Nemst equation kinetic derivation

The potential of this electrode is defined (Section 5.2) as the voltage of the cell Pt H2(l atm) H (a = 1) M M, where the left-hand electrode, = 0, is the normal hydrogen reference electrode (described in Section 5.6). In Chapter 6, we derive the Nemst equation on the basis of the electrochemical kinetics. Here we use a simplified approach and consider that Eq. (5.9) can be used to determine the potential E of the M/M 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, and e, and only one product of reaction, M, Eq. (5.9) yields... 

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

Firstly, is a kinetic expression, a rate law, such as, e.g., the Langmuir-Hinshelwood-Hougen-Watson rate expressions in heterogeneous catalysis, and as such has no universal applicability. It is derived on the basis of mass action kinetics and does reduce to the fundamental thermodynamic Nemst equation for i = 0, thus q = 0. ° Nevertheless, experimental deviations can be expected as with any other, even most successful, rate expression. 

For impurity species present in dilute concentrations, some may find it more convenient to treat the species using dilute solution theory, which accounts only for interactions of the dilute species with the solvent Rigorously, Equation 12 was derived for a binary electrolyte with no impurity species in the solution. While it is not completely rigorous to treat one species with dilute solution theory while treating the main electrolyte with equations derived from concentrated solution theory in the absence of the impurity species, the error may be small. The flux of the dilute species is given by Equation 5. The mass balance for the main electrolyte remains unchanged. If 2 is defined by Equation 3, then Us must be defined as a function of the concentration of the impurity species in order to include the concentration overpotential of the impurity species in the kinetic expression. Equation 53. The Nemst equation. Us = Uf + /JTln( Ci cf). is often used to account for the concentration overpotential of dilute species i. If Og is defined by Equation 6, then Us should not be defined as a function of solution composition. 

At this point, and as somewhat of a digression, it is useful to consider a simple derivation of the Nemst half-cell equation from the kinetics principles that have been introduced. Thus, using activity rather than concentration, Eq 3.25 becomes ... 

The set of nonlinear independent differential equations of the SCM is derived by application of the principles of conservation of mass and charge during current flow to the surface compartments, and application of the principles of chemical reaction kinetics to ion binding at the surfaces. In the equations, the fluxes are driven by electrochemical potential differences given by Nemst-Planck equations. 

A more in-depth elucidation of the mechanism of permselective membranes can be done by using the Nemst-Planck/Poisson equations. As a model system, the gold nanoporous membranes introduced by Martin et al. were used however, the surface charge was established by their chemical modification with self-assembled monolayers (SAMs) of chemisorbed electrically charged thiol derivatives. The average pore diameters of such membranes can be very precisely determined with gas permeation experiments based on the kinetic theory of gases ... 

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