Faraday 2-form equation

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... 

M. Faraday was the first to observe an electrocatalytic process, in 1834, when he discovered that a new compound, ethane, is formed in the electrolysis of alkali metal acetates (this is probably the first example of electrochemical synthesis). This process was later named the Kolbe reaction, as Kolbe discovered in 1849 that this is a general phenomenon for fatty acids (except for formic acid) and their salts at higher concentrations. If these electrolytes are electrolysed with a platinum or irridium anode, oxygen evolution ceases in the potential interval between +2.1 and +2.2 V and a hydrocarbon is formed according to the equation... 

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. 

Standard addition. A particular COz compound electrode like the one in Figure 15-22 obeys the equation E = constant — [p/ T (In 10)/2F log[C02], where R is the gas constant, T is temperature (303.15 K), F is the Faraday constant, and P = 0.933 (measured from a calibration curve). [C02] represents all forms of dissolved carbon dioxide at the pH of the experiment, which was 5.0. Standard additions of volume Vs containing a standard concentration cs = 0.020 0 M NaHC03 were made to an unknown solution whose initial volume was V0 = 55.0 mL. 

Equation 14 is a form of the Nemst equation. The overall chemical reaction for the passage of 2 Faradays of charge in the external circuit from right to left... 

An electron transfer reaction, Equation 6.6, is characterised thermodynamically by the standard potential, °, i.e. the value of the potential at which the activities of the oxidised form (O) and the reduced form (R) of the redox couple are equal. Thus, the second term in the Nernst equation, Equation 6.7, vanishes. Here and throughout this chapter n is the number of electrons (for organic compounds, typically, n = 1), II is the gas constant, T is the absolute temperature and F is the Faraday constant. Parentheses, ( ), are used for activities and brackets, [ ], for concentrations /Q and /R are the activity coefficients of O and R, respectively. However, what may be measured directly is the formal potential E° defined in Equation 6.8, and it follows that the relationship between E° and E° is given by Equation 6.9. Usually, it maybe assumed that the activity coefficients are unity in dilute solution and, therefore, that E° = E°. 

Control of Potential and Measurement of Current. With the formulation of the laws of electrolysis by Michael Faraday in 1834, the basis for relating electrolysis currents to chemical quantities was established. Although the concept of electrolysis was known prior to then, its utility in terms of chemical analysis depended on a quantitative relationship between current and equivalents of substance. Because an electrolysis current always necessitates mass transfer to or away from the electrode, the formulation of equations for diffusion by Fick was an important event in developing quantitative relationships.1 With the laws of electrolysis and diffusion established, Heyrovsky combined these in a preferred form to provide a practical analytical method, namely, polarography.2 His real contribution beyond combining the important concepts of Faraday and Fick was to realize that a reproducible and continuously renewed... 

Here F is the Faraday, kc and kc the heterogeneous rate constants for electron transfer in either direction, cM and cM- are the concentrations of the electroactive species M and its electronated form M, (x is the transfer coefficient, and eq is the potential difference across the interface at equilibrium. This equilibrium potential is given by the Nernst equation,... 

To transform Equation 6.3 into a more useful form, we need to incorporate expressions for the chemical potentials of the species involved. The chemical potential of species j was presented in Chapter 2 (Section 2.2B), where Xj is a linear combination of various terms fij = fi + RT In cij +VjP -f ZjFE 4- mjgh (Eq. 2.4 fi is a constant, cij is the activity of species /, Vj is its partial molal volume, P is the pressure in excess of atmospheric, Zj is its charge number, Fis Faraday s constant, E is the electrical potential, m is its mass per mole, and h is the vertical position in the gravitational field). 

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