Nernst equation dependence

If the semipermeable membrane is selective for a particular ion (i), a potential gradient will develop across the membrane. The gradient, described by the Nernst equation, depends on the ratio of the activity of the ion on either side of the membrane ... 

The extent to which natural systems are described by the Nernst equation depends on the relative rates at which electrons are transferred to and from various substances. These rates vary over several orders of... 

Although EXo /ATcd is standard-state potential for the analyte s half-reaction, a matrix-dependent formal potential is used in its place. After the equivalence point, the potential is easiest to calculate using the Nernst equation for the titrant s half-reaction, since significant quantities of its oxidized and reduced forms are present. 

Despite the apparent ease of determining an analyte s concentration using the Nernst equation, several problems make this approach impractical. One problem is that standard-state potentials are temperature-dependent, and most values listed in reference tables are for a temperature of 25 °C. This difficulty can be overcome by maintaining the electrochemical cell at a temperature of 25 °C or by measuring the standard-state potential at the desired temperature. 

Another problem is that the Nernst equation is a function of activities, not concentrations. As a result, cell potentials may show significant matrix effects. This problem is compounded when the analyte participates in additional equilibria. For example, the standard-state potential for the Fe "/Fe " redox couple is +0.767 V in 1 M 1TC104, H-0.70 V in 1 M ITCl, and -H0.53 in 10 M ITCl. The shift toward more negative potentials with an increasing concentration of ITCl is due to chloride s ability to form stronger complexes with Fe " than with Fe ". This problem can be minimized by replacing the standard-state potential with a matrix-dependent formal potential. Most tables of standard-state potentials also include a list of selected formal potentials (see Appendix 3D). 

It should be noted that the simple Nernst equation cannot be used since the standard electrode potential is markedly temperature dependent. By means of irreversible thermodynamics equations have been computed to calculate these potentials and are in good agreement with experimentally determined results. 

Steady-state potential comparable with Types 4 and 5 reversible electrodes Potential of metal depends on pH of solution, although the dependence is confined to a limited range of pH and does not conform precisely to the Nernst equation. Ni in H2SO4 (Ni/Hj, H + ) Cu in NaOH (Cu/CujO/OH")... 

The Nernst equation shows that the glass electrode potential for a given pH value will be dependent upon the temperature of the solution. A pH meter, therefore, includes a biasing control so that the scale of the meter can be adjusted to correspond to the temperature of the solution under test. This may take the form of a manual control, calibrated in 0 C, and which is set to the temperature of the solution as determined with an ordinary mercury thermometer. In some instruments, arrangements are made for automatic temperature compensation by inserting a temperature probe (a resistance thermometer) into the solution, and the output from this is fed into the pH meter circuit. 

As a consequence, the equilibrium potential of the single half-cell also depends on the concentrations of the compounds involved. The Nernst equation [Eq. (24)], which is one of the most important electrochemical relations, explains this context... 

The dependence of the equilibrium potential on the activities of hydrogen and sulfuric acid is given by the corresponding Nernst equation ... 

It is very often necessary to characterize the redox properties of a given system with unknown activity coefficients in a state far from standard conditions. For this purpose, formal (solution with unit concentrations of all the species appearing in the Nernst equation its value depends on the overall composition of the solution. If the solution also contains additional species that do not appear in the Nernst equation (indifferent electrolyte, buffer components, etc.), their concentrations must be precisely specified in the formal potential data. The formal potential, denoted as E0, is best characterized by an expression in parentheses, giving both the half-cell reaction and the composition of the medium, for example E0,(Zn2+ + 2e = Zn, 10-3M H2S04). 

Activity Dependence of Electrode Potentials - The Nernst Equation... 

The Nernst equation defining the potential of the silver-silver chloride electrode is Equation (14.9). Since the [CF] in such an electrode is a constant, the potential also must be a constant (the requirement of a reference electrode) because [CF] is the only variable on which the potential depends. 

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... 

Figure 5.13 pH dependence of Eswitch arid at 45°C as determined from the derivatives of data such as those shown in Fig. 5.1 I.The solid line indicates the best fit to the Eswitch data.Also shown is the potential of the 2H /H2 potential at 4S°C and I bar hydrogen as calculated from the Nernst equation.

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 ... 

The activation overpotentials for both electrodes are high therefore, the electrochemical kinetics of the both electrodes can be approximated by Tafel kinetics. The concentration dependence of exchange current density was given by Costamagna and Honegger.The open-circuit potential of a SOFC is calculated via the Nernst equation.The conductivity of the electrolyte, i.e., YSZ, is a strong function of temperature and increases with temperature. The temperature dependence of the electrolyte conductivity is expressed by the Arrhenius equation. 

CONCENTRATION DEPENDENCE OF EQUILIBRIUM CELL VOLTAGE THE GENERAL NERNST EQUATION... 

Nernst Equation for the Concentration Dependence of Metal/Metal-Ion Potential. 

Nernst Equation for Concentration Dependence of RedOx Potential. Equation (5.9) applied to the general RedOx electrode (5.16) yields... 

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... 

Unlike anions that specifically adsorb at electrodes, cations normally do not lose their solvation shell due to their smaller size and are electrostatically adsorbed at electrodes at potentials negative to the pzc. However, depending on the affinity with the foreign substrate, cations can be reduced to a lower oxidation state or even discharged completely to the corresponding metal atom at the sub-monolayer or monolayer level at potentials positive to the equilibrium Nernst potential for bulk deposition. This deposition of metal atoms on foreign metal electrodes at potential positive to that predicted by the Nernst equation for bulk deposition has been called underpotential deposition and has been extensively investigated in recent years. Detailed discussion of the... 

Quasi-reversible charge transfer differs from the Nernstian case in that Co (0, f)/CR (0, t) is not dictated by the Nernst equation and depends both on the rates of the forward and reverse charge transfer reactions. The flux of O at the surface, where f = F/RT, is given by [15]... 

When hydrogen ion is involved in a half-reaction, such as ox + mH+ + ne -w- == red, the potential is pH-dependent, as the following Nernst equation shows. 

Equation (5.9) is the general Nernst equation giving the concentration dependence of the equilibrium cell voltage. It will be used in the next section of this chapter to derive the equilibrium electrode potential for metal/metal-ion and redox electrodes. 

The Nernst Equation for the Concentration Dependence of Metal/Metal-Ion Potential. In the general case of a metal/metal-ion electrode, a metal M is in an equilibrium with its ions in the solution... 

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