Standard electrode potential equilibrium constants from

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)... 

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 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. 

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. 

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. 

To derive a general relationship for computing equilibrium constants from standard-potential data, consider a reaction in which a species A d reacts with a species to yield and B d- The two electrode reactions are... 

EXERCISE 20.12 Calculate the equilibrium constant for the following reaction from standard electrode potentials. 

When a biochemical half-reaction involves the production or consumption of hydrogen ions, the electrode potential depends on the pH. When reactants are weak acids or bases, the pH dependence may be complicated, but this dependence can be calculated if the pKs of both the oxidized and reduced reactants are known. Standard apparent reduction potentials E ° have been determined for a number of oxidation-reduction reactions of biochemical interest at various pH values, but the E ° values for many more biochemical reactions can be calculated from ArG ° values of reactants from the measured apparent equilibrium constants K. Some biochemical redox reactions can be studied potentiometrically, but often reversibility cannot be obtained. Therefore a great deal of the information on reduction potentials in this chapter has come from measurements of apparent equilibrium constants. 

The third largest class of enzymes is the oxidoreductases, which transfer electrons. Oxidoreductase reactions are different from other reactions in that they can be divided into two or more half reactions. Usually there are only two half reactions, but the methane monooxygenase reaction can be divided into three "half reactions." Each chemical half reaction makes an independent contribution to the equilibrium constant E for a chemical redox reaction. For chemical reactions the standard reduction potentials ° can be determined for half reactions by using electrochemical cells, and these measurements have provided most of the information on standard chemical thermodynamic properties of ions. This research has been restricted to rather simple reactions for which electrode reactions are reversible on platinized platinum or other metal electrodes. 

When the pH is specified, each biochemical half reaction makes an independent contribution to the apparent equilibrium constant K for the reaction written in terms of reactants rather than species. The studies of electochemical cells have played an important role in the development of biochemical thermodynamics, as indicated by the outstanding studies by W. Mansfield Clarke (1). The main source of tables of ° values for biochemical half reactions has been those of Segel (2). Although standard apparent reduction potentials ° can be measured for some half reactions of biochemical interest, their direct determination is usually not feasible because of the lack of reversibility of the electrode reactions. However, standard apparent reduction potentials can be calculated from for oxidoreductase reactions. Goldberg and coworkers (3) have compiled and evaluated the experimental determinations of apparent equilibrium constants and standard transformed enthalpies of oxidoreductase reactions, and their tables have made it possible to calculate ° values for about 60 half reactions as functions of pH and ionic strength at 298.15 K (4-8). 

Another important use of standard potentials is for the determination of sdubility products, for these are essentially equilibrium constants ( 39j). If M Al, is a sparingly solvble salt, a knowledge of the standard potentials of the electrodes M, M, A, (s), A - and M, M + permits the solubility product to be evaluated. A simple example is provided by silver chloride Ifor which the standard (oxidation) potential of the Ag, AgCl( ), Cl electrode is known to be — 0.2224 volt at 25 C. The activity of the chloride ion in the standard electrode is unity, and hence the silver ion activity must be equal to the solubility product of silver chloride. The value of Oa may be derived from equation (45.13), utilizing the standard potential of silver thus Eu i — 0.22 volt, E for silver is — 0.799, and z is 1, so that at 25 C,... 

Since the values of equilibrium constants are obtained from the standard half-cell potentials, the method of obtaining the S° of a half-cell has great importance. Suppose we wish to determine the of the silver-silver ion electrode. Then we set up a cell that includes this electrode and another electrode the potential of which is known for simplicity we choose the SHE as the other electrode. Then the cell is... 

From the basic parameters initial concentration of ions, their standard transfer potential, distribution coefficients for neutral components, equilibrium constants of reactions taking place in the system, volume of phases, and temperature, a unique general problem for the Galvani potential difference and distribution concentration of all components was established. A numerical solution to the problem with the help of computer program EXTRA.FIFIl provided a good means for quantitative investigation of the liquid-liquid interface. It is also useful for the study of liquid-liquid extraction, electroextraction, voltammetry at interface of two immiscible electrolyte solutions (ITIES) [15,18], liquid-liquid membrane ion-selective electrodes, biomembrane transport, and other fields of science and engineering. 

Lipoi( acid is rediunblo at the dropping mercury electrode (Reed et al., 1953a Ke, 1957). The half-wave potential at pH 7.0 is —0.567 volt versus the saturated calomel electrode (Ke, 1957). This value corresponds to a reduction potential of —0.325 volt with respect to the standard hydrogen electrode. The reduction potential of the dihydrolipoic acid-lipoic acid system has been calculated from the equilibrium constant of the dihydro-... 

When one wants to calculate the equilibrium constant of reaction (1.2.3) from the standard potentials of the system hexacyanoferrate(II/III) and 2H" /H2, it is essential that one writes this equation with the oxidized form of the system and hydrogen on the left side and the reduced form and protons on the right side. Only then does the sign convention hold true and Eq. (1.2.13) yields the equilibrium constant for the reaction when the tabulated standard potentials are used. Note also that the standard potential of the hydrogen electrode is 0 V for the reaction written as 2H+ - - 2e H2, or written as H+ - - e 1 2- Table 1.2.1 gives a compilation of standard potentials of electrode reactions. (Standard potentials are available from many different sources [2].) Although only single redox couples are listed, the standard potentials of each system always refer to the reaction ... 

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