The rate laws

A first-order heterogeneous rate law has the form Product flux = k[species] where [species] is the molar concentration of the relevant species in solution close to the electrode, just outside the double layer. The rate constant has dimensions of length/time (with units, for example, of centimetres per second, cm s⁻¹). If the molar concentrations of the oxidized and reduced materials outside the double layer are [Ox] and [Red], respectively, then the rate of reduction of O_x, v_Ox, is vOx =kc [Ox] and the rate of oxidation of Red, v_Red, is v_Red = ka [Red] (The notation kc and ka is justified below.) Now consider a reaction at the electrode in which an ion is reduced by the transfer of a single electron in the rate-determining step. For instance, in the deposition of cadmium only one electron is transferred in the rate-determining step even though overall the deposition involves the transfer of two electrons. The net current density at the electrode is the difference between the current densities arising from the reduction of Ox and the oxidation of Red. Because the redox processes at the electrode involve the transfer of one electron per reaction event, the current densities, j, arising from the redox processes are the rates (as expressed above) multiplied by the charge transferred per mole of reaction, which is given by Faraday’s constant. Therefore, there is a cathodic current density of magnitude j_c = Fk_c[Ox] for   Ox +e⁻→Red arising from the reduction (because, as we saw in Chapter 7, the cathode is the site of reduction). There is also an opposing anodic current density of magnitude j_a = Fk_a [Red] for Red →Ox+e⁻ arising from the oxidation (because the anode is the site of oxidation). The net current density at the electrode is the difference j = ja − jc = Fka[Red] − Fkc[Ox] Note that, when ja > jc, so that j > 0, the current is anodic (Fig. 25.35a); when jc > ja, so that j < 0, the current is cathodic (Fig. 25.35b).

Fig. 25.36 The potential, φ, varies linearly between two plane parallel sheets of charge, and its effect on the Gibbs energy of the transition state depends on the extent to which the latter resembles the species at the inner or outer planes.

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مواضيع ذات صلة

Units

Names of quantities

Working galvanic cells

Electrolysis

Experimental techniques

The electric potential at the interface

The structure of the interface

Catalytic activity at surfaces

Mechanisms of heterogeneous catalysis

Mobility on surfaces

The rate of desorption

The rate of adsorption