Equilibrium potentials example calculations

The Tafel expressions for both the anodic and the cathodic reaction can be directly incorporated into a mixed potential model. In modeling terms, a Tafel relationship can be defined in terms of the Tafel slope (b), the equilibrium potential for the specific half-reaction ( e), and the exchange current density (70), where the latter can be easily expressed as a rate constant, k. An attempt to illustrate this is shown in Fig. 10 using the corrosion of Cu in neutral aerated chloride solutions as an example. The equilibrium potential is calculated from the Nernst equation e.g., for the 02 reduction reaction,... 

Results using this technique are better for force helds made to describe geometries away from equilibrium. For example, it is better to use Morse potentials than harmonic potentials to describe bond stretching. Some researchers have created force helds for a specihc reaction. These are made by htting to the potential energy surface obtained from ah initio calculations. This is useful for examining dynamics on the surface, but it is much more work than simply using ah initio methods to hnd a transition structure. 

Equations and provide a method for calculating equilibrium constants from tables of standard reduction potentials. Example illustrates the technique. 

From the given Hamiltonian, adiabatic potential energy surfaces for the reaction can be calculated numerically [Santos and Schmickler 2007a, b, c Santos and Schmickler 2006] they depend on the solvent coordinate q and the bond distance r, measured with respect to its equilibrium value. A typical example is shown in Fig. 2.16a (Plate 2.4) it refers to a reduction reaction at the equilibrium potential in the absence of a J-band (A = 0). The stable molecule correspond to the valley centered at g = 0, r = 0, and the two separated ions correspond to the trough seen for larger r and centered at q = 2. The two regions are separated by an activation barrier, which the system has to overcome. 

Here, we have substituted E, the standard potential for oxidation of H2, for —2FAG°, where AG° is the free energy change for reaction under standard conditions. Obviously, similar relationships can be written to calculate the equilibrium potentials for other fuels. For example, for alkanes, C, Azn z, the analogous relationship between partial pressures and the equilibrium cell potential is the following... 

The symbols in parentheses denote the electrochemical potential levels for the corresponding reaction (the level Fdec is a particular case of the level Fred0J for a redox reaction, in which the electrode material is destructed). Once Fdec is calculated (from tabular values of thermodynamic characteristics of substances involved see, for example, Latimer, 1952), the equilibrium potentials of the reactions of anodic [Pg.286]

Calculate the equilibrium constant for a reaction from the standard cell potential, Example 12.7. 

In the equilibrium state, the anodic and cathodic partial reactions of an electrochemical reaction have equal rates. The system is in a dynamic equilibrium state, and no net reaction occurs. For example, when a copper sheet is immersed in copper sulfate solution, in the equilibrium state the anodic dissolution rate of copper from sheet to solution equals the cathodic deposition rate from the solution to the surface of the sheet. Theoretically, one can calculate the equilibrium state of an electrochemical reaction from thermodynamic values. This is the standard electrode potential, E°, or equilibrium potential of the electrochemical reaction. The standard electrode potential corresponds to a determined standard state of 0.1 MPa, 25 °C, activity of reactive species of 1 or ideal solution of 1.0 mol L-1, and equilibrium potential of any other state. 

In this section, the behavior of a redox system at the equilibrium potential has been discussed. It should, however, be noted that impedance spectroscopy of irreversible systems can also yield useful information. For example, the charge-transfer resistance determined at the corrosion potential corresponds to the slope of the current-potential curve (/ ct = dV(t)/dI (t) at that potential and allows calculation of the rate of corrosion [1]. 

Example 5 Calculation of the impedance at the equilibrium potential for the electrode reaction... 

Example 6 The calculation of the I-t response in a thin layer cell bounded by two electrodes acting as working and counter electrodes (the reference electrode is external to the thin layer). The potential of the working electrode is stepped from the equilibrium potential to that for the diffusion controlled reduction O + we"" R and the solution contains excess R so that only the reverse reaction occurs at the counter electrode, O and R are both stable. 

Phase and chemical equilibrium calculations are essential for the design of processes involving chemical transformations. Even in the case of reactions that cannot reach chemical equilibrium, the solution of this problem gives information on the expected behaviour of the system and the potential thermodynamic limitations. There are several problems in which the simultaneous calculation of chemical and phase behaviour is mandatory. This is the case, for example, of reactive distillations where phase separation is used to shift chemical equilibrium. Also, the calculation of gas and solid solubility in liquids of high dielectric constants requires at times the resolution of chemical equilibrium between the different species that are formed in the liquid phase. Several algorithms have been proposed in the literature to solve the complex non-linear problem however, proper thermodynamic model selection has not received much attention. 

The Cu Cu(II), glycine system, in which a consecutive transfer of two electrons takes place, can serve as an example. StabiUty constants of complexes are log = 8.46, log 2 = and relevant protonation constants are log (3 = 9.68, log = 12.05. These values were used in calculating the composition of the IPS series [11]. As protonated ligands prevail in acid solutions, rather low concentrations of deprotonated L form must be set (Table 6.1). The open-circuit potentials 0.218 0.004V are in line with equilibrium potential... 

A quite different response is found for couples O/R where Iq is large (in fact, where Iq > 10" /l or k > 10" cm s ). Then the electron transfer reaction at the surface is rapid enough that under most mass transport conditions obtainable experimentally, the electron transfer couple at the surface appears to be in equilibrium. Then the surface concentrations may, at each potential, be calculated from the Nernst equation, a purely thermodynamic equation, and the current may be calculated, for example, from equation (1.57). The I-E curve has the form shown in Fig. 1.16 the I-E curve crosses the zero current axis steeply and there is no overpotential for oxidation or reduction. Systems with these characteristics are often termed reversible . On the other hand, the limiting current densities do not depend on the kinetics of electron transfer closer to E. Hence the limiting current densities for reversible and irreversible reactions are the same. 

A simulation is also a tool to calculate the thermophysical properties of a real fluid, and there are a number of circumstances for which computer simulations using reasonably accurate potentials provide the only reliable experimental information. Estimating the properties of a fluid under extreme conditions of temperature and pressure is one example calculating the properties of a system far from equilibrium is another. Clearly, then, the most useful simulation algorithm should both evaluate a prc rty to within a reasonable accuracy, assuming the pair potential is known to a first approximation, and give an insight into the behavior of the system. 

Calculating the potential of a solution that contains only one redox couple is the simplest case. The potential is given by Nemst s law. For example, for a solution containing ferrous and ferric ions, the equilibrium potential is given by... 

In this case, the calculation of the equilibrium potential as a function of the coneen-trations Ci and C2 is far more difficult than previously. Let s consider, for example. 

Let us implement the earlier-described definitions and approach to calculate the equilibrium potential of the Daniell cell at 25°C and 1 bar when concentrations of the cell electrolytes are well defined and relatively low in order to use the Debye-Hiickel theory for calculating the individual activity coefficients of the electrochemically active ions. In this example, the Daniel cell diagram is as follows ... 

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