Half-cell potential, definition

Because the standard-state half-cell potential, , is measured relative to the zero potential of the hydrogen half-cell, = El, and the definition of " given by equation 7.27 is substituted into equation 7.22 to give... 

Erhe andELHE are equilibrium half-cell potentials, or electrode potentials, which depend in sign on the definitions of positive and negative electricity and assignment of Eu + = 0 at standard condi-... 

The cathode consists of platinum which is an inert conductor in contact with the 1 M ions surrounded by hydrogen gas at 1 atm. Such an electrode is called a standard hydrogen electrode which per definition has a half cell potential (symbolised at 298 K by the symbol of s°) of 0.00 volt. The figure below shows the principle in the build up of the standard hydrogen electrode. 

The standard hydrogen electrode has per definition a half cell potential of 0.0 Volt at a Tf concentration of 1,0 M. 

Epoxy coated rebars present particular problems to determining the corrosion condition of the steel. In the first place the bars are electrically isolated from the concrete except at areas of damage. The sizes and locations of the areas of damage are obviously unknown. Attempts to carry out half cell potential surveys and linear polarization measurements have therefore been unable to come up with definitive criteria for corroding and non-corroding areas. The other problem is that the bars are isolated from each other so a connection must be made to each bar measured to be sure that contact is being made. 

One definition of effective cathodic protection is to depress the potential of the cathodes to the level of the anodes, thus stopping current from flowing between anodic and cathodic areas (Mears and Brown, 1938). This works because cathodes are more easily polarized (potential shifted) than anodes. We saw this phenomenon in Section 4.11 where the effect of an external current on the half cell potential allows us to calculate the corrosion rate. 

Zn + 2HC1 ZnCl2 + H2 The series is based on ELECTRODE POTENTIALS, which measure the tendency of elements to form positive ions. The series is one of increasing electrode potential for half cells of the type M IM. Thus, copper (E" " for Cu +ICu = + 0.34 V) is lower than zinc (E" " for Zn IZn = -0.76V). The hydrogen half cell by definition has the value E = 0. 

The most widely used reference electrode, due to its ease of preparation and constancy of potential, is the calomel electrode. A calomel half-cell is one in which mercury and calomel [mercury(I) chloride] are covered with potassium chloride solution of definite concentration this may be 0.1 M, 1M, or saturated. These electrodes are referred to as the decimolar, the molar and the saturated calomel electrode (S.C.E.) and have the potentials, relative to the standard hydrogen electrode at 25 °C, of 0.3358,0.2824 and 0.2444 volt. Of these electrodes the S.C.E. is most commonly used, largely because of the suppressive effect of saturated potassium chloride solution on liquid junction potentials. However, this electrode suffers from the drawback that its potential varies rapidly with alteration in temperature owing to changes in the solubility of potassium chloride, and restoration of a stable potential may be slow owing to the disturbance of the calomel-potassium chloride equilibrium. The potentials of the decimolar and molar electrodes are less affected by change in temperature and are to be preferred in cases where accurate values of electrode potentials are required. The electrode reaction is... 

It is very often necessary to characterize the redox properties of a given system with unknown activity coefficients in a state far from standard conditions. For this purpose, formal (solution with unit concentrations of all the species appearing in the Nernst equation its value depends on the overall composition of the solution. If the solution also contains additional species that do not appear in the Nernst equation (indifferent electrolyte, buffer components, etc.), their concentrations must be precisely specified in the formal potential data. The formal potential, denoted as E0, is best characterized by an expression in parentheses, giving both the half-cell reaction and the composition of the medium, for example E0,(Zn2+ + 2e = Zn, 10-3M H2S04). 

In Equation (18b), the activity quotient is separated into the terms relating to the silver electrode and the hydrogen electrode. We assume that both electrodes (Ag+/Ag and H+/H2) operate under the standard condition (i.e. the H+/H2 electrode of our cell happens to constitute the SHE). This means that the equilibrium voltage of the cell of Figure 3.1.6 is identical with the half-cell equilibrium potential E°(Ag+l Ag) = 0.80 V. Furthermore, we note that the activity of the element silver is per definition unity. As the stoichiometric number of electrons transferred is one, the Nemst equation for the Ag+/Ag electrode can be formulated in the following convenient and standard way ... 

The foregoing example illustrates how equilibrium constants for overall cell reactions can be determined electrochemically. Although the example dealt with redox equilibrium, related procedures can be used to measure the solubility product constants of sparingly soluble ionic compounds or the ionization constants of weak acids and bases. Suppose that the solubility product constant of AgCl is to be determined by means of an electrochemical cell. One half-cell contains solid AgCl and Ag metal in equilibrium with a known concentration of CP (aq) (established with 0.00100 M NaCl, for example) so that an unknown but definite concentration of Kg aq) is present. A silver electrode is used so that the half-cell reaction involved is either the reduction of Ag (aq) or the oxidation of Ag. This is, in effect, an Ag" Ag half-cell whose potential is to be determined. The second half-cell can be any whose potential is accurately known, and its choice is a matter of convenience. In the following example, the second half-cell is a standard H30" H2 half-cell. 

As already discussed, the standard hydrogen electrode (SHE) is the chosen reference half-cell upon which tables of standard electrode potentials are based. The potential of this system is zero by definition at all temperatures. Although this reference electrode was often used in early work in electrochemistry, it is almost never seen in chemical laboratories at the present time. It is simply too awkward to use because of the requirement for H2 gas at 1 bar pressure and safety considerations. 

Table 19.1 lists standard reduction potentials for a number of half-cell reactions. By definition, the SHE has an E° value of 0.00 V. Above the SHE the negative standard reduction potentials increase, and below it the positive standard reduction potentials increase. It is important to know the following points about the table ... 

This electrical work is by definition (Chapter 5) the AG associated with the process, as long as the electrical work is the only non-PAV work done. Therefore for any half-cell or complete cell or indeed any electrostatic process in which nT coulombs are moved through a potential difference ,... 

Equation (18.16) could also be considered to represent a half-cell reaction, except that the electron is not shown. If you have followed our discussion of the single-ion and SHE conventions, you will not be surprised to leam that it does not matter what value the chemical potential of the electron is considered to have because it always cancels out in balanced reactions, and that by convention it is given the value zero. This means that the Nemst equation applies to half-cell reactions as well as cell reactiohs, as do equations (18.15). And if you have followed all this, you now know what Eh is, because (18.17) when applied to half-cells is the definition of Eh. Thus... 

In this figure, Ihc half-cell on the right consists of a strip of the metal M in contact with a solution of M . The half-cell on the left is a SHE. By definition, the potential E observed on the voltmeter is the electrode potential for the M /M couple. In this general example, we assume that the junction potentials across the salt... 

The total voltage developed under standard conditions is -1-0.76 V. But the voltage of the SHE is 0 by definition therefore the standard reduction potential of the Zn half-cell is ... 

Equation (5) or (11) can be applied directly to half-cell reactions such as (6) and (7) and the resulting potentials obtained will be identical to those obtained from the overall reactions (9) and (10) because of the definition of the SHE as the universal standard. A selection of standard potentials of half-cell reactions is shown in Table 1 [5]. By international convention, electrode reactions in thermodynamic tables are always written as reduction reactions, so the more noble metals have a positive standard potential. Lists such as that in Table 1 are also called electromotive force series or tables of standard reduction potentials. 

Any cell reaction can be considered to be an electron transfer between two coupled half-cells. The measured potential corresponds to the difference of the electron energy. The arbitrary definition of a reference electrode raises the question of whether the electrochemical potential scale can be correlated with energy scales of electrons in surface physics. If measuring work functions or electron affinities, the reference value is the free electron in vacuum. Mehl and Lohmann calculated for the electron affinity of a hydrogen electrode —4.5 eV using the following Bom-Haber process... 

By definition, the potential of a redox couple vs SHE is the emf of the Active electrochemical cell, whereby the working electrode is in the half-cell involving the redox couple in question. The counter-electrode is the standard hydrogen electrode at the same temperature. The terminals are made of the same metals and the sum of the possible ionic junction voltages are considered to be equal to zero. In this case we therefore have E,she =... 

Definition of the electrochenncal window I2Q Potential range of non-electroactivity of a half-cell when only the solvent and the supporting electrolyte are in contact with a given electrode it is also called the redox stability window of this half-cell... 

The two-half cells contain the aqueous substrate. The mixed monolayers are spread onto the surface of one of the two-hetlf cells. Two "identical" 24lAm 0.7 mCi ionizing electrodes, purchased from the Radiochemical Center Amersham (U.K.), are placed above the hedf cells close to the substrate surface. The difference in electric potenticd of the two electrodes is measured with a high impedence electrometer. By definition this difference is equal to the surface potentietl AV of the monolayer located on the surface on one of the two-hedf cells. The surface potential AV is measured as a function of the spread monolayer molecular area a for each one of the mixed film compositions as above (see surface pressure studies). 

In cells where the reduced form is the metal, for example, in the Cu/Cu + half-cell, [red] = 1 because pure metals such as Cu have unit activity. There is the equivalent definition of formal potential for each half-cell. 

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