Electrode kinetics Nernst

This is the Nernst equation defined from the electrode kinetics considerations. Later, we derive the same relationship on purely thermodynamic grounds. 

Two boundary conditions are required for each species one in bulk and one at the electrode. Conventionally the concentrations are set to their initial values in bulk, and at the electrode either the Nernst equation or Butler-Volmer equation is applied to describe the electrode kinetics. These equations have the general form/(c,o E) = 0, where the applied potential is a linear function of time. Conservation of mass also requires that the fluxes of reactant A and product B are equal and opposite at the electrode surface. 

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. 

Diffusion overpotential. When high current densities j exist at electrodes (at the boundary to the electrolyte), an impoverishment of the reacting substances is possible. In this case the reaction kinetics are determined only by diffusion processes through this zone, the so-called Nernst layer. Without dealing with the derivation in detail, the following formula is obtained for the diffusion overpotential that occurs (with as the maximum current density) ... 

Before treating specific faradaic electroanalytical techniques in detail, we shall consider the theory of electrolysis more generally and along two different lines, viz., (a) a pragmatic, quasi-static treatment, based on the establishment of reversible electrode processes, which thermodynamically find expression in the Nernst equation, and (b) a kinetic, more dynamic treatment, starting from passage of a current, so that both reversible and non-reversible processes are taken into account. 

In an earlier note (p. 9) we mentioned the occurrence of overvoltage in an electrolytic cell (and overpotentials at single electrodes), which means that often the breakthrough of current requires an Uappl = Eiecomp r] V higher than Ehack calculated by the Nernst equation as this phenomenon is connected with activation energy and/or sluggishness of diffusion we shall treat the subject under the kinetic treatment of the theory of electrolysis (Section 3.2). 

This is an extremely important equation since it tells us that, in the limit of very facile kinetics, the surface concentrations of O and R are constrained to satisfy the local Nernst equation. Under these conditions, the net current is always dictated by the diffusion of the electroactive species to the electrode i.e. the flux of O. 

We consider now the case where the kinetics of the electrode electron transfer may interfere. Equations (6.213) and (6.214) are still valid and Nernst s law is replaced by equation (4.9). Combination of these three equations leads to equation (4.10), and from it, to equation (4.11). 

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. 

The Nernst equation defines the equilibrium potential of an electrode. A simplified thermodynamic derivation of this equation is given in the Sections 5.3 to 5.5. Here we will give the kinetic derivation of this equation. 

With any electrochemical technique to study kinetics, the electrode-solution interface is perturbed from its initial situation. The initial conditions may be such that the system is in a chemical equilibrium and this usually means that the interfacial potential difference is determined by Nernst s law holding for the two components O and R of a redox couple being present... 

The potential of this electrode is defined (Section 5.2) as the voltage of the cell Pt H2(l atm) H+(<2 = 1) MZ+ M, where the left-hand electrode, Et = 0, is the normal hydrogen reference electrode (described in Section 5.6). We will derive the Nernst equation on the basis of the electrochemical kinetics in Chapter 6. Here we will use a simplified approach and consider that Eq. (5.9) can be used to determine the potential E of the M/Mz+ electrode as a function of the activity of the products and reactants in the equilibrium equation (5.10). Since in reaction (5.10) there are two reactants, Mz+ and e, and only one product of reaction, M, Eq. (5.9) yields... 

The dynamics of the system are described by k°, with its units being s 1 for an adsorbed reactant. A redox couple with a large k° will establish the equilibrium concentrations given by the Nernst equation on a short timescale. Kinetically facile systems of this type require high-speed electrochemical techniques to successfully probe the electrode dynamics. The largest k° values that have been reliably measured are of the order of 106 s-1 and are associated with mechanistically simple reactions, i.e. there are no coupled chemical kinetics or significant structural differences between the oxidized and reduced forms. 

In a system involving reagents and products at equilibrium, the rates of the reactions in each direction are equal. Equilibrium can thus be seen as a limiting case, and any kinetic model must give the correct equilibrium expression. For reactions at an electrode, half-reactions > the equilibrium expression is the Nernst equation. 

Factors Involved in Galvanic Corrosion. Emf series and practical nobility of metals and metalloids. The emf. series is a list of half-cell potentials proportional to the free energy changes of the corresponding reversible half-cell reactions for standard state of unit activity with respect to the standard hydrogen electrode (SHE). This is also known as Nernst scale of solution potentials since it allows to classification of the metals in order of nobility according to the value of the equilibrium potential of their reaction of dissolution in the standard state (1 g ion/1). This thermodynamic nobility can differ from practical nobility due to the formation of a passive layer and electrochemical kinetics. 

---