Equilibrium constant calculated from electrode potentials

According to C Hj yield and concentrations of the four components, the equilibrium constant of the reaction in Scheme 2.6 was determined as 4 X 10 . The value calculated from the potential difference was 4.4 X 10. Consequently, there is a coincidence between the calculated equilibrium constant based on the electrode potentials and the equilibrium constant determined from the liquid-phase experiment. 

Calculation of equilibrium constant from electrode potentials of the halfreactions The two half-reactions involved in the chemical reaction (12-37) are... 

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. 

Polarography is valuable not only for studies of reactions which take place in the bulk of the solution, but also for the determination of both equilibrium and rate constants of fast reactions that occur in the vicinity of the electrode. Nevertheless, the study of kinetics is practically restricted to the study of reversible reactions, whereas in bulk reactions irreversible processes can also be followed. The study of fast reactions is in principle a perturbation method the system is displaced from equilibrium by electrolysis and the re-establishment of equilibrium is followed. Methodologically, the approach is also different for rapidly established equilibria the shift of the half-wave potential is followed to obtain approximate information on the value of the equilibrium constant. The rate constants of reactions in the vicinity of the electrode surface can be determined for such reactions in which the re-establishment of the equilibria is fast and comparable with the drop-time (3 s) but not for extremely fast reactions. For the calculation, it is important to measure the value of the limiting current ( ) under conditions when the reestablishment of the equilibrium is not extremely fast, and to measure the diffusion current (id) under conditions when the chemical reaction is extremely fast finally, it is important to have access to a value of the equilibrium constant measured by an independent method. 

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... 

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. 

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). 

In many calculations the hydrogen ion concentration is more accessible than the activity. For example, the electroneutrality condition is written in terms of concentrations rather than activities. Also, from stoichiometric considerations, the concentrations of solution components are often directly available. Therefore, the hydrogen ion concentration is most readily calculated from equilibrium constants written in terms of concentration. When a comparison of hydrogen ion concentrations with measured pH values is required (in calculation of equilibrium constants, for example), an estimate of the hydrogen ion activity coeflScient can be made by application of the Debye-Huckel theory if necessary, an estimate of liquid-junction potentials also can be made. Alternatively, the glass electrode can be calibrated with solutions of known hydrogen ion concentration and constant ionic strength. " ... 

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. 

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 ... 

Fig. II.1.25 (a) Schematic representation of the transfer of anion from the aqueous into the organic phase upon oxidation of Mn(II)TPP to Mn(III)TPP . (b) In the presence of the boronic acid B as a facilitator the tiansfer of the anion A leads to the formation of the complex AB in the oiganic phase, (c) Cyclic voltammograms [120] (scan rate 10 mVs ) for the oxidation and le-ieduction of 75 mM Mn(II)TPP dissolved in PPP (4-(3-phenylpropyl)-pyridine, 75 nL) and immobilised in the form of microdroplets onto a 4.9-mm diameter graphite electrode immersed in aqueous 0.1 M sodium lactate pH = 7.34. The presence of (i) 0 and (ii) 973 mM naphthyl-2-borDnic add is shown to cause a negative shift in the voltammetric response, (d) Plot of the midpoint potential versus the natural logarithm of the naphthyl-2-boronic add concentration in the microdroplets. Lines indicate calculated data [120] for reversible lactate-4)oronic add complex formation for three equilibrium constants...

The generally accepted formal potential, E°, of the NAD+/NADH redox couple at pH 7.0 (25 °C) is —315 mV versus normal hydrogen electrode (NHE)(—560 mV vs. saturated calomel electrode (SCE) [23, 24). From thermal data and the equilibrium constants of the ethanol/acetaldehyde and 2-propanol/acetone reactions catalyzed by alcohol dehydrogenase, a value of —320 mV was calculated, which was later recalculated to be —315 5 mV versus NHE by Clark [23]. Through direct potentiometric titrations using several different mediators and xanthine oxidase as catalyst, Rodkey [25, 26] obtained an E° value of —311 mV versus NHE (25 °C) and a temperature variation of the E° of —1.31 mV/ C in the range of 20 to 40 °C. A variation of the E° with pH of —30.3 mV/pH (30 C) was found, which... 

In this method, [37] an electrode at equilibrium is polarized by a small shift of potential, thus keeping a constant concentration of inserted atoms on the surface of the electrode. The DC can be calculated from the registered current-versus-time curve called chronoamperogram. The method is also called single-step chrono-amperometry (SSCAM). In this method, the condition D const is under better control than in the GSPM. 

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

This equation was used when calculating potentials of the first and second kind of electrodes (Figure 2.12). In the first case, [Cu ] was obtained from the constant K=6x 10 M at the equilibrium... 

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