Electrode Potentials & Electrochemical Cells | A-Level Chemistry 电极电势与电化学电池

Electrode Potentials and Electrochemical Cells — A Complete A-Level Guide

Electrode potentials and electrochemical cells are fundamental concepts in A-Level Chemistry that bridge thermodynamics and electricity. Understanding how chemical reactions can generate electrical energy — and how electrical energy can drive chemical reactions — is essential for mastering topics ranging from redox chemistry to industrial electrolysis. This guide covers everything you need for A-Level success, from standard hydrogen electrodes to the feasibility of reactions using E^⦵ values.

1. What Are Electrode Potentials?

An electrode potential is the voltage produced when a metal is dipped into a solution containing its own ions. This potential arises from the equilibrium established at the metal/solution interface:

M(s) ⇌ Mⁿ⁺(aq) + ne⁻

When a metal is placed in a solution of its ions, two competing processes occur: metal atoms can lose electrons and enter the solution as ions (oxidation), or metal ions in solution can gain electrons and deposit onto the metal surface (reduction). The position of this equilibrium determines the magnitude and sign of the electrode potential.

Consider zinc in ZnSO₄ solution:

• Zinc atoms tend to lose electrons more readily → oxidation favoured → negative electrode potential
• The solution becomes positively charged relative to the metal
• An electrical double layer forms at the interface

For copper in CuSO₄ solution, the equilibrium lies further to the right (reduction side), giving copper a positive electrode potential. The more reactive the metal, the more negative its electrode potential.

1. 什么是电极电势？

电极电势是当金属浸入含有其自身离子的溶液时产生的电压。这一电势源于金属/溶液界面建立的平衡状态。

当金属置于其离子溶液中时，两个竞争过程同时发生：金属原子可以失去电子进入溶液（氧化），或者溶液中的金属离子获得电子沉积在金属表面（还原）。这个平衡的位置决定了电极电势的大小和符号。

以锌在ZnSO₄溶液中为例：

• 锌原子更容易失去电子 → 反应倾向氧化 → 电极电势为负
• 溶液相对于金属带正电
• 界面形成双电层

对于铜在CuSO₄溶液中的情况，平衡更偏向还原方向，因此铜具有正的电极电势。金属越活泼，其电极电势越负。

2. The Standard Hydrogen Electrode (SHE)

Since we cannot measure the absolute potential of a single electrode, we need a reference point. The Standard Hydrogen Electrode (SHE) is assigned a potential of exactly 0.00 V under standard conditions:

• Temperature: 298 K (25°C)
• Pressure: 100 kPa (for H₂ gas)
• Concentration: 1.00 mol dm⁻³ H⁺(aq)
• Electrode: Platinum (inert, coated with platinum black to catalyse the equilibrium)

The half-cell reaction is:

2H⁺(aq) + 2e⁻ ⇌ H₂(g)     E⦵ = 0.00 V

Hydrogen gas is bubbled over a platinum electrode immersed in a solution of H⁺ ions (typically 1 mol dm⁻³ HCl or ½H₂SO₄). The platinum provides a surface for the H₂/2H⁺ equilibrium but does not participate chemically.

Any other electrode potential is measured by connecting it to the SHE in an electrochemical cell and measuring the emf. The measured voltage is the standard electrode potential (E⦵) of that half-cell, with the sign indicating whether it is more (negative) or less (positive) reducing than hydrogen.

2. 标准氢电极 (SHE)

由于我们无法测量单个电极的绝对电势，需要一个参考点。标准氢电极在标准条件下被赋予恰好 0.00 V 的电势：

• 温度：298 K (25°C)
• 压力：100 kPa（H₂气体）
• 浓度：1.00 mol dm⁻³ H⁺(aq)
• 电极：铂（惰性电极，表面镀铂黑以催化平衡反应）

半电池反应为：2H⁺(aq) + 2e⁻ ⇌ H₂(g)，E⦵ = 0.00 V。将氢气通入浸在H⁺溶液中的铂电极，铂为H₂/2H⁺平衡提供表面但不参与化学反应。

任何其他电极电势都是通过将其与SHE连接在电化学电池中并测量电动势来确定的。测得的电压即为该半电池的标准电极电势 (E⦵)，符号表示它比氢还原性更强（负值）还是更弱（正值）。

3. Measuring Standard Electrode Potentials

To measure the standard electrode potential of a Zn²⁺/Zn half-cell:

1. Set up a Zn²⁺/Zn half-cell with [Zn²⁺] = 1.00 mol dm⁻³ at 298 K
2. Connect it to the SHE using a salt bridge (typically filter paper soaked in saturated KNO₃)
3. Connect a high-resistance voltmeter between the two electrodes
4. Read the voltage

The voltmeter reading gives the cell emf (E⦵_cell), which is the difference between the two electrode potentials:

E⦵cell = E⦵(right-hand electrode) − E⦵(left-hand electrode)

Since E⦵(SHE) = 0.00 V, the measured voltage directly gives the standard electrode potential of the other half-cell:

For Zn²⁺/Zn: E⦵ = −0.76 V
For Cu²⁺/Cu: E⦵ = +0.34 V

The salt bridge is crucial — it completes the circuit by allowing ions to flow between the two half-cells while preventing the solutions from mixing directly. Without it, charge buildup would quickly stop the reaction.

3. 测量标准电极电势

测量 Zn²⁺/Zn 半电池的标准电极电势的步骤：

1. 设置 [Zn²⁺] = 1.00 mol dm⁻³ 的 Zn²⁺/Zn 半电池，温度298 K
2. 用盐桥（通常为浸泡在饱和KNO₃溶液中的滤纸条）将其与SHE连接
3. 在两个电极之间连接高电阻伏特计
4. 读取电压

伏特计读数给出电池电动势 (E⦵_cell)，即两个电极电势之差。由于 E⦵(SHE) = 0.00 V，测得的电压直接给出另一个半电池的标准电极电势。例如 Zn²⁺/Zn：E⦵ = −0.76 V；Cu²⁺/Cu：E⦵ = +0.34 V。

盐桥至关重要——它允许离子在两个半电池之间流动以完成电路，同时防止溶液直接混合。没有盐桥，电荷积累会迅速停止反应。

4. The Electrochemical Series

The electrochemical series lists half-equations in order of their standard electrode potentials, from most negative to most positive. The more negative the E⦵ value, the stronger the reducing agent (the equilibrium lies to the left, favouring oxidation). The more positive the E⦵ value, the stronger the oxidising agent (the equilibrium lies to the right, favouring reduction).

Half-Equation	E⦵ / V
Li⁺ + e⁻ ⇌ Li	−3.04
K⁺ + e⁻ ⇌ K	−2.92
Mg²⁺ + 2e⁻ ⇌ Mg	−2.37
Zn²⁺ + 2e⁻ ⇌ Zn	−0.76
Fe²⁺ + 2e⁻ ⇌ Fe	−0.44
2H⁺ + 2e⁻ ⇌ H₂	0.00
Cu²⁺ + 2e⁻ ⇌ Cu	+0.34
I₂ + 2e⁻ ⇌ 2I⁻	+0.54
Fe³⁺ + e⁻ ⇌ Fe²⁺	+0.77
Ag⁺ + e⁻ ⇌ Ag	+0.80
Br₂ + 2e⁻ ⇌ 2Br⁻	+1.07
Cl₂ + 2e⁻ ⇌ 2Cl⁻	+1.36
F₂ + 2e⁻ ⇌ 2F⁻	+2.87

Key patterns to remember:

• Reactive metals (Group 1, Group 2) have very negative E⦵ values — they are strong reducing agents
• Halogens have very positive E⦵ values — they are strong oxidising agents
• Transition metals have intermediate values, often with multiple oxidation states

4. 电化学系列

电化学系列按标准电极电势从最负到最正的顺序列出半反应方程式。E⦵ 值越负，还原剂越强（平衡偏向左，倾向氧化）；E⦵ 值越正，氧化剂越强（平衡偏向右，倾向还原）。

需要记住的关键规律：活泼金属（第1族、第2族）具有很负的E⦵值——它们是强还原剂；卤素具有很正的E⦵值——它们是强氧化剂；过渡金属具有中间值，通常有多种氧化态。

5. Predicting Reaction Feasibility Using E⦵ Values

One of the most important A-Level applications of electrode potentials is predicting whether a redox reaction is thermodynamically feasible. The rule is simple: for a reaction to be feasible, the cell emf must be positive.

E⦵cell = E⦵(reduction half-cell) − E⦵(oxidation half-cell) > 0

Worked Example: Will zinc displace copper from CuSO₄ solution?

Step 1 — Identify the half-equations:

• Zn²⁺ + 2e⁻ → Zn E⦵ = −0.76 V
• Cu²⁺ + 2e⁻ → Cu E⦵ = +0.34 V

Step 2 — Zinc is oxidised (loses electrons), copper ions are reduced:

E⦵cell = E⦵(Cu²⁺/Cu) − E⦵(Zn²⁺/Zn)
       = (+0.34) − (−0.76)
       = +1.10 V

Since E⦵_cell > 0, the reaction is feasible. Indeed, zinc metal will displace copper from solution, and the familiar observation is a colour change from blue to colourless as Cu²⁺ ions are consumed.

Important Limitation: A positive E⦵_cell only indicates thermodynamic feasibility — it says nothing about the rate of reaction. A reaction may be feasible but kinetically slow (high activation energy). For example:

2H₂O → 2H₂ + O₂    E⦵cell = −1.23 V → not feasible
2H₂ + O₂ → 2H₂O    E⦵cell = +1.23 V → feasible but kinetically slow at room temperature

5. 利用 E⦵ 值预测反应可行性

电极电势在A-Level中最重要的应用之一是预测氧化还原反应在热力学上是否可行。规则很简单：反应要可行，电池电动势必须为正。

例题：锌能否从CuSO₄溶液中置换出铜？

步骤——确定半反应式并计算：E⦵_cell = E⦵(Cu²⁺/Cu) − E⦵(Zn²⁺/Zn) = (+0.34) − (−0.76) = +1.10 V。由于 E⦵_cell > 0，反应是可行的。锌金属确实会从溶液中置换出铜，观察到的现象是随着Cu²⁺离子被消耗，溶液从蓝色变为无色。

重要限制：正的E⦵_cell仅表示热力学可行性——它并不说明反应速率。一个反应可能可行但动力学缓慢（高活化能）。例如水的电解在标准条件下E⦵_cell = −1.23 V（不可行），而氢氧生成水的逆反应E⦵_cell = +1.23 V（热力学可行），但在室温下动力学极其缓慢。

6. Types of Electrochemical Cells

6a. Voltaic (Galvanic) Cells

A voltaic cell converts chemical energy into electrical energy. It consists of two half-cells connected by a salt bridge, with a spontaneous redox reaction driving electrons through an external circuit.

The Daniell Cell is the classic example:

Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s)

Anode (oxidation):  Zn(s) → Zn²⁺(aq) + 2e⁻
Cathode (reduction): Cu²⁺(aq) + 2e⁻ → Cu(s)
Overall:            Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)    E⦵cell = +1.10 V

In cell notation:

• The single vertical line | represents a phase boundary (solid | solution)
• The double vertical line || represents the salt bridge
• The left-hand side is the anode (oxidation)
• The right-hand side is the cathode (reduction)
• Electrons flow from anode to cathode through the external wire

6b. Electrolytic Cells

An electrolytic cell uses electrical energy to drive a non-spontaneous chemical reaction. Unlike voltaic cells, an external power source forces electrons in the reverse direction.

Key differences from voltaic cells:

• The anode is POSITIVE (connected to the positive terminal of the power supply)
• The cathode is NEGATIVE (connected to the negative terminal)
• Both electrodes share the same electrolyte (usually)
• No salt bridge is needed

Electrolysis of molten NaCl:

Cathode (−): Na⁺ + e⁻ → Na(l)     (reduction)
Anode (+):   2Cl⁻ → Cl₂(g) + 2e⁻  (oxidation)
Overall:     2NaCl(l) → 2Na(l) + Cl₂(g)

6c. Fuel Cells

Fuel cells are a special type of voltaic cell where reactants are continuously supplied from an external source. The hydrogen-oxygen fuel cell is the most common:

• Acidic electrolyte:

  Cathode: O₂ + 4H⁺ + 4e⁻ → 2H₂O
  Anode:   2H₂ → 4H⁺ + 4e⁻
  Overall: 2H₂ + O₂ → 2H₂O    E⦵cell = +1.23 V

• Alkaline electrolyte:

  Cathode: O₂ + 2H₂O + 4e⁻ → 4OH⁻
  Anode:   2H₂ + 4OH⁻ → 4H₂O + 4e⁻
  Overall: 2H₂ + O₂ → 2H₂O

Fuel cells are more efficient than combustion engines, produce only water as the waste product, and are central to the development of sustainable energy technologies.

6. 电化学电池的类型

6a. 伏打电池（原电池）

伏打电池将化学能转化为电能。它由两个通过盐桥连接的半电池组成，自发的氧化还原反应驱动电子流经外电路。丹尼尔电池是经典例子：Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s)，E⦵_cell = +1.10 V。

在电池表示法中：单竖线 | 表示相界面（固体|溶液），双竖线 || 表示盐桥，左侧为阳极（氧化），右侧为阴极（还原）。电子通过外部导线从阳极流向阴极。

6b. 电解池

电解池利用电能驱动非自发化学反应。与伏打电池不同，外部电源迫使电子反向流动。主要区别：阳极为正极（连接电源正极），阴极为负极（连接电源负极），两电极通常共享同一电解质，不需要盐桥。

6c. 燃料电池

燃料电池是一种特殊的伏打电池，反应物从外部源持续供应。氢氧燃料电池是最常见的类型。在酸性电解质中：2H₂ + O₂ → 2H₂O，E⦵_cell = +1.23 V。燃料电池比内燃机效率更高，仅产生水作为废产物，是可持续能源技术发展的核心。

7. The Nernst Equation — Beyond Standard Conditions

Standard electrode potentials are measured under standard conditions. But what happens when concentrations or pressures change? The Nernst equation allows us to calculate electrode potentials under non-standard conditions:

E = E⦵ − (RT/nF) × ln Q

Where:

• E = electrode potential under non-standard conditions
• E⦵ = standard electrode potential
• R = gas constant (8.314 J K⁻¹ mol⁻¹)
• T = temperature in Kelvin
• n = number of electrons transferred
• F = Faraday constant (96,500 C mol⁻¹)
• Q = reaction quotient

At 298 K, this simplifies to:

E = E⦵ − (0.059/n) × log₁₀ Q

Worked Example: Calculate the electrode potential of a Zn²⁺/Zn half-cell where [Zn²⁺] = 0.1 mol dm⁻³ (E⦵ = −0.76 V).

Zn²⁺ + 2e⁻ ⇌ Zn    n = 2
Q = 1/[Zn²⁺] = 1/0.1 = 10

E = −0.76 − (0.059/2) × log₁₀(10)
  = −0.76 − (0.0295) × 1
  = −0.76 − 0.0295
  = −0.79 V

The electrode potential becomes more negative as [Zn²⁺] decreases — which makes sense: lower ion concentration shifts the equilibrium further to the left (oxidation side), producing a more negative potential.

For the A-Level exam: You typically won’t need to calculate using the full Nernst equation, but you should be able to predict how changing concentration affects electrode potential using Le Chatelier’s principle: increasing [Mⁿ⁺] shifts equilibrium right → E becomes more positive; decreasing [Mⁿ⁺] shifts equilibrium left → E becomes more negative.

7. 能斯特方程——超越标准条件

标准电极电势是在标准条件下测量的。但当浓度或压力改变时会发生什么？能斯特方程允许我们计算非标准条件下的电极电势。

在298 K时简化为：E = E⦵ − (0.059/n) × log₁₀ Q

例题：计算 [Zn²⁺] = 0.1 mol dm⁻³ 时 Zn²⁺/Zn 半电池的电极电势。结果 E = −0.79 V，电势变得更负——这符合逻辑：较低的离子浓度使平衡进一步左移（氧化方向），产生更负的电势。

A-Level考试提示：通常不需要用完整的能斯特方程计算，但应能运用勒夏特列原理预测浓度变化如何影响电极电势：增加[Mⁿ⁺]使平衡右移 → E变得更正；降低[Mⁿ⁺]使平衡左移 → E变得更负。

8. Common Exam Questions and Pitfalls

8a. Explaining the Salt Bridge

A common 2-mark question: “Explain the function of the salt bridge.” The answer must include TWO points: (1) It completes the electrical circuit by allowing ion movement; (2) It prevents the solutions from mixing, which would cause direct reaction rather than electron flow through the external circuit.

8b. Standard Conditions

Students often lose marks by forgetting to state all three standard conditions. Always mention: 298 K, 100 kPa (for gases), and 1.00 mol dm⁻³ (for solutions). Also remember: if a half-cell involves a gas, you need a platinum electrode and the gas must be at 100 kPa.

8c. Choosing the Right Electrode for Gas Half-Cells

When a half-cell involves a gas (like H₂/H⁺ or Cl₂/Cl⁻), an inert electrode is required — typically platinum. The electrode itself does not participate in the reaction; it merely provides a surface for electron transfer.

8d. Interpreting Cell Diagrams

Always write the more negative half-cell on the LEFT. The cell emf is then calculated as RIGHT minus LEFT. Getting the sign convention wrong is one of the most common errors.

8e. Feasibility and Rate

Do NOT claim a reaction is ‘fast’ just because E⦵_cell is positive. Thermodynamic feasibility ≠ kinetic feasibility. Always qualify your answer: “The reaction is thermodynamically feasible, but the rate may be slow.”

8. 常见考题与易错点

8a. 解释盐桥的作用

常见的2分题。答案必须包含两点：(1) 它通过允许离子移动来完善电路；(2) 它防止溶液混合，否则会导致直接反应而非电子流经外电路。

8b. 标准条件

学生常因忘记陈述全部三个标准条件而失分。务必提及：298 K、100 kPa（气体）、1.00 mol dm⁻³（溶液）。

8c. 气体半电池的电极选择

当半电池涉及气体时，需要使用惰性电极——通常是铂电极。

8d. 解读电池图示

始终将更负的半电池写在左侧。电池电动势计算为右侧减左侧。符号约定搞错是最常见的错误之一。

8e. 可行性与速率

不要因为E⦵_cell为正就声称反应’快’。热力学可行性 ≠ 动力学可行性。始终限定你的答案：”该反应在热力学上可行，但速率可能很慢。”

9. Summary — Key Takeaways

• Electrode potentials arise from the equilibrium at a metal/solution interface
• The Standard Hydrogen Electrode (SHE) is the reference with E⦵ = 0.00 V
• The electrochemical series lists half-equations by E⦵ values
• Feasibility: E⦵_cell = E⦵(right) − E⦵(left) > 0 → thermodynamically feasible
• Voltaic cells produce electricity; electrolytic cells consume electricity
• The Nernst equation relates electrode potential to concentration
• Thermodynamic feasibility does NOT guarantee a fast reaction
• Salt bridges are essential for completing the circuit without mixing solutions

9. 总结——核心要点

• 电极电势源于金属/溶液界面的平衡
• 标准氢电极 (SHE) 是参考点，E⦵ = 0.00 V
• 电化学系列按E⦵值排列半反应方程式
• 可行性判断：E⦵_cell = E⦵(右) − E⦵(左) > 0 → 热力学可行
• 伏打电池产生电能，电解池消耗电能
• 能斯特方程关联电极电势与浓度
• 热力学可行性不保证反应速率快
• 盐桥对完善电路且防止溶液混合至关重要

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This article covers the core A-Level Chemistry syllabus content for Electrode Potentials and Electrochemical Cells. For exam practice, attempt past paper questions on predicting feasibility using E⦵ values, writing cell diagrams, and explaining the function of the salt bridge under standard and non-standard conditions.

本文涵盖了A-Level化学大纲中关于电极电势与电化学电池的核心内容。备考建议：练习利用E⦵值预测反应可行性的历年真题，书写电池图示，并解释标准与非标准条件下盐桥的功能。