Nernst equation dimensionless

In (19-6), n has been made dimensionless. For a half-reaction, n is the number of electrons in the half-equation for the whole-cell reaction, n is the number of electrons in one of the multiplied half-equations before canceling the electrons. The Nernst equation is closely related to the laws of chemical equilibrium. Le Chatelier s principle applies to the potential of a cell in the same sense as it applies to the yield of an equilibrium process. Since Q is a fraction that has product concentrations in the numerator (top) and reactant concentrations in the denominator (bottom), an increased concentration of the product reduces the potential and an increased concentration of reactant raises the potential. 

Note the rather simple form of the Nernst equation here, and the fact that the dimensionless sweep rate is now unity, that is, one p-unit per one T-unit. 

For the reversible case, the Nernst equation applies instead of the Butler-Volmer equation, that is, in dimensionless terms as in (2.32), rewritten as... 

In LSV and CV, a redox system may show a Nernstian, quasireversible or totally irreversible behavior depending on the scan rate employed, since V determine the time available for the electrodesolution interphase to attain the equilibrium condition dictated by the Nernst equation. Such a dependence is usually rationalized by the following dimensionless parameter, comparing the standard heterogeneous rate constant with the scan rate v ... 

These pose a nontrivial problem and demand some fundamental thought. We have (Fig. 4.2) a cell containing oxidised and reduced species at concentrations c and Cg, both functions of x (and t). We have just completed a calculation of all c values, including for x=0 (c q and Cg q) and are now ready for the next time step. This introduces a new electrode potential parameter p (if the potential varies with time, this will be a new value). Reversibility implies that equilibrium appropriate to the new p is established immediately, so the Nernst equation applies we can rewrite it, using our dimensionless p ... 

In the Nernst equation, the molar convention is used and is a pure number (dimensionless). 

For the activities we can write a, = Yt(Cilc°) where y- is a dimensionless activity coefficient, c, is the concentration of the species i in mol L, and c° is the unit concentration 1 mol L". Introducing this into the Nernst equation yields ... 

Application of Nernst s law to equations (6.20) and (6.23) finally leads to the dimensionless expression of the voltammogram in the general case (KG zone in Figure 2.1) reported in Table 6.4. 

The Nernst boundary layer thickness is a simple characteristic of the mass transfer but its definition is formal since no boundary layer is in fact stagnant and least of all boundary layers on gas-evolving electrodes furthermore, the Schmidt number, known to influence mass transfer, is not incorporated in the usual dimensionless form. For this reason, lines representing data from gas evolution in two different solutions can be displaced from one another because of viscosity differences. Nevertheless, the exponent in the equation = aib (32)... 

Equations 8.44 and 8.45 form the basis of the Poisson-Nernst-Planck (PNP) theory, which is widely used in the context of ion transport through biological membranes [145-147]. In dimensionless form the equations are... 

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