📚 Electrochemical Cells | 电化学电池
Electrochemical cells lie at the heart of redox chemistry, converting chemical energy into electrical energy or driving non-spontaneous reactions using an external power source. At the Higher Level, IB Chemistry demands a deep understanding of standard electrode potentials, the Nernst equation, the thermodynamic link between cell potential and Gibbs free energy, and quantitative electrolysis via Faraday's laws. This article explores both galvanic (voltaic) and electrolytic cells, examines how to measure and predict cell potentials under standard and non-standard conditions, and reveals the quantitative relationships that govern electrochemical processes.
电化学电池是氧化还原化学的核心，它将化学能转化为电能，或利用外部电源驱动非自发反应。在高级水平，IB 化学要求深入理解标准电极电势、能斯特方程、电池电动势与吉布斯自由能之间的热力学关系，以及通过法拉第定律进行的定量电解计算。本文将探讨原电池和电解池，考察如何在标准和非标准条件下测量和预测电池电动势，并揭示支配电化学过程的定量关系。
1. Galvanic vs Electrolytic Cells | 原电池与电解池
A galvanic cell, also known as a voltaic cell, spontaneously converts chemical energy into electrical energy. It consists of two half-cells connected by a salt bridge and an external circuit. Oxidation occurs at the anode (negative electrode) and reduction at the cathode (positive electrode), with electrons flowing from anode to cathode through the external wire. In contrast, an electrolytic cell uses an external power supply to force a non-spontaneous redox reaction to occur. Here the anode becomes positive and the cathode negative; oxidation still occurs at the anode and reduction at the cathode, but the electron flow is driven by the battery.
原电池（也称为伏打电池）自发地将化学能转化为电能。它由两个半电池组成，通过盐桥和外电路连接。氧化发生在负极（阳极），还原发生在正极（阴极），电子通过外部导线从阳极流向阴极。相反，电解池利用外部电源迫使非自发氧化还原反应发生。此时阳极变为正极，阴极为负极；氧化仍然在阳极发生，还原在阴极发生，但电子流动由外接电池驱动。
The key differences between the two types can be summarised in a simple table:
两种电池的主要区别可以简单地总结如下表：
| Feature | Galvanic Cell | Electrolytic Cell |
|---|---|---|
| Energy conversion | Chemical → electrical | Electrical → chemical |
| ΔG | Negative (spontaneous) | Positive (non-spontaneous) |
| Anode | Negative; oxidation | Positive; oxidation |
| Cathode | Positive; reduction | Negative; reduction |
| Electron flow | Anode to cathode via wire | Anode to cathode via wire (driven by power source) |
In both cases, the overall cell reaction is a redox process, and the fundamental definitions of oxidation and reduction remain unchanged.
在这两种情况下，总电池反应都是氧化还原过程，氧化和还原的基本定义保持不变。
2. Electrode Potentials and Half-Cells | 电极电势与半电池
Every half-cell consists of an electrode in contact with a solution of its ions. The potential difference that develops at the electrode–solution interface is called the electrode potential. It cannot be measured directly; only the potential difference between two half-cells can be determined. The tendency of a half-cell to undergo reduction is given by its reduction potential E. Half-cells with a greater tendency to be reduced have larger (more positive) reduction potentials.
每个半电池由一个电极和与其离子溶液接触组成。在电极-溶液界面产生的电势差称为电极电势。它不能直接测量；只能测定两个半电池之间的电势差。半电池被还原的趋势由其还原电势 E 给出。更容易被还原的半电池具有更大（更正）的还原电势。
Common half-cells include metal/metal-ion systems such as Zn²⁺/Zn, Cu²⁺/Cu, and non-metal systems such as Fe³⁺/Fe²⁺ with a platinum electrode. A typical half-cell is assembled by dipping a metal rod into a solution containing its ions (e.g., Zn in ZnSO₄(aq)), or by using an inert platinum electrode when no solid metal participates in the redox couple (e.g., for the Fe³⁺/Fe²⁺ couple).
常见的半电池包括金属/金属离子体系，如 Zn²⁺/Zn、Cu²⁺/Cu，以及非金属体系如 Fe³⁺/Fe²⁺ 搭配铂电极。典型的半电池通过将金属棒浸入含有其离子的溶液中（例如 Zn 在 ZnSO₄(aq) 中），或者当没有固体金属参与氧化还原对时使用惰性铂电极（例如 Fe³⁺/Fe²⁺ 对）来组装。
3. Standard Hydrogen Electrode and Measuring Potentials | 标准氢电极与电势测量
K, 1 atm H₂ gas, and 1 mol dm⁻³ H⁺ ions (i.e., pH = 0). The half-reaction is 2H⁺(aq) + 2e⁻ ⇌ en as a positive E° value; if it acts as the anode (oxidation), the potential is negative.
标准氢电极 (SHE) 是所有其他半电池电势测量的参照基准。在标准条件下（298 K、1 atm H₂ 气体、1 mol dm⁻³ H⁺，即 pH = 0），它被指定为恰好 0.00 V。其半反应为 2H⁺(aq) + 2e⁻ ⇌ H₂(g)。通过将另一个半电池与 SHE 相连并测量电池电动势，可以确定未知半电池的标准还原电势 E°。如果未知半电池作为阴极（还原），测得的电池电动势取为正值 E°；如果作为阳极（氧化），其电势为负。
ron flow and to calculate the standard cell potential (E°_cell) of any galvanic cell using E°_cell = E°_cathode − E°_anode.
在实际应用中，标准电极电势表列出了许多半反应在标准条件下的还原电势。这些值用于预测电子流动的方向，并利用 E°_cell = E°_cathode − E°_anode 计算任何原电池的标准电池电动势。
4. Electrochemical Series and Cell EMF | 电化学系列与电池电动势
The electrochemical series arranges half-cells in order of decreasing (or increasing) standard reduction potentials. Elements at the top have the highest tendency to be reduced (strongest oxidising agents), while those at the bottom are the strongest reducing agents. For example, F₂/F⁻ has a very high positive E° (+2.87 V), while Li⁺/Li has a very negative E° (−3.04 V). The cell electromotive force (EMF) is the potential difference between the two half-cells when no current flows, and it equals the difference in their reduction potentials under the same conditions.
电化学系列按照标准还原电势递减（或递增）的顺序排列半电池。顶端的元素最容易发生还原（最强的氧化剂），而底端的元素是最强的还原剂。例如，F₂/F⁻ 具有非常高的正 E° (+2.87 V)，而 Li⁺/Li 具有非常负的 E° (−3.04 V)。电池电动势 (EMF) 是指没有电流流过时两个半电池之间的电势差，它等于相同条件下它们还原电势的差值。
_cell indicates a spontaneous reaction in the forward direction under standard conditions.
按照惯例，当电池用简写符号书写且右侧电极为阴极时，电池电动势计算为 E°_cell = E°_right − E°_left。正的 E°_cell 表示在标准条件下正向反应是自发的。
5. Cell Diagrams and Notation | 电池图与表示法
An electrochemical cell is commonly represented using cell notation, which specifies the composition of each half-cell. A single vertical line (|) indicates a phase boundary between electrode and electrolyte, while a double vertical line (||) represents the salt bridge. The anode is written on the left and the cathode on the right. For example, the Daniell cell is written as: Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s). Inert electrodes like Pt are included when the couple has no solid metal; e.g., Pt(s) | Fe²⁺(aq), Fe³⁺(aq) || MnO₄⁻(aq), H⁺(aq) | Pt(s).
电化学电池通常用电池符号表示，它给出了每个半电池的组成。单竖线 (|) 表示电极与电解质之间的相界面，双竖线 (||) 表示盐桥。阳极写在左侧，阴极写在右侧。例如，丹尼尔电池写作：Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s)。当氧化还原对没有固体金属时，需要包括惰性电极如 Pt；例如 Pt(s) | Fe²⁺(aq), Fe³⁺(aq) || MnO₄⁻(aq), H⁺(aq) | Pt(s)。
s oxidation and which is reduction, and to apply the formula E°_cell = E°_right − E°_left.
使用这种符号有助于正确识别哪个半反应是氧化、哪个是还原，并应用公式 E°_cell = E°_right − E°_left。
6. The Nernst Equation | 能斯特方程
Standard potentials apply only at 1 mol dm⁻³, 298 K and, for gases, 1 atm. When concentrations, temperature or pressure deviate from standard conditions, the cell potential changes. The Nernst equation allows us to calculate the cell potential under non-standard conditions. For a half-reaction aA + ne⁻ ⇌ bB, the reduction potential is given by:
标准电势仅适用于 1 mol dm⁻³、298 K 以及气体 1 atm 的条件。当浓度、温度或压力偏离标准条件时，电池电动势会发生变化。能斯特方程使我们能够计算非标准条件下的电池电动势。对于半反应 aA + ne⁻ ⇌ bB，其还原电势由下式给出：
E = E° − (RT / nF) ln Q
where R is the gas constant (8.31 J K⁻¹ mol⁻¹), T is the temperature in kelvin, F is the Faraday constant (96 500 C mol⁻¹), n is the number of electrons transferred, and Q is the reaction quotient. At 298 K, substituting the constants gives:
其中 R 为气体常数 (8.31 J K⁻¹ mol⁻¹)，T 为开尔文温度，F 为法拉第常数 (96 500 C mol⁻¹)，n 为转移电子数，Q 为反应商。在 298 K 下代入常数得到：
E = E° − (0.0257 V / n) ln Q
Using log₁₀ : E = E° − (0.0592 V / n) log Q (at 298 K).
使用常用对数：E = E° − (0.0592 V / n) log Q (在 298 K 下)。
For a whole cell, the Nernst equation is written as Ecell = E°_cell − (RT/nF) ln Qcell, where Qcell is the reaction quotient for the overall cell reaction. This equation is powerful: it explains why a battery voltage drops as reactants are consumed, and it allows the determination of concentrations via potentiometry.
对于整个电池，能斯特方程写为 Ecell = E°_cell − (RT/nF) ln Qcell，其中 Qcell 是总电池反应的反应商。该方程功能强大：它解释了为什么电池电压会随着反应物的消耗而下降，并且可以通过电位分析法测定浓度。
7. EMF and Thermodynamics: ΔG = −nFE | 电动势与热力学：ΔG = −nFE
The cell potential is directly linked to the maximum electrical work that a galvanic cell can perform, and hence to the Gibbs free energy change. The relationship is:
电池电动势与电池能做的最大电功直接相关，因此也与吉布斯自由能变化相关。关系式为：
ΔG = −n F Ecell
equation also allows the calculation of equilibrium constants because ΔG° = −RT ln K, so:
其中 ΔG 单位为焦耳，n 为转移电子的摩尔数，F = 96 500 C mol⁻¹。在标准条件下，ΔG° = −n F E°_cell。正的 E°_cell 给出负的 ΔG°，表明氧化还原反应是自发的。该方程还可计算平衡常数，因为 ΔG° = −RT ln K，所以：
ln K = (n F E°_cell) / (R T)
Thus, measuring the cell potential provides a direct route to thermodynamic data. For example, a cell with a large positive E° has a very large equilibrium constant, meaning the reaction goes essentially to completion.
因此，测量电池电动势为获取热力学数据提供了直接途径。例如，具有较大正 E° 的电池具有非常大的平衡常数，意味着反应几乎进行到底。
8. Electrolysis: Driving Non-Spontaneous Reactions | 电解：驱动非自发反应
When electrical energy is supplied to an electrolytic cell, non-spontaneous reactions are forced to occur. The key is that the external power source must provide a potential difference greater than the cell potential of the reverse spontaneous reaction. In aqueous electrolysis, competing reactions may occur; for instance, during the electrolysis of aqueous NaCl, water may be oxidised or reduced instead of the solute ions. To predict the products, one must compare the standard reduction potentials of all possible half-reactions, but also account for overpotential effects, particularly for gas evolution.
当向电解池提供电能时，非自发反应被迫发生。关键在于外部电源必须提供大于逆自发反应电池电动势的电势差。在水溶液电解中，可能发生竞争反应；例如，电解 NaCl 水溶液时，水可能被氧化或还原，而不是溶质离子。为预测产物，必须比较所有可能半反应的标准还原电势，同时还要考虑过电位效应，特别是对于气体析出。
Molten ionic compounds, such as molten NaCl, lead to simple electrolysis products: sodium metal at the cathode and chlorine gas at the anode. In aqueous NaCl, however, the cathode produces H₂ gas and the anode produces Cl₂ gas under most conditions, leaving NaOH in solution. The mass of substance produced during electrolysis is quantified by Faraday's laws.
熔融离子化合物，如熔融 NaCl，简单电解产物为：阴极生成金属钠，阳极生成氯气。然而在 NaCl 水溶液中，大多数条件下阴极产生 H₂ 气体，阳极产生 Cl₂ 气体，溶液中留下 NaOH。电解过程中产生的物质质量由法拉第定律定量计算。
9. Faraday's Laws of Electrolysis | 法拉第电解定律
Michael Faraday established the quantitative relationship between the amount of electricity passed and the amount of substance liberated at an electrode. The first law states that the mass of an element discharged is directly proportional to the quantity of charge (Q) passed. The second law states that the masses of different substances liberated by the same quantity of electricity are proportional to their equivalent weights (molar mass / number of electrons per ion).
迈克尔·法拉第确立了通过的电量与电极上释放的物质数量之间的定量关系。第一定律指出，析出元素的质量与通过的电量 (Q) 成正比。第二定律指出，相同电量下析出的不同物质的质量与其当量（摩尔质量 / 每离子电子数）成正比。
The core relation is:
核心关系为：
Q = I × t and n(e⁻) = Q / F
where I is current in amperes, t is time in seconds, and n(e⁻) is the moles of electrons. The mass m of substance deposited is:
其中 I 为电流（安培），t 为时间（秒），n(e⁻) 为电子的摩尔数。沉积物质的质量 m 为：
m = (M × I × t) / (n × F)
are central to electroplating, metal refining, and the industrial extraction of elements.
这里 M 是摩尔质量，n 是半反应中的电子数。例如，从 Cu²⁺ 沉积 1 mol 铜需要 2 mol 电子，因此 n = 2。这些计算对电镀、金属精炼和元素工业提取至关重要。
10. Factors Affecting Cell EMF | 影响电池电动势的因素
cell, identical half-cells with different ion concentrations produce a voltage purely due to the concentration difference; at equilibrium E = 0 and Q = K.
有几个因素会改变电池可测的电动势，使其偏离标准值。浓度是最重要的变量，正如能斯特方程所描述。改变反应物或产物的浓度会改变平衡位置和电池电动势。在浓差电池中，相同半电池离子浓度不同，仅因浓度差而产生电压；在平衡时 E = 0 且 Q = K。
Temperature also influences EMF because the Nernst factor (RT/nF) is temperature-dependent. Pressure affects gaseous electrodes. Additionally, the nature of the electrodes and salt bridge affect internal resistance but not the theoretical EMF. Overpotential in real cells, especially for gas evolution, can make the required voltage for electrolysis significantly higher than the thermodynamic value.
温度也会影响电动势，因为能斯特因子 (RT/nF) 与温度有关。压力影响气体电极。此外，电极和盐桥的性质影响内阻，但不影响理论电动势。实际电池中的过电位，尤其是气体析出时，可能使电解所需电压显著高于热力学值。
11. Applications: Batteries and Corrosion | 应用：电池与腐蚀
ll, directly convert chemical energy of a fuel into electricity with high efficiency. In the hydrogen fuel cell, the overall reaction is 2H₂ + O₂ → 2H₂O, with oxidation of H₂ at the anode and reduction of O₂ at the cathode. The standard cell EMF is 1.23 V.
电化学电池是现代储能的基础。一次电池（不可充电）如碱性电池使用不可逆的氧化还原反应。二次电池（可充电）如锂离子电池依赖于可逆反应。燃料电池，特别是氢燃料电池，直接将燃料的化学能高效转化为电能。在氢燃料电池中，总反应为 2H₂ + O₂ → 2H₂O，H₂ 在阳极氧化，O₂ 在阴极还原。标准电池电动势为 1.23 V。
Corrosion, especially rusting of iron, is a spontaneous electrochemical process that degrades metals. Iron acts as the anode, oxidising to Fe²⁺, while oxygen is reduced at the cathode. Salt water accelerates corrosion because it increases the conductivity of the electrolyte. Prevention strategies include coating, sacrificial protection (using a more reactive metal like zinc to corrode preferentially), and impressed current cathodic protection.
腐蚀，尤其是铁的锈蚀，是一个自发的电化学过程，会降解金属。铁充当阳极，氧化成 Fe²⁺，而氧在阴极还原。盐水加速腐蚀，因为它增加了电解质的导电性。防护策略包括涂层、牺牲保护（使用更活泼的金属如锌优先腐蚀）和外加电流阴极保护。
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