Equilibrium Nernst equation

Ladder diagrams can also be used to evaluate equilibrium reactions in redox systems. Figure 6.9 shows a typical ladder diagram for two half-reactions in which the scale is the electrochemical potential, E. Areas of predominance are defined by the Nernst equation. Using the Fe +/Fe + half-reaction as an example, we write... 

In a redox reaction, one of the reactants is oxidized while another reactant is reduced. Equilibrium constants are rarely used when characterizing redox reactions. Instead, we use the electrochemical potential, positive values of which indicate a favorable reaction. The Nernst equation relates this potential to the concentrations of reactants and products. 

At the equivalence point, the moles of Fe + initially present and the moles of Ce + added are equal. Because the equilibrium constant for reaction 9.16 is large, the concentrations of Fe and Ce + are exceedingly small and difficult to calculate without resorting to a complex equilibrium problem. Consequently, we cannot calculate the potential at the equivalence point, E q, using just the Nernst equation for the analyte s half-reaction or the titrant s half-reaction. We can, however, calculate... 

Influence of the Kinetics of Electron Transfer on the Faradaic Current The rate of mass transport is one factor influencing the current in a voltammetric experiment. The ease with which electrons are transferred between the electrode and the reactants and products in solution also affects the current. When electron transfer kinetics are fast, the redox reaction is at equilibrium, and the concentrations of reactants and products at the electrode are those specified by the Nernst equation. Such systems are considered electrochemically reversible. In other systems, when electron transfer kinetics are sufficiently slow, the concentration of reactants and products at the electrode surface, and thus the current, differ from that predicted by the Nernst equation. In this case the system is electrochemically irreversible. 

When no net current is flowing, the equilibrium potential of the fuel cell is given by the Nernst equation ... 

It must not be assumed that the protection potential is numerically equal to the equilibrium potential for the iron/ferrous-ion electrode (E ). The standard equilibrium potential (E ) for iron/ferrous-ion is -0-440V (vs. the standard hydrogen electrode). If the interfacial ferrous ion concentration when corrosion ceases is approximately 10 g ions/1 then, according to the Nernst equation, the equilibrium potential (E ) is given by ... 

These considerations show the essentially thermodynamic nature of and it follows that only those metals that form reversible -i-ze = A/systems, and that are immersed in solutions containing their cations, take up potentials that conform to the thermodynamic Nernst equation. It is evident, therefore, that the e.m.f. series of metals has little relevance in relation to the actual potential of a metal in a practical environment, and although metals such as silver, mercury, copper, tin, cadmium, zinc, etc. when immersed in solutions of their cations do form reversible systems, they are unlikely to be in contact with environments containing unit activities of their cations. Furthermore, although silver when immersed in a solution of Ag ions will take up the reversible potential of the Ag /Ag equilibrium, similar considerations do not apply to the NaVNa equilibrium since in this case the sodium will react with the water with the evolution of hydrogen gas, i.e. two exchange processes will occur, resulting in an extreme case of a corrosion reaction. 

It must be emphasised that standard electrode potential values relate to an equilibrium condition between the metal electrode and the solution. Potentials determined under, or calculated for, such conditions are often referred to as reversible electrode potentials , and it must be remembered that the Nernst equation is only strictly applicable under such conditions. 

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 potential of the electrode surface is determined by the Nernst equation introduced in Sec. 1.3.3. In an equilibrium, the currents in anodic and cathodic directions are equal. If they are related to an electrode area, they are called exchange-current densities, j0 ... 

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

Figure 19. Electrochemical isotherm for Ti () 5Zr0 5 V0 5 Ni,, Fe0 2 Mn 0 2. The /)( is calculated from the equilibrium voltage,, by the Nernst equation 156].

The Nernst equation is of limited use at low absolute concentrations of the ions. At concentrations of 10 to 10 mol/L and the customary ratios between electrode surface area and electrolyte volume (SIV 10 cm ), the number of ions present in the electric double layer is comparable with that in the bulk electrolyte. Hence, EDL formation is associated with a change in bulk concentration, and the potential will no longer be the equilibrium potential with respect to the original concentration. Moreover, at these concentrations the exchange current densities are greatly reduced, and the potential is readily altered under the influence of extraneous effects. An absolute concentration of the potential-determining substances of 10 to 10 mol/L can be regarded as the limit of application of the Nernst equation. Such a limitation does not exist for low-equilibrium concentrations. 

It is obvious from the above conditions that the transfer of strongly hydrophylic Zf anions from phase w to s and of strongly hydrophobic X2 anions from phase 5 to vr is much more difficult compared to the transfer of the common hydrophylic-hydrophobic cations. In the equilibrium state, the Galvani potential is defined in terms of the Nernst equation (4) ... 

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. 

A chemical reaction subsequent to a fast (reversible) electrode reaction (Eq. 5.6.1, case b) can consume the product of the electrode reaction, whose concentration in solution thus decreases. This decreases the overpotential of the overall electrode process. This mechanism was proposed by R. Brdicka and D. H. M. Kern for the oxidation of ascorbic acid, converted by a fast electrode reaction at the mercury electrode to form dehydro-ascorbic acid. An equilibrium described by the Nernst equation is established at the electrode between the initial substance and this intermediate product. Dehydroascorbic acid is then deactivated by a fast chemical reaction with water to form diketogulonic acid, which is electroinactive. 

What is the difference between the concentration ratio in the equilibrium constant expression and that in the Nernst equation (Chap. 14) ... 

Ans. In a reaction at equilibrium, the ratio can have only one value at any given temperature. In the Nernst equation, the value can change, since the reaction can be stopped short of equilibrium simply by disconnecting a wire or the salt bridge. 

Equilibrium potentials calculated at 37°C from the Nernst equation. Calculated assuming a —90 mV resting potential for the muscle membrane and assuming that chloride ions are at equilibrium at rest. 

Many natural waters, including most waters at low temperature, do not achieve redox equilibrium (e.g., Lindberg and Runnells, 1984 see Chapter 7). In this case, no single value of pe or Eh can be used to represent the redox state. Instead, there is a distinct value for each redox couple in the system. Applying the Nernst equation to Reaction 3.46 gives a pe or Eh representing the hydrolysis of water. Under disequilibrium conditions, this value differs from those calculated from reactions such as,... 

We need the Nernst equation to determine the change of the equilibrium potential with concentration. For this purpose the overall reaction is usually rewritten in such a way that all coefficients are integers, with negative stochiometric coefficients denoting the reactants. This results in an equation of the form ... 

Comparison with Eq. (2.10) shows that the measured potential is simply the difference between the equilibrium potentials of the two redox couples, each measured with respect to its own reference electrode. Admittedly, this is an obvious result, but it is useful to derive it from first principles. The corresponding Nernst equation is ... 

Experiments involving the Nernst equation are primarily concerned with concentrations. One or more of the concentrations in the Q portion of the Nernst equation are calculated by measuring the nonstandard cell potential and comparing this to the standard cell potential. Remember, you calculate the concentration from a measured voltage. Once the concentration is determined, it may be combined with other concentrations and used to calculate an equilibrium constant. 

Under equilibrium conditions the Nernst equation holds ... 

Since we have preliminarily stated that any kinetic theory must involve agreement between kinetic and thermodynamic data, it follows that, under equilibrium conditions, kinetic theory must afford relationships that coincide with the Nernst equation. 

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... 

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