Number of electrons involved

A selected list of redox indicators will be found in Table 8.26. A redox indicator should be selected so that its if" is approximately equal to the electrode potential at the equivalent point, or so that the color change will occur at an appropriate part of the titration curve. If n is the number of electrons involved in the transition from the reduced to the oxidized form of the indicator, the range in which the color change occurs is approximately given by if" 0.06/n volt (V) for a two-color indicator whose forms are equally intensely colored. Since hydrogen ions are involved in the redox equilibria of many indicators, it must be recognized that the color change interval of such an indicator will vary with pH. 

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). 

Faraday s Law the quantity of charge (Q) passed in an electrochemical reaction is directly proportional to the number of moles (n) of substance reacted. Thus Q = zFn, where z is the number of electrons involved in one molecule of the reaction and F is the Faraday constant. 

The amounts of different substances liberated or dissolved by the same quantity of electricity are proportional to their relative atomic (or molar) masses divided by the number of electrons involved in the respective electrode... 

Coulometric analysis is an application of Faraday s First Law of Electrolysis which may be expressed in the form that the extent of chemical reaction at an electrode is directly proportional to the quantity of electricity passing through the electrode. For each mole of chemical change at an electrode (96487 x n) coulombs are required i.e. the Faraday constant multiplied by the number of electrons involved in the electrode reaction. The weight of substance produced or consumed in an electrolysis involving Q coulombs is therefore given by the expression... 

Here p is the coordination number of the complex ion formed, Xb is the ligand and n is the number of electrons involved in the electrode reaction. The concentration of the complex ion does not enter into equation (15), so that the observed half-wave potential will be constant and independent of the concentration of the complex metal ion. Furthermore, the half-wave potential is more negative the smaller value of Kinstabi, i.e. the more stable the complex ion. The half-wave potential will also shift with a change in the concentration... 

A more general and fundamental view is obtained by a consideration of (a) the number of electrons involved in the partial ionic equation representing the reaction, and (b) the change in the oxidation number of a significant element in the oxidant or reductant. Both methods will be considered in some detail. 

At the end of the paper, condensed tables of the higher approximations have been carried out with respect to atomic and molecular systems. For atoms, the tables are arranged after the number of electrons involved, which means that, e.g., N = 2 refers to the series of He-like ions H", He, Li+, Be2+, etc. For molecules, there is a table for H2 a table for other simple molecules (LiH, BeH+, H20, NH3, etc.) with all or almost all electrons treated, and finally a special table for the n electron systems in the two latter cases, the references to the best SCF data available are also contained for comparison. 

See also Oxidation, Reduction). Some dissolved substances in water occur either in an oxidized or a reduced form, and their state can be changed by either the acquisition of electrons (reduction) or the loss of electrons (oxidation). This transfer system is an reduction-oxidation system, or redox. (Red. - Oxid. n+ = ne—, where n is number of electrons involved), and can be used to measure and... 

The results of such predictions can be summarized according to whether the number of electrons involved in the cyclic process is of the form 4n or 4n -h 2 (where n is any... 

The distances and angles of the model compound are W=0 = 1.76 A, Os-0 = 2.2 A, and W=0 Os = 93°. The similarity in the stereochemistry of the two heterobinuclear centers raises the possibility that, in the unready Ni-A form, the Ni center is double-bonded to an 0X0 ligand. This would explain why the activation is very slow unless the temperature of the reaction is raised (72). This notion (or idea) could be tested by quantitating the number of electrons involved in the Ni-A Ni-SI transition. 

Here, m is the number of electrons involved in the change, Rq the initial bond distance, and N the number of ligand atoms bonded to the metal. Covalent as well as electrostatic theories suggest that n 5. Note that for both A and /, the values appropriate for the initial state of bond length Rq should be employed. 

Before summing the two foregoing half-equations, it is necessary to adjust the second equation by multiplying each member involved with the equation by three. This process makes the number of electrons involved in the reduction of silver equal to the number of electrons which aluminum atom contributes by oxidation. The final picture emerges as ... 

A few electrochemical reductions of formazans to hydrazidine have been reported.370,372 Ho wever, as discussed in Section 7.4.2.6, electrochemical techniques have been widely used to study the redox chemistry of tetrazolium salts and formazans. Opinions about the reversibility of the electron transfer step, the number of electrons involved, and the identity of the rate-determining step differ widely.369- 371,656 The electrochemical oxidation of some novel formazans, e.g., 215 produces the dicationic species 216 (Eq. 28). The mechanism is not clearly understood.372,373... 

In this equation, e is the actual potential and f° is the standard potential, n is the number of electrons involved, and Q is a ratio of concentration terms. Q is equal to the ratio of concentrations of products to concentrations of reactants, each raised to the power corresponding to the coefficient in the balanced chemical equation. Pure solids and liquids and the solvent water are not included in Q their effective concentrations are assumed to be 1. Gas pressures in atmospheres are used instead of concentrations. For a general reaction... 

In any fast multielectron transfer reaction all the electrons cannot be transferred in one step but only by a succession of single-electron transfer steps, whereas Eq. (6) was arrived at by Devanathan31 for the simple case in which it is assumed that the same step is rate determining in both directions, irrespective of the number of electrons involved in the reaction. 

Provided the reaction is, in some sense, reversible, so that equilibrium can be attained, and provided the reactants and products arc all gas-phase, solution or solid-state species with well-defined free energies, it is possible to define the free energies for all such reactions under any defined reaction conditions with respect to a standard process this is conventionally chosen to be the hydrogen evolution/oxidation process shown in (1.11). The relationship between the relative free energy of a process and the emf of a hypothetical cell with the reaction (1.11) as the cathode process is given by the expression AC = — nFE, or, for the free energy and potential under standard conditions, AG° = — nFEl where n is the number of electrons involved in the process, F is Faraday s constant and E is the emf. 

An immediate consequence of Eqn. 11.17 is that Eqn. II.5 is also valid when pi represents number of VAOs (Def. 11.17) rather than number of A —A bonds (Def. II.9). This limitation implies that the total number of electrons involved in A—A bonds (Def. II.3) equals the total number of VAOs used in the construction of the A—A MOs (Def. 11.17). The discussion of Eqn. 11.17 can be continued along one of two lines, depending on the value of n. ... 

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