Reduction potential, Nernst equation

Redox reactions Oxidation states Reduction potentials Nernst equation Disproportionation Potential diagrams Frost-Ebsworth diagrams... 

Note, again, that the Nernst equations for both E and Ta are written for reduction reactions. The cell potential, therefore, is... 

The potential needed for a quantitative reduction of Cu + can be calculated using the Nernst equation... 

The difference between the potential actually required to initiate an oxidation or reduction reaction, and the potential predicted by the Nernst equation. 

The free energy changes of the outer shell upon reduction, AG° , are important, because the Nernst equation relates the redox potential to AG. Eree energy simulation methods are discussed in Chapter 9. Here, the free energy change of interest is for the reaction... 

The oxidation and reduction should be reversible. At a potential E the ratio of the concentrations of the two forms is given by the Nernst equation ... 

In agreement with the theory of electrolysis, treated in Sections 3.1 and 3.2, the parts of the residual current and the limiting current are clearly shown by the nature of the polarographic waves because for the cathodic reduction of Cd2+ and Zn2+ at the dme we have to deal with rapid electron transfer and limited diffusion of the cations from the solution towards the electrode surface and of the metal amalgam formed thereon towards the inside of the Hg drop, we may conclude that the half-wave potential, Eh, is constant [cf., Fig. 3.13 (a ] and agrees with the redox potential of the amalgam, i.e., -0.3521V for Cd2+ + 2e - Cd(Hg) and -0.7628 V for Zn2+ + 2e -> Zn(Hg) (ref. 10). The Nernst equation is... 

The formal potential of a reduction-oxidation electrode is defined as the equilibrium potential at the unit concentration ratio of the oxidized and reduced forms of the given redox system (the actual concentrations of these two forms should not be too low). If, in addition to the concentrations of the reduced and oxidized forms, the Nernst equation also contains the concentration of some other species, then this concentration must equal unity. This is mostly the concentration of hydrogen ions. If the concentration of some species appearing in the Nernst equation is not equal to unity, then it must be precisely specified and the term apparent formal potential is then employed to designate the potential of this electrode. 

Electrode and therefore cell potentials are very important analytically as their magnitudes are determined by the activities of the reactants and products involved in the electrode reactions. The relation between such activities and the electrode potential is given by the Nernst equation. For a general half-cell reaction written as a reduction, i.e. aA + bB +. .. ne = xX + yY +. . ., the equation is of the form... 

This important equation can be qualitatively interpreted in the following way. When the two components Ox and Red are present in solution at certain concentrations, the working electrode will spontaneously find its equilibrium potential (imposed by the Nernst equation) and there will be no overall current flow. In order for Ox to be reduced or Red oxidized, the system must be moved from equilibrium. This can be achieved by setting a potential different from that for equilibrium. The process of oxidation or reduction will be favoured depending on whether... 

These observations are in accord with a scheme involving a reversible electron transfer, followed by a reaction that depletes the concentration of the initially formed reduced species, R. They are also reminiscent of the observations made earlier in regard to the electrohydrocyclization process. The greater the rate of the follow-up process, the more significant its effect on the concentration of R in a given time period, that associated with the CV scan rate, for example. From a moments consideration of the Nernst equation, it is clear that this event should manifest itself in terms of a shift in the peak potential to a more positive value, as observed for 255 and 257b [4]. In the present instance, it is suggested that a rapid or concerted loss of the mesylate anion in the reductive cyclization is likely to be associated with this so-called kinetic shift of the peak potentials [69]. 

The reducing equivalents transferred can be considered either as hydrogen atoms or electrons. The driving force for the reaction, E, is the reduction/oxidation (redox) potential, and can be measured by electrochemistry it is often expressed in millivolts. The number of reducing equivalents transferred is n. The redox potential of a compound A depends on the concentrations of the oxidized and reduced species [Aqx] and [Area] according to the Nernst equation ... 

A typical set of optical spectra for the spectroelectrochemical titration of a nitrophorin-NO complex, NPl-NO at pH 5.5, is shown in Fig. 22. These experiments are carried out by setting the potential at some value E° and waiting until the optical spectrum does not change with time, then recording the optical spectrum, followed by setting a new potential E° and repeating the process, etc. As is evident, clear isosbestic behavior is observed, indicating a smooth reduction of the chromophore as the applied potential is lowered, with only two species present. The insert shows the plot, based upon the Nernst equation. 

The reader should recall that the concentrations of the electron, pure solids, and the solvent (water), are defined as 1. The calculated value of —2.77 v matches the value of —2.8 v which was estimated from the diagram. It is interesting to note from the Nernst equation that the reduction potential for the half-reaction is dependent only upon the concentration of the sodium ion, Na" ". Neither the concentration of the hydrogen ion nor the hydroxide ion influences the potential at which the half-reaction occurs since they do not appear in the above equation. Similar calculations may be made for other concentrations of Na" ". It will be found that the horizontal line separating Na" " and Na moves from —2.71 v at 1.00 M Na+ to —2.89 v at 10 M, to —3.06 V at 10 M, to —3.24 v at 10 M, and so on. 

I he Nernst equation and its relevance to the dependence of the values of reduction potentials upon the pH of the solution... 

Find the values of the standard oxidation-reduction potentials of the indicated systems (see Appendix 1, Table 21). Write the Nernst equation. 

In the Figure 3.18 example, after imposing Ej across the electrode-solution interface, the potential is scanned negatively toward the standard redox potential of the O/R couple. The ratios of O and R that must exist at the electrode surface (Cr/Cq) at several potentials during the scan are given in each figure. These values are dictated by the Nernst equation for a reversible system (see Table 3.1). Since the solution initially contained only O, the R required to satisfy the Nernst equation is obtained from O by reduction, causing cathodic current. 

For a reversible couple, the surface concentrations of the electroactive species for a simple reduction can be substituted into the Nernst equation to give an expression describing the potential-time response curve. At x = 0, CyC can be related to time by (xI/2 - t1/2)/t1/2, which gives... 

In such a case the one-electron reduction potential of A(Ered) may be shifted to the positive direction with an increase in the concentration of M according to Eq. 4, which is derived from the Nernst equation of the one-electron reduction potential in the presence of M [38] ... 

We can calculate the standard cell potential E° from the standard reduction potentials in Table 18.1. Then we use the Nernst equation to find the cell potential E under the cited conditions. 

Potentiometric measurements are based on the Nernst equation, which was developed from thermodynamic relationships and is therefore valid only under equilibrium (read thermodynamic) conditions. As mentioned above, the Nernst equation relates potential to the concentration of electroactive species. For electroanalytical purposes, it is most appropriate to consider the redox process that occurs at a single electrode, although two electrodes are always essential for an electrochemical cell. However, by considering each electrode individually, the two-electrode processes are easily combined to obtain the entire cell process. Half reactions of electrode processes should be written in a consistent manner. Here, they are always written as reduction processes, with the oxidised species, O, reduced by n electrons to give a reduced species, R ... 

From Nernst s equation related to individual equilibrium potentials we may deduce that the oxidizing power of hydrogen peroxide, which is higher with a more positive reduction potential of the system (lb), grows with increasing concentration of the hydrogen ions in the solution. On the other hand the... 

The correct answer is (B). This problem requires the use of the Nernst equation (or at least its application). However, before you can solve the equation, you need to know which electrode is the cathode and which is the anode. Remember, the substance with the most negative reduction potential is the most easily oxidized, making it the anode. In this problem, lead is the anode and cobalt the cathode. The emf of the second cell can be determined by ... 

The standard reversible potential is that listed in the EMF series of Table 1 and represents a special case of the Nernst equation in which the second term is zero. The influence of the solution composition manifests itself through the logarithmic term. The ratio of activities of the products and reactants influences the potential above which the reaction is thermodynamically favorted toward oxidation (and conversely, below which reduction is favored). By convention, all solids are considered to be at unit activity. Activities of gases are equal to their fugacity (or less strictly, their partial pressure). 

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