Equilibrium standard electrode potentials

If both electrode processes operate under standard conditions, this voltage is E°, the equilibrium standard electrode potential difference. Values of E and E° may be conveniently measured with electrometers of so large an internal resistance that the current flow is nearly zero. Figure 3.1.6 illustrates the measurement and the equilibrium state. The value of E° is a most significant quantity characterizing the thermodynamics of an electrochemical cell. Various important features of E and E° will be addressed in the following chapters. 

The standard electrode potentials , or the standard chemical potentials /X , may be used to calculate the free energy decrease —AG and the equilibrium constant /T of a corrosion reaction (see Appendix 20.2). Any corrosion reaction in aqueous solution must involve oxidation of the metal and reduction of a species in solution (an electron acceptor) with consequent electron transfer between the two reactants. Thus the corrosion of zinc ( In +zzn = —0-76 V) in a reducing acid of pH = 4 (a = 10 ) may be represented by the reaction ... 

The equilibrium potentials and E, can be calculated from the standard electrode potentials of the H /Hj and M/M " " equilibria taking into account the pH and although the pH may be determined an arbitrary value must be used for the activity of metal ions, and 0 1 = 1 is not unreasonable when the metal is corroding actively, since it is the activity in the diffusion layer rather than that in the bulk solution that is significant. From these data it is possible to construct an Evans diagram for the corrosion of a single metal in an acid solution, and a similar approach may be adopted when dissolved O2 or another oxidant is the cathode reactant. 

The values in Table 2.16 show how the potentials obtained under service conditions differ from the standard electrode potentials which are frequently calculated from thermodynamic data. Thus aluminium, which is normally coated with an oxide film, has a more noble value than the equilibrium potential 3 + / = — 1-66V vs. S.H.E. and similar considerations apply to passive stainless steel (see Chapter 21). 

Equations 20.176 and 20.179 emphasise the essentially thermodynamic nature of the standard equilibrium e.m.f. of a cell or the standard equilibrium potential of a half-reaction E, which may be evaluated directly from e.m.f. meeisurements of a reversible cell or indirectly from AG , which in turn must be evaluated from the enthalpy of the reaction and the entropies of the species involved (see equation 20.147). Thus for the equilibrium Cu -)-2e Cu, the standard electrode potential u2+/cu> hence can be determined by an e.m.f. method by harnessing the reaction... 

Thus the equilibrium constant K can be evaluated from standard electrode potential or from the standard chemical potentials x . 

Standard Electrode Potential (E ) the equilibrium potential of an electrode reaction when the components are ail in their standard states. 

It must be emphasised that standard electrode potential values relate to an equilibrium condition between the metal electrode and the solution. Potentials determined under, or calculated for, such conditions are often referred to as reversible electrode potentials , and it must be remembered that the Nernst equation is only strictly applicable under such conditions. 

During the determination of standard electrode potentials an electrochemical equilibrium must always exist at the phase boundaries, e.g. that of the elec-trode/electrolyte. From a macroscopic viewpoint no external current flows and no reaction takes place. From a microscopic viewpoint or a molecular scale, a continuous exchange of charges occurs at the phase boundaries. In this context Fig. 6 demonstrates this fact at the anode of the Daniell element. 

In the introductory chapter we stated that the formation of chemical compounds with the metal ion in a variety of formal oxidation states is a characteristic of transition metals. We also saw in Chapter 8 how we may quantify the thermodynamic stability of a coordination compound in terms of the stability constant K. It is convenient to be able to assess the relative ease by which a metal is transformed from one oxidation state to another, and you will recall that the standard electrode potential, E , is a convenient measure of this. Remember that the standard free energy change for a reaction, AG , is related both to the equilibrium constant (Eq. 9.1)... 

The standard electrode potential of reaction (15.20) calculated thermodynamically is 1.229 V (SHE) at 25°C. For reachons (15.21) and (15.22), these values are 0.682 and 1.776 V, respechvely. The equihbrium potenhals of all these reactions have the same pH dependence as the potential of the reversible hydrogen electrode therefore, on the scale of potentials (against the RHE), these equilibrium potenhals are... 

The standard electrode potential of this reaction is 1.358 V vs. SHE the equilibrium potential is independent of solution pH. 

The standard electrode potential [1] of an electrochemical reaction is commonly measured with respect to the standard hydrogen electrode (SHE) [2], and the corresponding values have been compiled in tables. The choice of this reference is completely arbitrary, and it is natural to look for an absolute standard such as the vacuum level, which is commonly used in other branches of physics and chemistry. To see how this can be done, let us first consider two metals, I and II, of different chemical composition and different work functions 4>i and 4>ii-When the two metals are brought into contact, their Fermi levels must become equal. Hence electrons flow from the metal with the lower work function to that with the higher one, so that a small dipole layer is established at the contact, which gives rise to a difference in the outer potentials of the two phases (see Fig. 2.2). No work is required to transfer an electron from metal I to metal II, since the two systems are in equilibrium. This enables us calculate the outer potential difference between the two metals in the following way. We first take an electron from the Fermi level Ep of metal I to a point in the vacuum just outside metal I. The work required for this is the work function i of metal I. 

Standard electrode potential is the potential developed by an active electrode when in equilibrium with a molar solution of its ions. 

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. 

Having revised a few basic electrochemical ideas, such as the nature of reference electrodes, the standard hydrogen electrode and the scale based on it, we next looked briefly at thermodynamic parameters such as the electrode potential E, the standard electrode potential f and emf, and then discussed how AG, AH and AS (where the prime indicates a frustrated cell equilibrium ) may be determined. 

Table 7.1 Standard Electrode Potentials and Equilibrium Constants for Some Reduction Half-Reactions. ...

Thus, the overall reaction [Eq. (8.2)] is the outcome of the combination of two different partial reactions, Eqs. (8.4) and (8.5). As mentioned above, these two partial reactions, however, occur at one electrode, the same metal-solution interphase. The equilibrium (rest) potential of the reducing agent, E eq,Red [Eq. (8.5)] must be more negative than that of the metal electrode, E eq,M [Eq. (8.4)], so that the reducing agent Red can function as an electron donor and as an electron acceptor. This is in accord with the discussion in Section 5.7 on standard electrode potentials. 

However, silicon material in an aqueous solution is not a system in equilibrium. It is considered as a mixed system containing two redox couples with standard electrode potentials Ei and Ei separated by a wide interval. Then Eq. (13) must be modified to account for both components ... 

To avoid cumbersome notation, it is taken for granted that the standard electrode potential is an equilibrium potential and that therefore one can write E° instead of... 

The most important thing about Equations 17-6 and 17-7 is that the equilibrium constant for electron-transfer reactions can be calculated from standard electrode potentials without ever having to make experimental measurements. 

The predictive value of standard electrode potentials is nicely illustrated following Bard and Faulkner (an excellent source of fundamental theory) in Figure 2.4 As the potential of the Pt or Hg electrode is moved from its equilibrium (zero current) value to more negative potentials, the species of more positive E° should be reduced first. This prediction is verified for the Pt electrode, but Cr3+ is reduced before H+ for the Hg electrode. 

This equation has a standard electrode potential of -0.447 V. Thus, the solution containing mercuric and chloride ions in contact with iron forms a battery. The reduction of the complex ions to metallic mercury is the cathodic reaction. The dissolution of iron is the anodic reaction. The overall reaction in the battery is given by the addition of Equation (13.42) and Equation (13.43). Due to the high value of its reversible cell voltage under standard conditions (0.85 V), it is expected that a very low equilibrium concentration of the complex ion can be achieved. 

The SOFC consists of cathode, electrolyte and anode collectively referred to as the PEN - positive electrode, electrolyte, negative electrode. A single cell operated with hydrogen and oxygen provides at equilibrium a theoretical reversible (Nernst) or open circuit voltage (OCV) of 1.229 V at standard conditions (STP, T = 273.15 K. i> = 1 atm). With the standard electrode potential E°, universal gas constant R. temperature T. Faraday s constant F, molar concentration x and pressure p, the OCV is given by... 

The free energies in (18) are illustrated in Fig. 10. It can be seen that GA is that part of AG ° available for driving the actual reaction. The importance of this relation is that it allows AGXX Y to be calculated from the properties of the X and Y systems. In thermodynamics, from a list of n standard electrode potentials for half cells, one can calculate j (m — 1) different equilibrium constants. Equation (18) allows one to do the same for the %n(n— 1) rate constants for the cross reactions, providing that the thermodynamics and the free energies of activation for the symmetrical reactions are known. Using the... 

The following table lists the standard electrode potentials (in V) of some electrodes of the first kind.1-3 These are divided into cationic and anionic electrodes. In cationic electrodes, equilibrium is established between atoms or molecules of the substance and the corresponding cations in solution. Examples include metal, amalgam, and the hydrogen electrode. In anionic electrodes, equilibrium is achieved between molecules and the corresponding anions in solution. The potential of the electrode is given by the Nemst equation in the form... 

The following table lists the standard electrode potentials (in V) of some electrodes of the second kind.13 These consist of three phases. The metal is covered by a layer of its sparingly soluble salt and is immersed in a solution of a soluble salt of the anion. Equilibrium is established between the metal atoms and the solution anions through two partial equilibria one between the metal and its cation in the sparingly soluble salt and the other between the anion in the solid phase of the sparingly soluble salt and the anion in solution. The silver chloride electrode is preferred for precise measurements. 

For half-reactions at equilibrium, the potential, Ey can be related to the standard electrode potential through the Nernst equation... 

The thermodynamic information is normally summarized in a Pourbaix diagram7. These diagrams are constructed from the relevant standard electrode potential values and equilibrium constants and show, for a given metal and as a function of pH, which is the most stable species at a particular potential and pH value. The ionic activity in solution affects the position of the boundaries between immunity, corrosion, and passivation zones. Normally ionic activity values of 10 6 are employed for boundary definition above this value corrosion is assumed to occur. Pourbaix diagrams for many metals are to be found in Ref. 7. 

A standard electrode potential series consists of equilibrium potentials, not corrosion potentials as you have been measuring in this laboratory. These potentials are usually referenced to NHE but could be referenced to any reference electrode system. How would you convert a standard electrode potential series from Vnhe to Vsce ... 

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