Reaction-current equation

In simplified electrode models, the irreversible reaction pathway is typically represented by a resistor Ri. The resistor denotes that charge is consumed and not stored. However, the pathway actually behaves more like a diode. The reaction-current equation is described approximately by ... 

There are 250 g of Pb02, and the headlights draw 5.9 A of current. Equation links current with moles of electrons. Moles of electrons and moles of Pb02 are related as described by the balanced half-reaction, determined in Example ... 

The Gibbs-Helmholtz equation also links the temperature coefficient of Galvani potential for individual electrodes to energy effects or entropy changes of the electrode reactions occurring at these electrodes. However, since these parameters cannot be determined experimentally for an isolated electrode reaction (this is possible only for the full current-producing reaction), this equation cannot be used to calculate this temperature coefficient. 

This equation describes the cathodic current-potential curve (polarization curve or voltammogram) at steady state when the rate of the process is simultaneously controlled by the rate of the transport and of the electrode reaction. This equation leads to the following conclusions ... 

For a number of flow situations, the mass-transfer rate can be derived directly from the equation of convective diffusion (see Table VII, Part A). The velocity profile near the electrode is known, and the equation is reduced to a simpler form by appropriate similarity transformations (N6). These well-defined flows, therefore, are being exploited increasingly by electrochemists as tools for the kinetic characterization of electrode reactions. Current distributions at, or below, the limiting current, transient mass transfer, and other aspects of these flows are amenable to analysis. Especially noteworthy are the systematic investigations conducted by Newman (review until 1973 in N7 also N9b, N9c, H6b and references in Table VII), by Daguenet and other French workers (references in Table VII), and by Matsuda (M4a-d). Here we only want to comment on the nature of the velocity profile near the electrode, and on the agreement between theory and mass-transfer experiment. 

The experiments were performed at 25°C, where the adsorption of both forms of hydride was assumed to follow the Langmuir isotherm. Thus, the current for the forward (cathodic) and reverse (anodic) reactions in equation (3.3) can be written as ... 

In this notation, anodic current is positive, while cathodic current is negative. As the later section on oxygen reduction will show, the Tafel slope can change with overpotential. This is because the Butler-Volmer law only applies to outer-sphere reactions. Although it can describe electrode reactions, the equation does not account for repulsive interactions of the adsorbates or changes in the reaction mechanism as potential is changed. 

Combination of equations (6.9) to (6.12) leads to the final expression of the current [equation 1.58)], which is therefore exactly the same in the presence and absence of the disproportionation reaction, provided that the diffusion coefficients of the three species are the same. The individual fluxes and concentration profiles are different, however, as exemplified in Figure 6.3. 

These reaction currents given by Eqns. 7-32 and 7-33 are formally in agreement with the Tafel equation of Eqn. 7-19 obtained by experimental observations. Note that the rate equations in Eqns. 7-32 and 7-33 apply to the forward reaction only and disregard the backward reaction rate. 

Introducing Eqn. 8-17 into Eqn. 8-20, we obtain Eqn. 8—21 as an approximate equation for the exchange reaction current io ... 

The transfer currents of redox electrons and redox holes represented by Eqns. 8-63 and 8-64 are formally in agreement with the Tafel equation given by Eqn. 7-32. However, the Tafel constant (the transfer coefficient) a equals one or zero at semiconductor electrodes in contrast with metal electrodes at which a is close to 0.5. From Eqns. 8-64 and 8-65 for reaction currents, the Tafel constants is obtained as defined in Eqns. 8-66 and 8-67 ... 

We now consider a cathodic transfer of electrons from the conduction band of electrode to the vacant redox electron level in a hydrated oxidant particle to form a hydrated reductant particle in solution OX , + ecB- RED . Equation 8-72 expresses this reaction current, due to the direct transfer of electrons from the conduction band to the oxidant particle based on Eqn. 8-61 as follows ... 

In the range of potential away from the equilibrium potential, the backward reaction current can be disregarded, and the anodic and the cathodic reaction currents are expressed, respectively, by the Tafel equations described in Eqn. 9-11 ... 

Equation 10-48 is obtained by excluding the photocurrent ipb from the reaction current of Eqn. 10-44. In the stationary state, the total ciurent i in Eqn. 10-48 equals the transfer current of cathodic redox holes across the electrode interface. 

The simple, salt elimination reaction of Equation (8.1) has been employed for amides of all the group 13 metals. In addition, it is currently the only well-established route to M(I) metal amides where M = Ga or Tl. The alkane elimination route of eqn. (8.2) is generally employed only for M = Al or Ga. This synthetic approach is also used for the metal imides (RMNR )n where a primary amine H2NR is the reactant. The use of metal hydrides, of which Equation (8.3) is but one example, is limited mainly to aluminium and, to a lesser extent, gallium because of the decreased stability of the heavier metal hydrides. 

The actual current passed / = 2F/4Jt,[H + ]exp[ — J pAE] since two electrons are transferred for every occurrence of reaction I. Equation (1.64) constitutes the fundamental kinetic equation for the hydrogen evolution reaction (her) under the conditions that the first reaction is rate limiting and that the reverse reaction can be neglected. From this equation, we can calculate the two main observables that can be measured in any electrochemical reaction. The first is the Tafel slope, defined for historical reasons as ... 

Schuldiner (1959) studied the effect of Hi pressure on the hydrogen evolution reaction at bright (polished) Pt in sulphuric acid. The mechanism of the reaction was assumed to be as in equations (3.3) and (3.4). The step represented by equation (3.3) was assumed to be at equilibrium at all potentials and equation (3.4) represented the rate-determining step. The potentials were measured as overpotentials with respect to the hydrogen potential, i.e. the potential of the H +/H2 couple in the solution (0 V vs. RHE). The experiments were performed at 25CC, where the adsorption of both forms of hydride was assumed to follow the Langmuir isotherm. Thus, the current for the forward (cathodic) and reverse (anodic) reactions in equation (3.3) can be written as ... 

Table 23.1 reproduces data affected by breakdown of linear diffusion for the one-electron reduction of Cp2Rh at a Pt disk electrode (r = 2 mm). At sweep rates above about 0.1 V/s, the current function is essentially constant, consistent with the simple one-electron reaction of Equation 23.8. The increase of over 10% in X that is observed at lower scan rates arises from the breakdown of linear diffusion, rather than from additional reactions coupled to Equation 23.8. The radial diffusion contribution is less than 3% [5], with convection accounting for most of the additional mass transport. 

The detrimental consequence of liquid water on the CL voltage loss primarily comes from the impeded oxygen transport and reduced electrochemically active area as explained above which can be described by the electrochemical kinetics in terms of the reaction current density,/, through the Tafel equation.27... 

Electrochemical carbocyclization reactions involving the preparation of 3-, 4-, 5-, or 6-membered rings have been described. The reaction involves complexing of olefinic compounds, such as dimethyl maleate 126 and a,co-dibromide, such as 1,3-dibromopropane 127 in an undivided cell fitted with a sacrificial aluminum anode, in A-methylpyrrolidone at constant current (equation 66)99. The reaction is of special interest for the preparation... 

It remains to consider whether oxidation of the adsorbed COadS or =C-OHads is taking place through H20 or OHads. This has proved a thorny issue, partly because of the sensitivity of the process to surface morphology and to the formation conditions of the adsorbed monolayer itself, but also because kinetic analysis has given ambiguous answers. In principle, both Tafel slope and pH dependence should differ for reactions (18.13) and (18.14) above, but whilst Bagotzky and Vassiliev s data [5] are most naturally interpreted in terms of reaction (14) above, the current equation derived from the studies of Inada et al. [93], i CMeOHcH 6 exp(0.6FE/RT)... 

In many cases Eq. (6) is called the Butler-Volmer equation since it describes the case when the charge-transfer step exclusively determines the rate of the reaction (current), i.e., the rate of mass transport is very high in comparison with the rate of the charge transfer. 

In order to understand the origin of the mixed corrosion potential, we must utilize mixed potential theory and the Cu/Cu system as an example. A Cu/Cu system is removed from the equilibrium given by Equation. (4.34) by the application of a driving force or an overpotential, t]. The application of an overpotential results in the system attempting to return to equilibrium by driving reaction (4.23) either in the reverse direction, for a positive overpotential, or in the forward direction, for a negative overpotential. Because electrochemical reactions involve the flow of electrons, the reaction rate may be considered as a reaction current or current density. The reaction current is the rate at which electrons flow from the site of the anodic reaction to the site of the cathodic reaction. The rate at which the reaction proceeds is determined by kinetics, and the magnitude of the overpotential which is related to the reaction current density by ... 

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