potentials are temperature-dependent. The SHE is shown schematically in Figure 3.3, while values of Eq r are tabulated in Appendix 3. 

The SHE is chosen as the ultimate reference electrode since its value is defined. By simply making a cell in which one half cell is the SHE, then straightaway we also know the potential of the second half cell. For this reason, we say that the SHE is a reference electrode. Since all potentials are ultimately cited with respect to the SHE, the latter is the reference electrode from which all other electrode potentials are derived we say that the SHE is the primary standard. It is also called the primary reference electrode. 

As it has been shown that the Gibbs function for formation of an individual ion has no operational meanings [12], no way exists to determine such a quantity experimentally. However, for the purposes of tabulation and calculation, it is possible to separate AfGm of an electrolyte arbitrarily into two or more parts, which correspond to the number of ions formed, in a way analogous to that used in tables of standard electrode potentials. In both cases, the standard Gibbs function for formation of aqueous H" " is defined to be zero at every temperature ... 

The standard electrode potential (F ", sometimes referred to as Ef) is defined as the potential that exists when the electrode is immersed in a solution of ions at unit activity. The factor ajon, the actual ionic activity, is the activity of the depositing cation in the film of the plating bath at the cathode face. 

The reduction-oxidation potential (typically expressed in volts) of a compound or molecular entity measured with an inert metallic electrode under standard conditions against a standard reference half-cell. Any oxidation-reduction reaction, or redox reaction, can be divided into two half-reactions, one in which a chemical species undergoes oxidation and one in which another chemical species undergoes reduction. In biological systems the standard redox potential is defined at pH 7.0 versus the hydrogen electrode and partial pressure of dihydrogen of 1 bar. 

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