📚 Electrochemical Cells | 电化学电池
Electrochemical cells are devices that convert chemical energy into electrical energy, or vice versa, through redox reactions. They are fundamental to batteries, fuel cells, corrosion, and electroplating. In the IB Chemistry curriculum, understanding how to build these cells, measure their potentials, and predict their spontaneity under standard and non‑standard conditions is essential for mastering Topic 9 and for practical laboratory work.
电化学电池是通过氧化还原反应将化学能转化为电能，或反过来将电能转化为化学能的装置。它们是电池、燃料电池、腐蚀和电镀的基础。在 IB 化学课程中，理解如何构建这些电池、测量其电势以及预测它们在标准和非标准条件下的自发性，对于掌握第 9 主题和实验操作至关重要。
1. Redox Reactions and Half-Cells | 氧化还原反应与半电池
Every electrochemical cell relies on a redox reaction in which oxidation (loss of electrons) and reduction (gain of electrons) occur separately. To harness the energy, the two half‑reactions are placed in different containers called half‑cells, connected by an external wire and a salt bridge. The electrode where oxidation takes place is the anode, and the electrode where reduction occurs is the cathode.
每一个电化学电池都依赖一个氧化还原反应，氧化（失去电子）和还原（得到电子）分别发生。为了利用能量，两个半反应被分置在不同的容器——半电池中，并通过外部导线和盐桥连接。发生氧化的电极是阳极，发生还原的电极是阴极。
A typical half‑cell consists of a metal rod (the electrode) immersed in a solution containing its own ions, such as a zinc rod in ZnSO₄(aq) or a copper rod in CuSO₄(aq). The overall cell reaction is the sum of the oxidation half‑reaction and the reduction half‑reaction, and electrons flow from the anode to the cathode through the external circuit.
典型的半电池由一根金属棒（电极）浸入含有其自身离子的溶液中组成，例如锌棒浸入 ZnSO₄(aq) 或铜棒浸入 CuSO₄(aq)。总的电池反应是氧化半反应和还原半反应之和，电子通过外电路从阳极流向阴极。
2. Galvanic (Voltaic) Cells | 原电池（伏打电池）
n electric current. The classic example is the Daniell cell, which combines a Zn/Zn²⁺ half‑cell with a Cu/Cu²⁺ half‑ hode: Cu²⁺(aq) + 2e⁻ → Cu(s). The overall reaction is Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s).
在原电池中，自发的氧化还原反应产生电流。经典的例子是丹尼尔电池，它将 Zn/Zn²⁺ 半电池与 Cu/Cu²⁺ 半电池组合起来。锌更容易被氧化，因此作为阳极：Zn(s) → Zn²⁺(aq) + 2e⁻。铜离子在阴极被还原：Cu²⁺(aq) + 2e⁻ → Cu(s)。总反应为 Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)。
The salt bridge, often a strip of filter paper soaked in KNO₃(aq), completes the circuit by allowing ions to migrate and maintain electrical neutrality. Without a salt bridge, the build‑up of charge would stop the reaction. In cell notation, the Daniell cell is written as Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s), where the double vertical line represents the salt bridge.
盐桥通常是一条浸泡过 KNO₃(aq) 的滤纸条，它通过允许离子迁移来维持电中性，从而构成完整回路。没有盐桥，电荷积累会使反应停止。在电池符号中，丹尼尔电池表示为 Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s)，其中双竖线代表盐桥。
3. Standard Electrode Potentials | 标准电极电势
The tendency of a half‑cell to gain or lose electrons is measured by its standard electrode potential, E°, in volts (V). All potentials are measured relative to the standard hydrogen electrode (SHE) under standard conditions: 298 K, 1 mol dm⁻³ ion concentration, 100 kPa pressure for gases. Each half‑cell is assigned a standard reduction potential, with the SHE defined as exactly 0.00 V.
半电池得到或失去电子的趋势通过标准电极电势 E° 来衡量，单位为伏特 (V)。所有电势均在标准条件（298 K，离子浓度为 1 mol dm⁻³，气体压强为 100 kPa）下相对于标准氢电极 (SHE) 进行测量。每个半电池都有一个标准还原电势，SHE 被定义为精确的 0.00 V。
A more positive E° value means the species has a greater tendency to be reduced (stronger oxidizing agent). Conversely, a more negative E° indicates a stronger reducing agent. The electrochemical series lists half‑reactions in order of decreasing reduction potential, allowing us to predict the direction of electron flow when two half‑cells are connected.
E° 值越正，表示该物质被还原的倾向越大（更强的氧化剂）。相反，E° 值越负，则表示还原剂越强。电化学序按照还原电势递减的顺序排列半反应，使我们能够预测两个半电池连接时电子的流动方向。
4. The Standard Hydrogen Electrode (SHE) | 标准氢电极
ode coated with finely divided platinum (platinum black) immersed in 1 mol dm⁻³ H⁺(aq) with hydrogen gas at 100 kPa bubbled over the surface. The half‑reaction is 2H⁺(aq) + 2e⁻ ⇌ t is impractical to use the SHE in every measurement, secondary reference electrodes such as the silver/silver chloride electrode are often used, but all tabulated values are ultimately referenced to the SHE.
SHE 由一根镀有铂黑的铂电极浸入 1 mol dm⁻³ H⁺(aq) 中，并在表面通入 100 kPa 的氢气构成。其半反应为 2H⁺(aq) + 2e⁻ ⇌ H₂(g)，E° 被定为 0.00 V。由于在每次测量中均使用 SHE 并不现实，常采用二级参比电极，如银/氯化银电极，但所有表列数值最终都以 SHE 为基准。
When measuring the potential of an unknown half‑cell, it is connected to the SHE via a salt bridge, and a high‑resistance voltmeter reads the cell potential. The sign and magnitude of the measured E° directly give the standard reduction potential of the half‑cell. If the half‑cell has a more negative potential than SHE, electrons will flow from it to the SHE.
在测量未知半电池的电势时，它通过盐桥与 SHE 相连，用高阻电压表读取电池电势。所测 E° 的符号和数值直接给出了该半电池的标准还原电势。如果半电池的电势比 SHE 更负，电子将从该半电池流向 SHE。
5. Calculating Cell Potential (EMF) | 计算电池电动势
For any galvanic cell, the standard cell potential (electromotive force, EMF) is calculated from the standard reduction potentials of the two half‑cells. The formula is:
E°cell = E°cathode − E°anode
对任何原电池，标准电池电势（电动势，EMF）可通过两个半电池的标准还原电势计算。公式为：
E°cell = E°cathode − E°anode
Both E° values must be taken as reduction potentials. A positive E°cell nditions. For the Daniell cell, E°(Cu²⁺/Cu) = +0.34 V and E°(Zn²⁺/Zn) = −0.76 V, giving E°cell = 0.34 − (−0.76) = +1.10 V. This value matches the voltage produced by a fresh battery.
两个 E° 值都必须采用还原电势。正的 E°cell 证实该反应在标准条件下是自发的。对于丹尼尔电池，E°(Cu²⁺/Cu) = +0.34 V，E°(Zn²⁺/Zn) = −0.76 V，故 E°cell = 0.34 − (−0.76) = +1.10 V。这一数值与新电池产生的电压一致。
When using cell notation, always write the anode half‑cell on the left and the cathode on the right. E°cell ion works because the left electrode is the one undergoing oxidation, so subtracting its reduction potential gives the correct cell EMF.
在使用电池符号时，始终将阳极半电池写在左侧，阴极在右侧。E°cell = E°(右) − E°(左)。这一惯例之所以成立，是因为左侧电极发生氧化，所以减去它的还原电势就能得出正确的电池电动势。
6. Spontaneity and Gibbs Free Energy | 自发性与吉布斯自由能
The relationship between the cell potential and Gibbs free energy change is given by:
ΔG° = −nFE°cell
where n is the number of moles of electrons transferred, and F is the Faraday constant (96 500 C mol⁻¹). A positive E°cell yields a negative ΔG°, confirming spontaneity.
电池电势与吉布斯自由能变之间的关系为：
ΔG° = −nFE°cell
其中 n 是转移电子的摩尔数，F 是法拉第常数 (96 500 C mol⁻¹)。正的 E°cell 会产生负的 ΔG°，从而确认反应自发。
The same relationship also allows calculation of equilibrium constants via ΔG° = −RT ln K.
这一方程极为有用，因为它将热力学数据与可测量的电量联系起来。对于丹尼尔电池，n = 2，ΔG° = −2 × 96 500 × 1.10 = −212 kJ mol⁻¹，说明这是一个高度自发的过程。同一关系还可通过 ΔG° = −RT ln K 计算平衡常数。
7. The Nernst Equation | 能斯特方程
When concentrations are not at standard conditions (1 mol dm⁻³), the cell potential deviates from E°cell. The Nernst equation, which can be derived from thermodynamic principles, describes this dependence:
E = E° − (RT / nF) ln Q
At 298 K, this simplifies to:
E = E° − (0.0592 V / n) log₁₀ Q
当浓度不处于标准条件（1 mol dm⁻³）时，电池电势会偏离 E°cell。能斯特方程可从热力学原理导出，描述了这种依赖关系：
E = E° − (RT / nF) ln Q
在 298 K 时，简化为：
E = E° − (0.0592 V / n) log₁₀ Q
ng E to drop. When Q = K, the system is at equilibrium and the cell potential becomes zero — the battery is 'flat'.
其中 Q 是反应商，定义方式与平衡常数相同，但使用的是实际浓度。随着电池放电，反应物被消耗，Q 增大，导致 E 下降。当 Q = K 时，体系达到平衡，电池电势变为零——电池耗尽。
The Nernst equation can also be applied to individual half‑cells to show how electrode potentials vary with ion concentration. For example, E(Zn²⁺/Zn) becomes more negative as [Zn²⁺] decreases, explaining why cells lose voltage over time.
能斯特方程也可以应用于单个半电池，以显示电极电势如何随离子浓度变化。例如，随着 [Zn²⁺] 降低，E(Zn²⁺/Zn) 变得更负，这就解释了为什么电池的电压会随时间下降。
8. Electrolytic Cells | 电解池
In contrast to galvanic cells, electrolytic cells use an external power source to drive a non‑spontaneous reaction. Here the anode is the positive electrode (connected to the positive terminal of the power supply) and the cathode is the negative electrode. Oxidation still occurs at the anode and reduction at the cathode, but the direction of electron flow is forced.
与原电池不同，电解池利用外部电源驱动非自发反应。此时阳极是正极（连接电源正极），阴极是负极。氧化仍发生在阳极，还原在阴极，但电子流动方向是强制性的。
ess requires a voltage at least as large as the cell potential of the reverse spontaneous reaction.
一个经典的例子是熔融溴化铅 PbBr₂(l) 的电解。在阴极，Pb²⁺ 离子得到电子生成液态铅：Pb²⁺ + 2e⁻ → Pb(l)。在阳极，Br⁻ 离子失去电子生成溴气：2Br⁻ → Br₂(g) + 2e⁻。总反应为 PbBr₂(l) → Pb(l) + Br₂(g)。该过程所需的电压至少等于逆反应（自发反应）的电池电势。
In aqueous electrolysis, the presence of water complicates the electrode reactions. For example, in the electrolysis of aqueous NaCl, possible cathode reactions are the reduction of Na⁺ or water. Since water has a less negative reduction potential compared with Na⁺, water is reduced preferentially, producing hydrogen gas and hydroxide ions.
在水溶液电解中，水的存在使电极反应变得更加复杂。例如，电解 NaCl 水溶液时，可能的阴极反应包括 Na⁺ 或水的还原。由于水的还原电势比 Na⁺ 的更正，水优先被还原，生成氢气和氢氧根离子。
9. Faraday's Laws of Electrolysis | 法拉第电解定律
Quantitative electrolysis is governed by Faraday' ass of a substance produced or consumed at an electrode is directly proportional to the quantity of electric charge passed: m ∝ cond law states that for a given amount of charge, the mass produced is proportional to the equivalent weight of the substance.
定量电解遵循法拉第定律。第一定律阐明：电极上产生或消耗的物质质量与通过的电量成正比：m ∝ Q，其中 Q = It（电流 × 时间）。第二定律阐明：对于给定的电量，产生的质量与物质的当量成正比。
Combining these laws gives the useful relationship:
n(e⁻) = Q / F = It / F
is molar mass and n is the number of electrons per ion. For instance, to deposit 0.500 g of silver from Ag⁺(aq) at a constant current of 0.800 A, you can calculate the time required.
综合这些定律得出以下实用关系：
n(e⁻) = Q / F = It / F
以及质量 m = (M × It) / (n × F)，其中 M 为摩尔质量，n 为每个离子对应的电子数。例如，若要以 0.800 A 的恒流从 Ag⁺(aq) 中沉积 0.500 g 银，即可计算所需时间。
ol. Q = 0.004635 × 96 500 = 447.3 C. t = Q / I = 447.3 / 0.800 = 559 s (about 9 min 19 s).
计算示例：M(Ag) = 107.87 g mol⁻¹，n = 1。Ag 的物质的量 = 0.500 / 107.87 = 0.004635 mol。电子物质的量 = 0.004635 mol。Q = 0.004635 × 96 500 = 447.3 C。t = Q / I = 447.3 / 0.800 = 559 s（约 9 分 19 秒）。
10. Factors Affecting Cell Potential | 影响电池电势的因素
Besides concentration, temperature and pressure also influence E according to the Nernst equation. For a half‑cell involving gases, changing the partial pressure shifts the potential. Additionally, the nature of the electrode material and the presence of complexing agents can alter the effective concentration of free metal ions, thereby modifying the cell voltage.
除了浓度，温度和压强也会根据能斯特方程影响 E。对于涉及气体的半电池，改变分压会使电势发生移动。此外，电极材料的性质和络合剂的存在也会改变游离金属离子的有效浓度，从而改变电池电压。
In concentration cells, the same half‑cell is used on both sides but with different concentrations. The cell potential is generated solely by the concentration gradient. For example, a cell with Cu²⁺ (0.10 mol dm⁻³) and Cu²⁺ (1.0 mol dm⁻³) will have a small EMF given by the Nernst equation. As the two concentrations become equal, the voltage drops to zero.
在浓差电池中，两侧使用相同的半电池但浓度不同，电池电势完全由浓度梯度产生。例如，使用 Cu²⁺（0.10 mol dm⁻³）和 Cu²⁺（1.0 mol dm⁻³）的电池将有一个由能斯特方程计算得出的微小电动势。随着两侧浓度相等，电压降为零。
11. Applications: Batteries and Corrosion | 应用：电池与腐蚀
Primary batteries, such as alkaline cells, are single‑use galvanic cells. Secondary batteries, like lithium‑ion and lead‑acid batteries, can be recharged by applying an external voltage to reverse the discharge reaction. Fuel cells, such as the hydrogen‑oxygen fuel cell, continuously convert chemical energy from a fuel into electricity, with water as the only by‑product, making them highly efficient and clean.
一次电池，例如碱性电池，是一次性原电池。二次电池，如锂离子电池和铅酸电池，可通过外加电压使放电反应逆转来充电。燃料电池，如氢氧燃料电池，将燃料的化学能持续转化为电能，水是唯一的副产物，因而效率高且清洁。
Electrochemical principles also explain corrosion. Iron rusts because it acts as an anode in a tiny galvanic cell formed with impurities on its surface. E° for Fe²⁺/Fe is −0.44 V, while the O₂/H₂O couple is +1.23 V, so oxidation of iron is spontaneous. Protective methods such as galvanising (coating with zinc) or sacrificial anodes use the reactivity series to prevent corrosion.
电化学原理也可解释腐蚀现象。铁生锈是因为它在与表面杂质构成的微小原电池中充当阳极。Fe²⁺/Fe 的 E° 为 −0.44 V，而 O₂/H₂O 电对的 E° 为 +1.23 V，因此铁的氧化是自发的。诸如镀锌或牺牲阳极等防护方法均利用反应性序列来防止腐蚀。
12. Summary and Key Points | 总结与要点
Electrochemical cells underpin a vast range of technologies and natural processes. The key takeaways include: (1) In all cells, oxidation occurs at the anode and reduction at the cathode. (2) E° values relative to SHE allow prediction of reaction spontaneity. (3) E°cell = E°cathode − E°anode and ΔG° = −nFE°cell. (4) The Nernst equation adjusts potentials for non‑standard conditions. (5) Electrolytic cells require an external voltage to force non‑spontaneous reactions, and Faraday's laws quantify product yields.
电化学电池是众多技术和自然过程的基础。核心要点包括：(1) 所有电池中，氧化在阳极发生，还原在阴极发生。(2) 相对于 SHE 的 E° 值可预测反应的自发性。(3) E°cell = E°cathode − E°anode，且 ΔG° = −nFE°cell。(4) 能斯特方程可针对非标准条件调整电势。(5) 电解池需要外加电压来驱动非自发反应，法拉第定律可定量计算产物收率。
Mastering these concepts will not only prepare you for IB examination questions on electrochemical stoichiometry and cell diagrams but also give you a deeper appreciation of the role of electrochemistry in energy storage and materials science.
掌握这些概念不仅能帮助你应对 IB 考试中有关电化学计量学和电池图示的题目，还能让你更深刻地理解电化学在能源储存和材料科学中的作用。
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