Nemst

We now consider briefly the matter of electrode potentials. The familiar Nemst equation was at one time treated in terms of the solution pressure of the metal in the electrode, but it is better to consider directly the net chemical change accompanying the flow of 1 faraday (7 ), and to equate the electrical work to the free energy change. Thus, for the cell... 

Because it is necessary to exclude some substances, including some crystals, from the Nemst heat theorem, Lewis and Gibson (1920) introduced the concept of a perfect crystal and proposed the following modification as a definitive statement of the third law of themiodynamics (exact wording due to Lewis and Randall (1923)) ... 

Because of the Nemst heat theorem and the third law, standard themrodynamic tables usually do not report entropies of fomiation of compounds instead they report the molar entropy 50 7 for each element and... 

In the Lewis and Gibson statement of the third law, the notion of a perfect crystalline substance , while understandable, strays far from the macroscopic logic of classical thennodynamics and some scientists have been reluctant to place this statement in the same category as the first and second laws of thennodynamics. Fowler and Guggenheim (1939), noting drat the first and second laws both state universal limitations on processes that are experunentally possible, have pointed out that the principle of the unattainability of absolute zero, first enunciated by Nemst (1912) expresses a similar universal limitation ... 

Consider how the change of a system from a thennodynamic state a to a thennodynamic state (3 could decrease the temperature. (The change in state a —> f3 could be a chemical reaction, a phase transition, or just a change of volume, pressure, magnetic field, etc). Initially assume that a and (3 are always in complete internal equilibrium, i.e. neither has been cooled so rapidly that any disorder is frozen in. Then the Nemst heat... 

For more complicated redox reactions, a general fonn of the Nemst equation may be derived by analogy with A2.4.113. If we consider a stoichiometric reaction of the following type ... 

The Nemst equation above for the dependence of the equilibrium potential of redox electrodes on the activity of solution species is also valid for uncharged species in the gas phase that take part in electron exchange reactions at the electrode-electrolyte interface. For the specific equilibrium process involved in the reduction of chlorine ... 

Once current passes tluough the interface, the Galvani potential difference will differ from that expected from the Nemst equation above the magnitude of the difference is temied the overpotential, which is defined heiiristically as... 

Light sources can either be broadband, such as a Globar, a Nemst glower, an incandescent wire or mercury arc lamp or they can be tunable, such as a laser or optical parametric oscillator (OPO). In the fomier case, a monocln-omator is needed to achieve spectral resolution. In the case of a tunable light source, the spectral resolution is detemiined by the linewidth of the source itself In either case, the spectral coverage of the light source imposes limits on the vibrational frequencies that can be measured. Of course, limitations on the dispersing element and detector also affect the overall spectral response of the spectrometer. 

For a simple electron transfer reaction containing low concentrations of a redox couple in an excess of electrolyte, the potential established at an inert electrode under equilibrium conditions will be governed by the Nemst equation and the electrode will take up the equilibrium potential for the couple 0/R. In temis of... 

The scan rate, u = EIAt, plays a very important role in sweep voltannnetry as it defines the time scale of the experiment and is typically in the range 5 mV s to 100 V s for nonnal macroelectrodes, although sweep rates of 10 V s are possible with microelectrodes (see later). The short time scales in which the experiments are carried out are the cause for the prevalence of non-steady-state diflfiision and the peak-shaped response. Wlien the scan rate is slow enough to maintain steady-state diflfiision, the concentration profiles with time are linear within the Nemst diflfiision layer which is fixed by natural convection, and the current-potential response reaches a plateau steady-state current. On reducing the time scale, the diflfiision layer caimot relax to its equilibrium state, the diffusion layer is thiimer and hence the currents in the non-steady-state will be higher. 

Cyclic voltammetry provides a simple method for investigating the reversibility of an electrode reaction (table Bl.28.1). The reversibility of a reaction closely depends upon the rate of electron transfer being sufficiently high to maintain the surface concentrations close to those demanded by the electrode potential through the Nemst equation. Therefore, when the scan rate is increased, a reversible reaction may be transfomied to an irreversible one if the rate of electron transfer is slow. For a reversible reaction at a planar electrode, the peak current density, fp, is given by... 

The expression for the mass-transport-limiting current density may be employed together with the Nemst equation to deduce the complete current-potential response in a solution containing only oxidized or reduced species... 

Figure Bl.28.6. (a) Convection within the electrolyte solution, due to rotation of the electrode (b) Nemst diflfiision model for steady state.

Gibbs values and the effective electrode potential follows the Nemst equation (see section C2.11). For the oxidation (anodic) reaction, the potential (E ) of the Nemst equation can be written as ... 

Combining equation 6 and 7 with the Van t Hoff isotherm the Nemst equation for electrochemicA reactions is obtained ... 

Equation 11 gives the conductivity for a particular ion having a transference number, in a crystal, which is the Nemst-Einstein relationship. 

The doped Zr02 stmctures are used as electrochemical sensors, as, for example, when used to detect oxygen in automotive exhaust (see Exhaust CONTROL, automotive). The sensor voltage is governed by the Nemst equation (eq. 17) where the activities are replaced by oxygen partial pressures and the air inside the chamber is used as reference. 

Corrosion occurs even if the two reactants involved are not at standard conditions. In this case the nonstandard equiUbrium potential for each reaction, often referred to as the reversible potential, can be calculated from the Nemst equation. Additional information on thermodynamic aspects of corrosion can be found in Reference 10. 

Smaller values of necessitate the appHcation of voltages greater than those calculated from the Nemst equation to obtain a corresponding set of surface concentrations of electroactive species. These voltages are called overpotentials and iadicate chemically related difficulties with the electrolysis. In other words, electron exchange between the electrode and the electroactive species is impeded by the chemistry of the process itself. 

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