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# 物理代写|电化学代写Electrochemical代考|E6050 Factors Affecting Electrode Reaction Rate and Current

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## 物理代写|电化学代写Electrochemical代考|Factors Affecting Electrode Reaction Rate and Current

Consider an overall electrode reaction, $\mathrm{O}+n e \rightleftharpoons \mathrm{R}$, composed of a series of steps that cause the conversion of the dissolved oxidized species, $\mathrm{O}$, to a reduced form, $\mathrm{R}$, also in solution (Figure 1.2.6). In general, the current (or electrode reaction rate) is governed by the rates of processes such as $(1,2)$ :

Mass transfer (e.g., of $\mathrm{O}$ from the bulk solution ${ }^{25}$ to the electrode surface).

Electron transfer at the electrode surface.

Chemical reactions preceding or following the electron transfer. These might be homogeneous processes (e.g., protonation or dimerization) or heterogeneous reactions on the electrode surface (e.g., catalytic decomposition).

Other surface reactions, such as adsorption, desorption, or crystallization.
The rate constants for some of these processes (e.g., electron transfer at the electrode surface or adsorption) depend upon the potential.

The simplest reactions involve only mass transfer of a reactant to the electrode, heterogeneous electron transfer involving nonadsorbed species, and mass transfer of the product to the bulk solution. A representative reaction of this sort is the reduction of the aromatic hydrocarbon 9,10-diphenylanthracene (DPA; Figure 1) to the radical anion (DPA $\bar{*}$ ) in an aprotic solvent [e.g., $N, N$-dimethylformamide (DMF)]. More complex reaction sequences are quite common. They may involve almost any kind of chemistry, including a series of electron transfers, coupling reactions in solution, protonations, branching mechanisms, parallel paths, or modifications of the electrode surface.

## 物理代写|电化学代写Electrochemical代考|Mass-Transfer-Controlled Reactions

Let us now become more quantitative about the sizes and shapes of current-potential curves. We must be able to describe the rate of reaction at the electrode surface if we are to understand $i$.
In the simplest electrode reactions, the participants are chemically stable, and the rates of all associated chemical reactions are very rapid compared to those of the mass-transfer processes.

We will find in Chapters 3 and 5 that if an electrode reaction involves only fast heterogeneous charge-transfer kinetics and mobile, reversible homogeneous reactions, then

• The homogeneous reactions can be regarded as being at equilibrium.
• The surface concentrations of species involved in the faradaic process are related to the electrode potential by an equation of the Nernst form.

Such electrode reactions are called reversible or nernstian, because the principal species obey thermodynamic relationships at the electrode surface.

In nernstian systems, the net rate of the electrode reaction is governed totally by the rate at which the electroreactant is brought to the surface by mass transfer, $v_{\mathrm{mt}}\left(\mathrm{mol} \mathrm{cm}^{-2} \mathrm{~s}^{-1}\right)$. From (1.1.15), ${ }^{27}$
$$v_{\mathrm{mt}}=\pm i / n F A \quad \text { (+ for a reduction, – for an oxidation) }$$
Since mass transfer plays a big role in electrochemical dynamics, we will next review its three modes and then consider mathematical methods for treating them.

## 物理代写|电化学代写电化学代考|传质控制反应

• 均相反应可视为处于平衡。

$$v_{\mathrm{mt}}=\pm i / n F A \quad \text { (+ for a reduction, – for an oxidation) }$$

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