Applications of standard potentials

The measurement of the potential of an electrochemical cell is a convenient source of thermodynamic information on reactions. In practice the standard values (and the biological standard values) of these quantities are the ones normally determined. 

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One of the most useful applications of standard potentials is in the calculation of equilibrium constants from electrochemical data. The techniques that we develop here can be applied to any kind of reaction, including neutralization and precipitation reactions as well as redox reactions, provided that they can be expressed as the difference of two reduction half-reactions. 

Once a successful set of rules for the folding of all a proteins is available, we can turn our attention to the known mainly a, a/jS and mainly p proteins and find, from a statistical analysis of their structures, which pairs of side chains destabilize helix-helix interactions and result in jS-sheet formation (previous investigations indicate that Phe-Phe, Phe-Tyr, Glu-Arg and Glu-Lys pairs are probable candidates for helix-helix destabilizers ). The rules thus derived from all the known protein structures can then be applied to the prediction of the three dimensional fold and packing of the secondary structures of other amino acid sequences whose structures are not known, that is, to the prediction of a cursory but full three-dimensional structure of a protein, which may be further refined by the application of standard potential energy functions. 

At the temperatures of interest for SOFC applications, the standard potentials for oxidation, Go, are similar for hydrocarbon fuels and for H2 and CO, as shown in Table 1. Since Eo for H2 is more temperature dependent than the Eg for hydrocarbons, the thermodynamic advantage for hydrocarbon fuels is more apparent at higher temperatures. However, the... 

Application of a potential between reservoirs 1 (sample) and 4 (injection waste) electrokinetically pumps sample solution as indicated in Fig. 3. In this way, a geometrically defined 150 pm (90 pi) section of the separation channel can be filled [19]. If the injection potential is applied long enough to ensure that even the slowest sample component has completely filled the injection volume, a representative aliquot of sample can be analyzed (so-called volume defined injection). This is in contrast to electrokinetic sample injection in conventional capillaries, which is known to bias the sample according to the respective ionic mobilities [61]. These characteristic differences are shown schematically in Fig. 4. It should be noted that this picoliter sample injector is exclusively controlled by the application of electric fields and does not require any active elements with moving parts such as valves and external pumps. The reproducibility of the peak height of the injected sample plugs has been reported to be within 2 % RSD (relative standard deviation) and less [19,23]. 

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... 

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. 

Chapter 18 Introduction to Electrochemistry 490 Chapter 19 Applications of Standard Electrode Potentials 523 Chapter 20 Applications of Oxidation/Reduction Titrations 560 Chapter 21 Potentiometry 588... 

The most important application of electrode potentials is the prediction of the spontaneity of redox reactions. Standard electrode potentials can be used to determine the spontaneity of redox reactions in general, whether or not the reactions can take place in electrochemical cells. 

The computational procedures now used in the application of density functional theory and molecular simulation for the prediction and analysis of physisorption isotherms are based on the statistical mechanics of confined fluids [14]. These important advances are described in several chapters of this book and therefore the present introductory remarks are confined to a few general comments. Whichever computational procedure is adopted [39, 40], it is first necessary to define a 3-D model of the pore structure within a sohd of known and uniform composition [14]. It has been customary to assume that the pores of different width are aU of the same shape (e.g., slits in activated carbons). Further assumptions made by many investigators are that the filling or emptying of each group of pores can occur independently and reversibly, that the internal surface is uniform and that the solid-fluid and fluid-fluid interactions can be expressed in terms of standard potential functions [14],... 

Simultaneous application of standard sequential leaching techniques can be used for geochemical characterization of anoxic, sulfide-bearing sediments in relation to the potential mobility of critical trace metals (Kersten and Fbrstner 1991). 

Despite this ubiquitous presence of relativity, the vast majority of quantum chemical calculations involving heavy elements account for these effects only indirectly via effective core potentials (ECP) [8]. Replacing the cores of heavy atoms by a suitable potential, optionally augmented by a core polarization potential [8], allows straight-forward application of standard nonrelativistic quantum chemical methods to heavy element compounds. Restriction of a calculation to electrons of valence and sub-valence shells leads to an efficient procedure which also permits the application of more demanding electron correlation methods. On the other hand, rigorous relativistic methods based on the four-component Dirac equation require a substantial computational effort, limiting their application in conjunction with a reliable treatment of electron correlation to small molecules [9]. 

The application of standard electrode potentials is further complicated by solvation, dissociation, association. and complex-formation reactions involving the species of interest. An example of this problem is the behavior of the potential of the iron(lll)-iron(ll) couple. As noted earlier, an equimoiar mixture of these two ions in 1 M perchloric acid has an electrode potential of -f O.liZ V, Substituting hydroehloric acid of the same concentration for perchioric acid alters the observed potential to +0.700 V, and we observe a value of + 0,600 V in I M phosphoric acid, These changes in potential occur because iron(III) forms more stable complexes with chloride and phosphate ions than does iron(ll), As a result, the actual concentration of iincomplexed iron(III) in such solutions is less than that of uncomplexeci iron(U), and the net effect is a shift in the observed potential. 

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