Hydrogen electrode, Nernst-equation

It must not be assumed that the protection potential is numerically equal to the equilibrium potential for the iron/ferrous-ion electrode (E ). The standard equilibrium potential (E ) for iron/ferrous-ion is -0-440V (vs. the standard hydrogen electrode). If the interfacial ferrous ion concentration when corrosion ceases is approximately 10 g ions/1 then, according to the Nernst equation, the equilibrium potential (E ) is given by ... 

The formal potential of a reduction-oxidation electrode is defined as the equilibrium potential at the unit concentration ratio of the oxidized and reduced forms of the given redox system (the actual concentrations of these two forms should not be too low). If, in addition to the concentrations of the reduced and oxidized forms, the Nernst equation also contains the concentration of some other species, then this concentration must equal unity. This is mostly the concentration of hydrogen ions. If the concentration of some species appearing in the Nernst equation is not equal to unity, then it must be precisely specified and the term apparent formal potential is then employed to designate the potential of this electrode. 

The purpose of the silver-silver chloride combination is to prevent the potential that develops from changing due to possible changes in the interior of the electrode. The potential that develops is a membrane potential. Since the glass membrane at the tip is thin, a potential develops due to the fact that the chemical composition inside is different from the chemical composition outside. Specifically, it is the difference in the concentration of the hydrogen ions on opposite sides of the membrane that causes the potential—the membrane potential—to develop. There is no half-cell reaction involved. The Nernst equation is... 

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 on the left of the junction (jj) is the standard hydrogen electrode (SHE), the potential of which is defined as zero at all temperatures. p° is the standard pressure and is equal to 105 Pa (lbar) by the IUPAC recommendation (1982). The liquid junction potential at jj is kept negligible by an appropriate salt bridge. The potential of the electrode on the right of the junction is expressed by the Nernst equation ... 

The values of the standard emf in eqs 2.24 and 2.24 are slightly different.) Since a half-reaction represents a cell involving a standard hydrogen electrode, the Nernst equation may also be applied to electrode potentials. Thus for the half-reaction... 

One important application of the Nernst equation is the measurement of pH (and, through pH, acidity constants). The pH of a solution can be measured electrochemically with a device called a pH meter. The technique makes use of a cell in which one electrode is sensitive to the H30+ concentration and the second electrode serves as a reference. An electrode sensitive to the concentration of a particular ion is called an ion-selective electrode. One combination is a hydrogen electrode connected through a salt bridge to a calomel electrode. The reduction half-reaction for the calomel electrode is... 

The electrochemical determination of pH using a pH meter is a particularly important application of the Nernst equation. Consider, for example, a cell with a hydrogen electrode as the anode and a second reference electrode as the cathode ... 

First, read the shorthand notation to obtain the cell reaction. Then, calculate the halfcell potential for the hydrogen electrode from the observed cell potential and the halfcell potential for the calomel reference electrode. Finally, apply the Nernst equation to... 

The potential of this electrode is defined (Section 5.2) as the voltage of the cell Pt H2(l atm) H+(<2 = 1) MZ+ M, where the left-hand electrode, Et = 0, is the normal hydrogen reference electrode (described in Section 5.6). We will derive the Nernst equation on the basis of the electrochemical kinetics in Chapter 6. Here we will use a simplified approach and consider that Eq. (5.9) can be used to determine the potential E of the M/Mz+ electrode as a function of the activity of the products and reactants in the equilibrium equation (5.10). Since in reaction (5.10) there are two reactants, Mz+ and e, and only one product of reaction, M, Eq. (5.9) yields... 

The potential of a glass electrode is given by a form of the Nernst equation very similar to that of an ordinary hydrogen electrode, but of course without the H2 ... 

The Nernst equation relates the activities of the species involved with the electrode potential, E, of the half-reaction and its standard electrode potential, which is the value of the potential relative to the standard hydrogen electrode when the activities of all species are unity. For the generic half-reaction... 

Measurements can be done using the technique of redox potentiometry. In experiments of this type, mitochondria are incubated anaerobically in the presence of a reference electrode [for example, a hydrogen electrode (Chap. 10)] and a platinum electrode and with secondary redox mediators. These mediators form redox pairs with Ea values intermediate between the reference electrode and the electron-transport-chain component of interest they permit rapid equilibration of electrons between the electrode and the electron-transport-chain component. The experimental system is allowed to reach equilibrium at a particular E value. This value can then be changed by addition of a reducing agent (such as reduced ascorbate or NADH), and the relationship between E and the levels of oxidized and reduced electron-transport-chain components is measured. The 0 values can then be calculated using the Nernst equation (Chap. 10) ... 

Formal potential — Symbol Efr (SI Unit V), has been introduced in order to replace the standard potential of -> cell reaction when the values of - activity coefficients of the species involved in the cell reaction are unknown, and therefore concentrations used in the equation expressing the composition dependence of ceii instead of activities. It also involves the activity effect regarding the -+ standard hydrogen electrode, consequently in this way the formal electrode potential is also defined. Formal potentials are similar to conditional (apparent) equilibrium constants (-> equilibrium constant), in that, beside the effect of the activity coefficients, side reaction equilibria are also considered if those are not known or too complex to be taken into account. It follows that when the logarithmic term which contains the ratio of concentrations in the -> Nernst... 

Fortunately, glass electrodes have wide applicability in solvents other than water. Even in a solvent as different from water as acetonitrile, glass electrodes respond reversibly to changes in hydrogen ion activity, in agreement with the Nernst equation. In setting up pH values for reference buffers, it is not always possible to use internal reference electrodes without liquid junction. For example, Ag-AgX electrodes are unstable in acetonitrile owing to slow formation of species of the type Ag X +j. When external reference electrodes must be substituted, the reliability of the measurements is reduced because uncertainties in the liquid junction are always present. 

Most pH determinations are made by electrometric methods, the pH of the unkown solution (X) being calculated from that of a known standard (S) and the emf ( x and s) of a cell composed of a hydrogen ion-responsive electrode (for example, a glass electrode or a hydrogen gas electrode) coupled with a reference electrode (calomel, silver-silver chloride). This cell is filled successively with the standard solution S and with the unknown solution X. A liquid junction potential j exists where these solutions make contact with the concentrated KCl solution of the reference electrode. From the Nernst equation for the cell reactions and assuming an ideal hydrogen ion response ... 

An important application of the Nernst equation -> Utilizes a galvanic cell containing an electrode sensitive to the concentration of the ion -> A calomel electrode connected by a salt bridge to a hydrogen electrode ... 

The electrode potential (reduction potential) for a redox couple is defined as the couple s potential measured with respect to the standard hydrogen electrode, which is set equal to zero (see hydrogen electrode later). This potential, by convention, is the electromotive force of a cell, where the standard hydrogen electrode is the reference electrode (left electrode) and the given half-cell is the indicator electrode (right electrode). The reduction potential for a given redox couple is given by the Nernst equation ... 

Formal potentials are empirically derived potentials that compensate for the types of activity and competing equilibria effects that we have just described. The formal potential of a system is the potential of the half-cell with respect to the standard hydrogen electrode measured under conditions such that the ratio of analytical concentrations of reactants and products as they appear in the Nernst equation is exactly unity and the concentrations of other species in the system are all carefully specified. For example, the formal potential for the half-reaction... 

A higher polarization curve when cell operating pressure is increased can be expected on the base of the Nernst equation (3.15), but the concomitant increase of / o, due to the higher concentration of reactant gases on electrodes, with the consequent improvement of the hydrogen/oxygen reaction rate, has to be also considered [34]. 

Nernst equations may also be written for the equilibria (9.2.4) and (9.2.5). These equations are written in terms of the EMF of a cell containing the electrode in question and a standard hydrogen electode (SHE). The latter is a defined point of reference which is obtained when a hydrogen electrode is operated with a H2 pressure of 1 bar and unit H" " activity in the electrolyte solution. On this basis the Nernst equation for the hydrogen electrode is... 

The consequence of all these effects is that oxygen, or hydrogen, evolution reactions follow quite different kinetics than would be expected from thermodynamical considerations. For example, oxygen evolution on a platinum electrode starts at a potential significantly higher than that predicted by the Nernst equation. The reason for this is the formation of surface oxide and its associated dynamics as elucidated, besides others, by B. Conway [4]. 

The Nernst equation may be applied to this electrode (relative to a standard hydrogen electrode) as before ... 

The redox potential (ORP) for a single redox couple is related to the activities of species in solution through the Nernst equation (7) which has the limitations inherent in any thermodynamic relationship. If a measured ORP (corrected to the standard hydrogen electrode, SHE) corresponds to one computed from the experimental activities of a particular redox couple, electrode behavior is said to be nernstian with respect to that couple. 

This general relationship was first given in 1889 by the German physical chemist Walter H. Nernst (1864-1941), and is known as the Nernst equation. Equation (8.13) is a simple form of it, applicable to a cell in which one electrode is the standard hydrogen electrode. 

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