📚 Using Eθ Values to Predict Reaction Direction | 利用Eθ值判断反应方向
Standard electrode potentials (Eθ) provide a powerful quantitative method for predicting whether a redox reaction will proceed spontaneously under standard conditions. By comparing the Eθ values of two half-cells, chemists can determine the direction of electron flow and the overall feasibility of a reaction.
标准电极电势（Eθ）为预测氧化还原反应在标准条件下能否自发进行提供了一种强大的定量方法。通过比较两个半电池的Eθ值，化学家可以确定电子流动的方向以及反应的整体可行性。
1. What Is Standard Electrode Potential? | 什么是标准电极电势？
The standard electrode potential, Eθ, is the voltage produced by a half-cell when it is connected to the standard hydrogen electrode (SHE) under standard conditions: 298 K, 1 mol dm⁻³ solutions, and 1 atm pressure for gases. It measures the tendency of a species to gain electrons (be reduced).
标准电极电势Eθ是指，在标准条件下（298 K，溶液浓度1 mol dm⁻³，气体压力1 atm），将某半电池与标准氢电极（SHE）连接时所产生的电压。它衡量的是物质获得电子（被还原）的趋势。
The standard hydrogen electrode is assigned an Eθ value of exactly 0.00 V, with the half-reaction:
标准氢电极被指定Eθ值正好为0.00 V，其半反应为：
2H⁺(aq) + 2e⁻ ⇌ H₂(g) Eθ = 0.00 V
More positive Eθ values indicate a stronger oxidising agent; more negative values indicate a stronger reducing agent.
Eθ值越正，表示氧化剂越强；Eθ值越负，表示还原剂越强。
2. Redox Couples and Half-Cell Notation | 氧化还原电对与半电池表示
Each half-cell is written as a redox couple, for example Zn²⁺/Zn or Cu²⁺/Cu. The oxidised form appears first, then the reduced form. The corresponding half-reaction is always written as a reduction:
每个半电池都以氧化还原电对表示，例如 Zn²⁺/Zn 或 Cu²⁺/Cu。氧化型写在前面，还原型写在后面。相应的半反应总是写成还原形式：
Zn²⁺(aq) + 2e⁻ ⇌ Zn(s) Eθ = −0.76 V
Cu²⁺(aq) + 2e⁻ ⇌ Cu(s) Eθ = +0.34 V
The Eθ value is an intensive property: it does not depend on the amount of material or the number of electrons transferred.
Eθ值是强度性质：它不依赖于物质的量或转移电子数的多少。
3. The Rule: More Positive Eθ Gains Electrons | 规则：Eθ较正者获得电子
When two half-cells are connected, the half-cell with the more positive Eθ value will undergo reduction (gain electrons). The half-cell with the more negative Eθ value will undergo oxidation (lose electrons).
当两个半电池连接时，Eθ值较正的半电池将发生还原反应（获得电子）。Eθ值较负的半电池将发生氧化反应（失去电子）。
This rule is the foundation of predicting electron flow in a galvanic cell and also determines the direction of spontaneous redox reactions.
这一规则是预测原电池中电子流动的基础，也决定了自发氧化还原反应的方向。
Positive electrode (cathode): more positive Eθ → reduction
Negative electrode (anode): more negative Eθ → oxidation
4. Calculating the Overall Cell Potential | 计算电池总电动势
The standard cell potential, Eθcell, is calculated using the formula:
标准电池电动势 Eθcell 使用以下公式计算：
Eθcell = Eθ(positive electrode) − Eθ(negative electrode)
tion), where both values are the standard reduction potentials of the relevant half-cells.
也可以写成 Eθcell = Eθ(还原) − Eθ(氧化)，其中两个值均为相应半电池的标准还原电势。
For a reaction to be spontaneous under standard conditions, Eθcell must be positive.
在标准条件下，反应自发进行的条件是 Eθcell 必须为正值。
5. Worked Example: Zinc and Copper | 实例：锌与铜
Consider the reaction between zinc and copper(II) ions:
考虑锌与铜(II)离子之间的反应：
Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)
Step 1: Identify the half-reactions and their Eθ values:
步骤1：确定半反应及其Eθ值：
- Cu²⁺/Cu: Eθ = +0.34 V
- Zn²⁺/Zn: Eθ = −0.76 V
Step 2: The more positive value is Cu²⁺/Cu, so Cu²⁺ is reduced; Zn is oxidised.
步骤2：Cu²⁺/Cu的Eθ值较正，因此Cu²⁺被还原；Zn被氧化。
Step 3: Calculate Eθcell:
步骤3：计算Eθcell：
Eθcell = (+0.34) − (−0.76) = +1.10 V
Since Eθcell > 0, the reaction is spontaneous under standard conditions.
因为Eθcell > 0，该反应在标准条件下自发进行。
6. Predicting Whether a Reaction Occurs | 判断反应是否发生
To predict if a given redox reaction is feasible, write the proposed overall equation, split it into two half-reactions, look up their standard reduction potentials, and calculate Eθcell. If Eθcell is positive, the reaction is thermodynamically feasible under standard conditions.
要判断给定的氧化还原反应是否可行，写出所提议的总方程式，将其拆分为两个半反应，查表得到它们的标准还原电势，并计算Eθcell。如果Eθcell为正，则该反应在标准条件下热力学可行。
For example, can chlorine oxidise bromide ions?
例如，氯气能否氧化溴离子？
Cl₂(g) + 2e⁻ ⇌ 2Cl⁻(aq) Eθ = +1.36 V
Br₂(l) + 2e⁻ ⇌ 2Br⁻(aq) Eθ = +1.07 V
ised. Eθcell = 1.36 − 1.07 = +0.29 V, so the reaction Cl₂ + 2Br⁻ → 2Cl⁻ + Br₂ is feasible.
Cl₂的Eθ值更正，因此它被还原；Br⁻被氧化。Eθcell = 1.36 − 1.07 = +0.29 V，所以反应 Cl₂ + 2Br⁻ → 2Cl⁻ + Br₂ 是可行的。
7. Comparing Oxidising and Reducing Strength | 比较氧化剂与还原剂的强度
The Eθ value directly ranks the strength of oxidising and reducing agents. A more positive Eθ means the oxidised form is a stronger oxidising agent; the reduced form is a weaker reducing agent.
Eθ值直接排列氧化剂和还原剂的强度。Eθ越正，其氧化型是更强的氧化剂；而其还原型则是较弱的还原剂。
Consider this short list:
思考以下简表：
| Half-reaction | Eθ (V) |
| F₂(g) + 2e⁻ ⇌ 2F⁻(aq) | +2.87 |
| Cl₂(g) + 2e⁻ ⇌ 2Cl⁻(aq) | +1.36 |
| Br₂(l) + 2e⁻ ⇌ 2Br⁻(aq) | +1.07 |
| I₂(s) + 2e⁻ ⇌ 2I⁻(aq) | +0.54 |
Thus, F₂ is the strongest oxidising agent and I⁻ is the strongest reducing agent among these species. Fluorine will oxidise Cl⁻, Br⁻, and I⁻; chlorine will oxidise Br⁻ and I⁻ but not F⁻; and so on.
因此，在这些物质中，F₂是最强的氧化剂，I⁻是最强的还原剂。氟气能氧化Cl⁻、Br⁻和I⁻；氯气能氧化Br⁻和I⁻，但不能氧化F⁻；依此类推。
8. Electron Transfer Numbers Do Not Affect Direction | 转移电子数不影响方向
When using Eθ values to determine reaction direction, the number of electrons transferred in each half-reaction does not affect the sign or magnitude of Eθcell. Eθ is an intensive property, so it is not multiplied by stoichiometric coefficients.
使用Eθ值判断反应方向时，每个半反应中转移的电子数不会影响Eθcell的正负号或大小。Eθ是强度性质，因此不能乘以化学计量系数。
quantity of chemical change (Faraday’s law) or Gibbs free energy, where ΔGθ = −nF Eθcell.
然而，电子数在计算化学变化量（法拉第定律）或吉布斯自由能时非常重要，其中 ΔGθ = −nF Eθcell。
For direction prediction, simply compare the two Eθ values directly.
对于方向预测，直接比较两个Eθ值即可。
9. Conditions and the Nernst Equation | 条件与能斯特方程
Eθ values apply only under standard conditions. In real cells, concentrations, pressures, and temperature may differ. The Nernst equation allows calculation of the electrode potential under non-standard conditions:
Eθ值仅在标准条件下适用。在实际电池中，浓度、压力和温度可能不同。能斯特方程允许计算非标准条件下的电极电势：
E = Eθ − (RT/nF) ln Q
where Q is the reaction quotient, R is the gas constant, T is temperature, n is the number of electrons transferred, and F is Faraday’s constant.
其中Q是反应商，R是气体常数，T是温度，n是转移的电子数，F是法拉第常数。
A non-spontaneous reaction under standard conditions might become spontaneous at different concentrations, and vice versa. In A-Level Chemistry, most prediction exercises assume standard conditions, but you should be aware of this limitation.
在标准条件下非自发的反应，在不同浓度下可能变为自发，反之亦然。在A-Level化学中，大多数判断练习假设标准条件，但你应该意识到这一局限。
10. Common Mistakes and Exam Tips | 常见错误与考试提示
Students often make several predictable errors when using Eθ values. Avoiding these will improve accuracy in examinations.
学生在使用Eθ值时经常犯一些可预测的错误。避免这些错误将提高考试的准确性。
lf-cell; use both as reduction potentials in the formula Eθcell = Eθ(cathode) − Eθ(anode).
错误1：改变负极的符号。不要为发生氧化的半电池改变Eθ值的符号；在公式 Eθcell = Eθ(阴极) − Eθ(阳极) 中，两者都用还原电势。
Mistake 2: Multiplying Eθ by coefficients. Eθ is intensive; never multiply it by 2, 3, etc.
错误2：将Eθ乘以系数。Eθ是强度性质；绝不能乘以2、3等。
Mistake 3: Assuming positive Eθcell guarantees a fast reaction. Eθ predicts thermodynamic feasibility, not kinetics. Many feasible reactions are extremely slow.
错误3：认为Eθcell为正就保证反应迅速。Eθ预测的是热力学可行性，而不是动力学。许多可行反应极其缓慢。
Mistake 4: Ignoring states of matter. Concentrations of solids and pure liquids are taken as 1 in equilibrium expressions, and their electrode potentials are still listed.
错误4：忽略物质状态。固体和纯液体在平衡表达式中的浓度视为1，但它们的电极电势仍然列出。
11. Worked Exam-Style Problem | 考试风格例题
Use the following data to decide whether Sn²⁺ ions can reduce Fe³⁺ ions to Fe²⁺:
使用以下数据判断 Sn²⁺ 离子能否将 Fe³⁺ 离子还原为 Fe²⁺：
Fe³⁺(aq) + e⁻ ⇌ Fe²⁺(aq) Eθ = +0.77 V
Sn⁴⁺(aq) + 2e⁻ ⇌ Sn²⁺(aq) Eθ = +0.15 V
If Sn²⁺ is to reduce Fe³⁺, then Sn²⁺ must be oxidised to Sn⁴⁺, while Fe³⁺ is reduced to Fe²⁺.
如果Sn²⁺要还原Fe³⁺，那么Sn²⁺必须被氧化为Sn⁴⁺，而Fe³⁺被还原为Fe²⁺。
The relevant potentials are:
相关电势为：
- Fe³⁺/Fe²⁺: Eθ = +0.77 V (cathode, reduction)
- Sn⁴⁺/Sn²⁺: Eθ = +0.15 V (anode, oxidation)
Eθcell = 0.77 − 0.15 = +0.62 V.
Since Eθcell is positive, the reaction is feasible under standard conditions. Sn²⁺ can reduce Fe³⁺.
因为Eθcell为正，该反应在标准条件下可行。Sn²⁺可以还原Fe³⁺。
12. Summary and Final Advice | 总结与最终建议
Using Eθ values to judge reaction direction is a core skill in A-Level Chemistry. Always remember:
利用Eθ值判断反应方向是A-Level化学的核心技能。始终记住：
- The half-cell with the more positive Eθ is reduced; the other is oxidised.
- ode) − Eθ(anode); a positive value means a spontaneous reaction under standard conditions.
- Eθ is intensive; do not adjust it for stoichiometry.
- Eθ predicts feasibility, not rate; kinetic factors may prevent a reaction from occurring.
半电池中Eθ值较正者被还原；另一个被氧化。
Eθcell = Eθ(阴极) − Eθ(阳极)；正值表示标准条件下反应自发。
Eθ是强度性质；不要因化学计量而调整它。
Eθ预测可行性，而非速率；动力学因素可能阻止反应发生。
Master these rules, practise with past exam questions, and you will handle any electrode potential problem confidently.
掌握这些规则，练习过去的考试题目，你就能自信地处理任何电极电势问题。
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