Equilibrium constant standard electrode potentials

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 ... 

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

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)... 

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

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 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 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. 

One of the first questions one might ask about forming a metal complex is how strong is the metal ion to ligand binding In other words, what is the equilibrium constant for complex formation A consideration of thermodynamics allows us to quantify this aspect of complex formation and relate it to the electrode potential at which the complex reduces or oxidizes. This will not be the same as the electrode potential of the simple solvated metal ion and will depend on the relative values of the equilibrium constants for forming the oxidized and reduced forms of the complex. The basic thermodynamic equations which are needed here show the relationships between the standard free energy (AG ) of the reaction and the equilibrium constant (K), the heat of reaction, or standard enthalpy (A// ), the standard entropy (AS ) and the standard electrode potential (E for standard reduction of the complex (equations 5.1-5.3). 

A frequent complication is that several simultaneous equilibria must be considered (Section 3-1). Our objective is to simplify mathematical operations by suitable approximations, without loss of chemical precision. An experienced chemist with sound chemical instinct usually can handle several solution equilibria correctly. Frequently, the greatest uncertainty in equilibrium calculations is imposed not so much by the necessity to approximate as by the existence of equilibria that are unsuspected or for which quantitative data for equilibrium constants are not available. Many calculations can be based on concentrations rather than activities, a procedure justifiable on the practical grounds that values of equilibrium constants are obtained by determining equilibrium concentrations at finite ionic strengths and that extrapolated values at zero ionic strength are unavailable. Often the thermodynamic values based on activities may be less useful than the practical values determined under conditions comparable to those under which the values are used. Similarly, thermodynamically significant standard electrode potentials may be of less immediate value than formal potentials measured under actual conditions. 

It should be emphasized that many of the potentials listed in tables of standard electrode potentials are values calculated from thermodynamic data rather than obtained directly from cell emf data. As such they are valuable for calculating equilibrium constants of reactions, but caution should be exercised in using them to predict the behavior of electrodes. A steady value for an electrode potential does not necessarily represent the thermodynamic or equilibrium value. 

Using (7) the cell emf method and (2) the electrode-potential method, calculate the equilibrium constants for the following chemical reactions. (Use the values for standard electrode potentials in Table 12-1.)... 

Standard electrode potentials can be calculated from the balanced halfreaction, thermodynamic tables of AGj (to 5ueld AGj ) and Eq. (3.59). Equation (3.63) can then be used to determine the equilibrium constant for the half-reaction. In addition, the E° for a specific half-reaction can... 

Numerous applications of standard electrode potentials have been made in various aspects of electrochemistry and analytical chemistry, as well as in thermodynamics. Some of these applications will be considered here, and others will be mentioned later. Just as standard potentials which cannot be determined directly can be calculated from equilibrium constant and free energy data, so the procedure can be reversed and electrode potentials used for the evaluation, for example, of equilibrium constants which do not permit of direct experimental study. Some of the results are of analjrtical interest, as may be shown by the following illustration. Stannous salts have been employed for the reduction of ferric ions to ferrous ions in acid solution, and it is of interest to know how far this process goes toward completion. Although the solutions undoubtedly contain complex ions, particularly those involving tin, the reaction may be represented, approximately, by... 

We will use standard electrode potentials throughout the rest of this text to calculate cell potentials and equilibrium constants for redox reactions as well as to calculate data for redox titration curves. You should be aware that such calculations sometimes lead to results that are significantly different from those you would obtain in the laboratory. There are two main sources of these differences (1) the necessity of using concentrations in place of activities in the Nernst equation and (2) failure to take into account other equilibria such as dissociation, association, complex formation, and solvolysis. Measurement of electrode potentials can allow us to investigate these equilibria and determine their equilibrium constants, however. 

The application of standard electrode potential data to many systems of interest in analytical chemistry is further complicated by association, dissociation, complex formation, and solvolysis equilibria involving the species that appear in the Nemst equation. These phenomena can be taken into account only if their existence is known and appropriate equilibrium constants are available. More often than not, neither of these requirements is met and significant discrepancies arise as a consequence. For example, the presence of 1 M hydrochloric acid in the iron(Il)/iron(llI) mixture we have just discussed leads to a measured potential of + 0.70 V in 1 M sulfuric acid, a potential of -I- 0.68 V is observed and in 2 M phosphoric acid, the potential is + 0.46 V. In each of these cases, the iron(II)/iron(III) activity ratio is larger because the complexes of iron(III) with chloride, sulfate, and phosphate ions are more stable than those of iron(II) thus, the ratio of the species concentrations, [Fe ]/[Fe ], in the Nemst equation is greater than unity and the measured potential is less than the standard potential. If fomnation constants for these complexes were available, it would be possible to make appropriate corrections. Unfortunately, such data are often not available, or, if they are, they are not very reliable. 

In this equation, and represent the surface concentrations of the oxidized and reduced forms of the electroactive species, respectively k° is the standard rate constant for the heterogeneous electron transfer process at the standard potential (cm/sec) and oc is the symmetry factor, a parameter characterizing the symmetry of the energy barrier that has to be surpassed during charge transfer. In Equation (1.2), E represents the applied potential and E° is the formal electrode potential, usually close to the standard electrode potential. The difference E-E° represents the overvoltage, a measure of the extra energy imparted to the electrode beyond the equilibrium potential for the reaction. Note that the Butler-Volmer equation reduces to the Nernst equation when the current is equal to zero (i.e., under equilibrium conditions) and when the reaction is very fast (i.e., when k° tends to approach oo). The latter is the condition of reversibility (Oldham and Myland, 1994 Rolison, 1995). 

F is the Faraday constant, K is the equilibrium constant of the reaction, R is the gas constant, and T is the thermodynamic temperature. However, E jj is not the standard potential of the electrode reaction (or sometimes called half-cell reaction), which is tabulated in the tables mentioned. It is the standard potential of the reaction in a chemical cell which is equal to the standard potential of an electrode reaction (abbreviated as standard electrode potential), E when the reaction involves the oxidation of molecular hydrogen to solvated protons... 

As will be shown later (Section 9.17 and Worked Problem 9.20), the standard electrode potential is related to the equilibrium constant for the cell reaction. This has proved extremely useful for determining equilibrium constants for the redox reactions of inorganic systems and for redox reactions occurring in biological systems. 

This modified standard electrode potential then relates to the equilibrium constant K at the particular pH of the solution thus... 

The splitting of redox reactions into two half cell reactions by introducing the symbol" e , which according to Eq.(II.28) is related to the standard electrode potential, is arbitrary, but useful (this e notation does not in any way refer to solvated electrons). When calculating the equihbrium composition of a chemical system, both e , and can be chosen as components and they can be treated numerically in a similar way equilibrium constants, mass balance, etc. may be defined for both. However, while represents the hydrated proton in aqueous solution, the above equations use only the activity of e , and never the concentration of e . Concentration to activity conversions (or activity coefficients) are never needed for the electron cf. Appendix B, Example B.3). 

These equations suggest that in oxidation-reduction reactions, the relationship of chemical reactions can be expressed as standard electrode potentials or equilibrium constants. 

Since many disciplines now use pe as much as Eh to express electron activity in a system, it is worthwhile to discuss the relationships between these two variables (Lindsay, 1979). Eive decades ago the Swedish chemist Lars Gunnar Sillen suggested that the electrons (e ) can be considered as any other reactant or product in chemical reactions. Sillen and Martell (1964) tabulated equilibrium constants for redox reactions in terms of both E° (standard electrode potentials) and log K (equilibrium activity constants), and encouraged the use of log K to calculate pe values for redox systems. Like pH, the electron activity in a reaction can be defined as... 

---