Nernst equation Subject

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). 

We consider again the redox reaction Ox + ze = Red with a solution initially containing only the oxidized form Ox. The electrode is initially subjected to an electrode potential Ei where no reaction takes place. For the sake of simplicity, it is assumed that the diffusion coefficients of species Ox and Red are equal, i.e., D = D0x = DKeA. Now, the potential E is linearly increased or decreased with E(t) = Ei vt (v is a potential scan rate, and signs + and represent anodic scan and cathodic scan, respectively.) Under the assumption that the redox couple is reversible, the surface concentrations of Ox and Red, i.e., cs0x and 4ed, respectively, are always determined by the electrode potential through the Nernst equation... 

Chan (Chapter 6) presents a simple graphical method for estimating the free energy of EDL formation at the oxide-water interface with an amphoteric model for the acidity of surface groups. Subject to the assumptions of the EDL model, the graphical method allows a comparison of the magnitudes of the chemical and coulombic components of surface reactions. The analysis also illustrates the relationship between model parameter values and the deviation of surface potential from the Nernst equation. 

Le Chatelier s principle is very powerful. It states that any system initially at equilibrium, when subjected to a change in temperature or pressure, will react in such a way as to reduce stress. Discuss this principle for equiUhrium in relation to the expected shifts in voltage for changes in reactant and product concentrations seen from the pressure-dependent component of the Nernst equation. Can you teU "just by looking" if the voltage will go up or down for a given shift in concentration of reactants or products ... 

Equations (4a) and (8) have only quite recently been subjected to the test of experiment, chiefly by Haber and Nernst. For historical reasons both Nernst and Haber make van t Hoff s equation their starting point. 

The original arguments of Nernst on this subject were based upon the view that AG and AH are equal not only at the absolute zero itself (as they must be from the general thermodynamic equation) but also in the immediate vicinity of this point, so that d AO)jdT and 8 AH)jdT vanish when T = 0. From these conditions it follows that J will be zero. Nemst put forward the hypothesis about the temperature coefficients as a fundamental thermodynamic principle (sometimes spoken of as the third law of thermodynamics). While there are reservations about the complete validity of this view, it is certainly one which is always nearly true, and may often be accurately so. 

There is much else in bioelectrochemistry apart from these modern developments in particular, there is the vast area associated with the names of Hodgkin and Huxley and the subject of electrophysiology, seen as an application of the Nernst-Planck equation. 

The probability distribution functions in Eq. [59] applied to the trajectories of particles flowing into and out of a system provides a justification for using the Nernst-Planck equation (Eq. [54]) The net ionic directional fluxes can be expressed in terms of differences between the probability fluxes, normalized to the concentration at the sides of the region of interest. That ionic fluxes and differences in probability fluxes are related thus supplies a connection between the solution of the Nernst-Planck equation (Eq. [54]) and the Smoluchowski equation (Eq. [59]), and it provides a direct justification for using Eq. [54] for the study of ions subjected to Brownian dynamics in solution. 

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