📚 Using Eθ Values | 标准电极电势的应用
Standard electrode potential (Eθ) is a fundamental concept in redox chemistry. It tells us how easily a species is reduced relative to the standard hydrogen electrode (SHE). This article explores how to use Eθ values to predict reaction feasibility, calculate cell potentials, and understand redox behaviour.
标准电极电势（Eθ）是氧化还原化学中的基础概念。它表示某物种相对于标准氢电极（SHE）被还原的难易程度。本文将探讨如何利用Eθ值预测反应可行性、计算电池电势以及理解氧化还原行为。
1. Understanding Standard Electrode Potential | 理解标准电极电势
Eθ is measured under standard conditions: 298 K, 1 atm for gases, and 1 mol dm⁻³ for solutions. The half-cell reaction is always written as a reduction: Mⁿ⁺ + n e⁻ → M. A positive Eθ means the half-cell more readily accepts electrons than the SHE.
Eθ是在标准条件下测得的：298 K，气体为1 atm，溶液浓度为1 mol dm⁻³。半电池反应总是写成还原形式：Mⁿ⁺ + n e⁻ → M。正的Eθ表示该半电池比标准氢电极更容易接受电子。
The standard hydrogen electrode is assigned a value of 0.00 V. It uses H⁺(aq, 1 mol dm⁻³) and H₂(g, 1 atm) at a platinum electrode.
标准氢电极被指定为0.00 V。它利用H⁺(aq, 1 mol dm⁻³)和H₂(g, 1 atm)，并采用铂电极。
2. Calculating Standard Cell Potential | 计算标准电池电势
The EMF (electromotive force) of an electrochemical cell is given by the difference in electrode potentials of the two half-cells. The convention is:
电化学电池的电动势（EMF）是两个半电池电极电势之差。约定为：
Eθcell = Eθcathode − Eθanode
The cathode is where reduction occurs and the anode where oxidation occurs. Always subtract the anode potential from the cathode potential, not the other way round.
阴极发生还原，阳极发生氧化。始终用阴极电势减去阳极电势，顺序不能颠倒。
For example, for the Daniell cell with Cu²⁺/Cu (Eθ = +0.34 V) and Zn²⁺/Zn (Eθ = −0.76 V), the cathode is copper and the anode is zinc:
例如，在丹尼尔电池中，Cu²⁺/Cu（Eθ = +0.34 V）和Zn²⁺/Zn（Eθ = −0.76 V），阴极为铜，阳极为锌：
Eθcell = (+0.34) − (−0.76) = +1.10 V
3. Predicting Spontaneity of Redox Reactions | 预测氧化还原反应的自发性
If Eθcell is positive, the reaction is thermodynamically feasible (spontaneous). If it is negative, the reaction will not occur under standard conditions without external energy input.
如果Eθcell为正，反应在热力学上是可行的（自发）。若为负，则在标准条件下不发生反应，除非有外部能量输入。
The more positive the Eθ, the stronger the driving force for the reaction. For example, the reaction between zinc and copper(II) sulphate gives Eθcell = +1.10 V, hence it occurs readily.
Eθ越正，反应的驱动力越强。例如，锌与硫酸铜的反应产生Eθcell = +1.10 V，因此很容易发生。
However, a positive Eθ only indicates thermodynamic feasibility. It does not guarantee a fast reaction; kinetic factors may make the reaction slow or non‑observable.
然而，正的Eθ只表明热力学可行性，并不保证反应速度快；动力学因素可能使反应缓慢或难以观察。
4. Comparing Oxidising and Reducing Agents | 比较氧化剂和还原剂的强弱
A species with a more positive Eθ is a stronger oxidising agent (it readily gains electrons). Its conjugate (the reduced form) is a weaker reducing agent. Conversely, a more negative Eθ indicates a stronger reducing agent.
Eθ越正的物种是更强的氧化剂（容易获得电子），其共轭还原形态是较弱的还原剂。相反，Eθ越负则表示还原剂越强。
For example, F₂/F⁻ has Eθ = +2.87 V, so F₂ is a very strong oxidising agent. Li⁺/Li has Eθ = −3.04 V, so Li is a very strong reducing agent.
例如，F₂/F⁻的Eθ = +2.87 V，所以F₂是非常强的氧化剂。Li⁺/Li的Eθ = −3.04 V，所以Li是非常强的还原剂。
This allows us to predict whether an oxidant can oxidise a given reductant: it will if Eθ(oxidant) > Eθ(reductant). The overall cell potential is then positive.
这使我们能够预测氧化剂能否氧化给定的还原剂：如果Eθ(氧化剂) > Eθ(还原剂)，则氧化反应可以发生，此时总电池电势为正。
5. Thermodynamic Relationship: ΔG° and Eθ | 热力学关系：ΔG°与Eθ
The standard free energy change ΔG° is related to Eθcell by the equation:
标准自由能变化ΔG°与Eθcell的关系式为：
ΔG° = − n F Eθcell
Here, n is the number of electrons transferred per mole of reaction, and F is the Faraday constant (96 500 C mol⁻¹). This equation links electrical potential to thermodynamic spontaneity.
其中n是每摩尔反应转移的电子数，F是法拉第常数（96 500 C mol⁻¹）。该方程将电势与热力学自发性联系起来。
A positive Eθ gives a negative ΔG°, confirming spontaneity. For example, if Eθcell = +0.30 V and n = 2, then ΔG° = −(2 × 96 500 × 0.30) = −57 900 J mol⁻¹ = −57.9 kJ mol⁻¹.
正的Eθ得到负的ΔG°，证实反应自发。例如，若Eθcell = +0.30 V且n = 2，则ΔG° = −(2 × 96 500 × 0.30) = −57 900 J mol⁻¹ = −57.9 kJ mol⁻¹。
6. Using Eθ to Determine Equilibrium Constant K | 利用Eθ求平衡常数K
The equilibrium constant K for a redox reaction can be found from the Nernst equation at equilibrium. At standard conditions, the relationship is:
氧化还原反应的平衡常数K可以通过能斯特方程在平衡状态下求得。在标准条件下，关系式为：
ln K = n F Eθcell / (R T)
where R is the gas constant (8.31 J K⁻¹ mol⁻¹) and T is the temperature in kelvin. At 298 K, this simplifies to:
其中R是气体常数（8.31 J K⁻¹ mol⁻¹），T是开尔文温度。在298 K时，可简化为：
log₁₀ K = n Eθcell / 0.0592
For a reaction with n = 1 and Eθcell = +0.46 V, log₁₀ K = 0.46 / 0.0592 ≈ 7.77, so K ≈ 5.9 × 10⁷. This large K indicates that the reaction lies far to the right.
对于n = 1且Eθcell = +0.46 V的反应，log₁₀ K = 0.46 / 0.0592 ≈ 7.77，所以K ≈ 5.9 × 10⁷。如此大的K值表明反应高度向右侧进行。
7. Disproportionation Reactions | 歧化反应
In a disproportionation reaction, a single species is both oxidised and reduced. Whether this occurs can be predicted using Eθ values for the two relevant half-reactions.
在歧化反应中，同一物种既被氧化又被还原。能否发生歧化可以通过两个相关半反应的Eθ值来预测。
Take copper(I) in aqueous solution. The two half-reactions are:
以水溶液中的铜(I)为例。两个半反应为：
- Cu⁺ + e⁻ → Cu, Eθ = +0.52 V
- Cu²⁺ + e⁻ → Cu⁺, Eθ = +0.15 V
For disproportionation: 2 Cu⁺ → Cu + Cu²⁺. The overall cell potential is Eθ(reduction of Cu⁺ to Cu) − Eθ(reduction of Cu²⁺ to Cu⁺) = 0.52 − 0.15 = +0.37 V. Since it is positive, Cu⁺ is unstable and disproportionates in aqueous solution.
对于歧化反应：2 Cu⁺ → Cu + Cu²⁺。总电池电势为Eθ(Cu⁺还原为Cu) − Eθ(Cu²⁺还原为Cu⁺) = 0.52 − 0.15 = +0.37 V。由于为正值，Cu⁺在水溶液中不稳定，会发生歧化。
In this calculation, the half‑reaction with the more positive Eθ is the cathode (reduction), and the other is the anode (oxidation).
在此计算中，Eθ更正的反应作为阴极（还原），另一个作为阳极（氧化）。
8. Limitations of Eθ Values | Eθ值的局限性
Eθ values are measured under standard conditions, which may not reflect actual laboratory or industrial conditions. Concentration changes alter the potential according to the Nernst equation.
Eθ值是在标准条件下测定的，可能无法反映实际实验室或工业条件。浓度变化会根据能斯特方程改变电势。
pH can significantly affect half‑cells involving H⁺ or OH⁻. For example, the reduction of MnO₄⁻ to Mn²⁺ depends on [H⁺]. At pH 7, the effective potential is lower than the standard value.
pH对涉及H⁺或OH⁻的半电池影响显著。例如，MnO₄⁻还原为Mn²⁺取决于[H⁺]。在pH 7时，实际电势低于标准值。
Complexation and precipitation can change the species present and hence alter Eθ. The formation of a stable complex may make a redox couple less oxidising.
配位和沉淀会改变存在的物种，从而影响Eθ。稳定配合物的形成可能使氧化还原电对的氧化性减弱。
Finally, Eθ only predicts thermodynamic feasibility. Many reactions with positive Eθ are slow due to high activation energy, e.g., the reaction between Mg and water.
最后，Eθ仅预测热力学可行性。许多具有正Eθ的反应因高活化能而缓慢，例如镁与水的反应。
9. Worked Examples | 例题分析
Example 1: The reaction of Fe³⁺ with I⁻. Given Eθ(Fe³⁺/Fe²⁺) = +0.77 V and Eθ(I₂/I⁻) = +0.54 V. To see if Fe³⁺ oxidises I⁻, treat Fe³⁺ reduction as cathode and I⁻ oxidation as anode.
例1：Fe³⁺与I⁻的反应。已知Eθ(Fe³⁺/Fe²⁺) = +0.77 V，Eθ(I₂/I⁻) = +0.54 V。要判断Fe³⁺能否氧化I⁻，把Fe³⁺的还原作为阴极，I⁻的氧化作为阳极。
Eθcell = 0.77 − 0.54 = +0.23 V. The reaction is feasible: 2Fe³⁺ + 2I⁻ → 2Fe²⁺ + I₂.
Eθcell = 0.77 − 0.54 = +0.23 V。反应可行：2Fe³⁺ + 2I⁻ → 2Fe²⁺ + I₂。
Example 2: Choosing a reductant. Which of Cl⁻, Br⁻, or I⁻ can reduce Fe³⁺? The potentials for oxidation of halides are: Cl₂/Cl⁻ = +1.36 V, Br₂/Br⁻ = +1.07 V, I₂/I⁻ = +0.54 V. Fe³⁺/Fe²⁺ = +0.77 V. Only I⁻ can reduce Fe³⁺ because the I⁻ oxidation potential is less than +0.77 V, giving a positive cell potential.
例2：选择合适的还原剂。Cl⁻、Br⁻、I⁻中哪一种能还原Fe³⁺？各卤化物氧化电势：Cl₂/Cl⁻ = +1.36 V，Br₂/Br⁻ = +1.07 V，I₂/I⁻ = +0.54 V。Fe³⁺/Fe²⁺ = +0.77 V。只有I⁻能还原Fe³⁺，因为I⁻的氧化电势小于+0.77 V，使得电池电势为正。
10. Applications in Batteries and Corrosion | 在电池与腐蚀中的应用
Eθ values help in designing batteries. A larger positive Eθcell means a higher maximum voltage. For example, the lithium‑ion cell has a high Eθ due to the very negative potential of lithium.
Eθ值有助于设计电池。Eθcell更正意味着最大电压更高。例如，锂离子电池因锂的极负电势而具有高Eθ。
Corrosion of iron is an electrochemical process. Using Eθ, we can understand why zinc protects iron (sacrificial protection): zinc has a more negative Eθ (−0.76 V) than iron (−0.44 V), so zinc is oxidised preferentially.
铁的腐蚀是一个电化学过程。利用Eθ，我们能够理解为什么锌可以保护铁（牺牲阳极保护）：锌的Eθ（−0.76 V）比铁（−0.44 V）更负，因此锌优先被氧化。
In a typical rusting reaction, oxygen (Eθ = +1.23 V for O₂/OH⁻) and iron (Eθ = −0.44 V) give a cell potential of about +1.67 V, which is why rusting is thermodynamically spontaneous.
在典型的生锈反应中，氧气（O₂/OH⁻的Eθ = +1.23 V）和铁（Eθ = −0.44 V）产生的电池电势约为+1.67 V，因此生锈在热力学上是自发的。
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