Faraday’s equation

The partial equilibria of equations 8.165 8.168 reveal the usefulness of standard potentials the Gibbs free energy change AG of the redox equilibrium is always given by applying Faraday s equation to the algebraic sum of the standard potentials of the redox couples in question. For equation 8.163, the bulk potential is thus... 

As repeatedly noted, standard potentials are linked to the standard molal Gibbs free energy of formation from the elements through Faraday s equation. Let us... 

Equations (30) and (31) are a solution of Faraday s equation provided that AE = A8 = A. Then, in a single stroke, Faraday s condition achieves two different things orthogonality and equal amplitude of fields E and B. 

Summarizing the discussion in this section. It seems as if the entire physical information about the behavior of the electromagnetic field were contained in Faraday s equation. The other three equations play a minor role definitions of current density, electric source, and absence of magnetic source. 

It is therefore more sensible (and probably easier and safer) to perform constant current iontophoresis, and this is by far the most common approach. In this case, the power supply adapts the voltage imposed to the resistance of the circuit to keep the intensity of current (and hence the drug flux) constant. Drug transport can now be modeled with Faraday s equation, which links current intensity to ionic flux. 

The relationship between thickness reduction per time unit ds/dt (on each corroding side of the specimen/component) and the corrosion current density icoir is determined from Faraday s equations ... 

In an electrical field, the rate of reaction process for metal reduction or oxidation is normally represented by the current density (t). Using eq. (321) the generalized Faraday s equation for the current density is... 

The integration of current transient with time could be used to determine the charge passed for each current transient spike. This charge is the result of the foimation of a pit and can be related to the physical volume of the pit by using Faraday s equation, Eq. 4.20, which was based on the correlation between optical pit size and anodic current transient charge [36]. If the pits are assumed to be hemispherical the pit radius/depth can be calculated, using Eq. 4.21 ... 

The corrosion current can be converted into material loss (m ) using Faraday s law according to equation C2.8.14) ... 

Quantitative Calculations The absolute amount of analyte in a coulometric analysis is determined by applying Faraday s law (equation 11.23) with the total charge during the electrolysis given by equation 11.24 or equation 11.25. Example 11.8 shows the calculations for a typical coulometric analysis. 

Studies aimed at characterizing the mechanisms of electrode reactions often make use of coulometry for determining the number of electrons involved in the reaction. To make such measurements a known amount of a pure compound is subject to a controlled-potential electrolysis. The coulombs of charge needed to complete the electrolysis are used to determine the value of n using Faraday s law (equation 11.23). 

These three terms represent contributions to the flux from migration, diffusion, and convection, respectively. The bulk fluid velocity is determined from the equations of motion. Equation 25, with the convection term neglected, is frequently referred to as the Nemst-Planck equation. In systems containing charged species, ions experience a force from the electric field. This effect is called migration. The charge number of the ion is Eis Faraday s constant, is the ionic mobiUty, and O is the electric potential. The ionic mobiUty and the diffusion coefficient are related ... 

As the corrosion rate, inclusive of local-cell corrosion, of a metal is related to electrode potential, usually by means of the Tafel equation and, of course, Faraday s second law of electrolysis, a necessary precursor to corrosion rate calculation is the assessment of electrode potential distribution on each metal in a system. In the absence of significant concentration variations in the electrolyte, a condition certainly satisfied in most practical sea-water systems, the exact prediction of electrode potential distribution at a given time involves the solution of the Laplace equation for the electrostatic potential (P) in the electrolyte at the position given by the three spatial coordinates (x, y, z). 

It will be interesting to express this through an equation which represents a combined form of Faraday s second and third laws. If W be the weight in grams of a substance (of equivalent weight E) deposited or dissolved at an electrode by (2 coulombs of electricity, then... 

R is the ideal gas constant, T is the Kelvin temperature, n is the number of electrons transferred, F is Faraday s constant, and Q is the activity quotient. The second form, involving the log Q, is the more useful form. If you know the cell reaction, the concentrations of ions, and the E°ell, then you can calculate the actual cell potential. Another useful application of the Nernst equation is in the calculation of the concentration of one of the reactants from cell potential measurements. Knowing the actual cell potential and the E°ell, allows you to calculate Q, the activity quotient. Knowing Q and all but one of the concentrations, allows you to calculate the unknown concentration. Another application of the Nernst equation is concentration cells. A concentration cell is an electrochemical cell in which the same chemical species are used in both cell compartments, but differing in concentration. Because the half reactions are the same, the E°ell = 0.00 V. Then simply substituting the appropriate concentrations into the activity quotient allows calculation of the actual cell potential. 

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