Principles of Electrochemical Cells | 电化学电池原理

📚 Principles of Electrochemical Cells | 电化学电池原理

Electrochemistry is the branch of chemistry concerned with the interconversion of chemical energy and electrical energy through redox reactions. Electrochemical cells are devices that either convert spontaneous chemical reactions into electrical energy (voltaic cells) or use electrical energy to drive non-spontaneous chemical reactions (electrolytic cells). This revision guide unpacks the core principles of electrochemical cells, tailored to the IB Chemistry syllabus.

电化学是研究化学能与电能之间通过氧化还原反应相互转化的化学分支。电化学电池是通过自发化学反应产生电能的装置（原电池），或利用电能驱动非自发化学反应的装置（电解电池）。本复习指南针对IB化学大纲，系统剖析电化学电池的核心原理。

1. Redox Reactions Revisited | 氧化还原反应回顾

Every electrochemical cell is built upon a redox reaction, which consists of two half-reactions. Oxidation is the loss of electrons, and reduction is the gain of electrons. These processes always occur simultaneously: the species that gives up electrons is oxidised, while the species that accepts them is reduced. The oxidising agent (oxidant) is the species that gains electrons and is itself reduced; the reducing agent (reductant) is the species that loses electrons and is itself oxidised.

每个电化学电池都建立在氧化还原反应的基础上，该反应由两个半反应组成。氧化是失去电子，还原是获得电子。这两个过程始终同时发生：失去电子的物质被氧化，接受电子的物质被还原。氧化剂（氧化性物质）是获得电子并被还原的物质；还原剂（还原性物质）是失去电子并被氧化的物质。

For example, in the reaction between zinc and copper(II) sulfate:

例如，在锌与硫酸铜的反应中：

Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)

Zinc is oxidised (Zn → Zn²⁺ + 2e⁻) and Cu²⁺ is reduced (Cu²⁺ + 2e⁻ → Cu). Zinc serves as the reducing agent, while Cu²⁺ serves as the oxidising agent.

锌被氧化（Zn → Zn²⁺ + 2e⁻），Cu²⁺被还原（Cu²⁺ + 2e⁻ → Cu）。锌充当还原剂，Cu²⁺充当氧化剂。

2. Half-Cells: The Building Blocks | 半电池：基本组成单元

A half-cell consists of a metal electrode immersed in a solution containing its own ions. Each half-cell represents one half-reaction, and when two half-cells are connected, they form a complete electrochemical cell. The tendency of a metal to lose electrons and form ions depends on its position in the reactivity series and its electrode potential.

半电池由浸入含有自身离子溶液中的金属电极组成。每个半电池代表一个半反应，当两个半电池连接时就构成一个完整的电化学电池。金属失去电子形成离子的趋势取决于其在反应活性系列中的位置及其电极电位。

There are several common types of half-cells:

常见的半电池类型有：

Metal–metal ion half-cell: e.g. Zn(s) | Zn²⁺(aq) — a zinc rod in a zinc sulfate solution.
金属–金属离子半电池：如 Zn(s) | Zn²⁺(aq)，即锌棒浸入硫酸锌溶液中。
Gas–ion half-cell: e.g. the standard hydrogen electrode (SHE), where H₂ gas bubbles over a platinum catalyst immersed in an H⁺ solution.
气体–离子半电池：如标准氢电极（SHE），氢气在浸入H⁺溶液中的铂催化剂表面鼓泡。
Ion–ion half-cell: e.g. Fe²⁺ | Fe³⁺, involving two ions of the same element in different oxidation states, with an inert platinum electrode.
离子–离子半电池：如Fe²⁺ | Fe³⁺，同一元素不同氧化态的两种离子，使用惰性铂电极。

3. The Voltaic (Galvanic) Cell | 伏打电池（原电池）

A voltaic cell (also called a galvanic cell) produces electrical energy from a spontaneous redox reaction. The two half-cells are connected externally by a wire, through which electrons flow, and internally by a salt bridge, which maintains electrical neutrality by allowing the migration of ions.

伏打电池（又称原电池）通过自发氧化还原反应产生电能。两个半电池通过导线在外部连接，电子经导线流动；内部通过盐桥连接，盐桥允许离子迁移以维持电中性。

The key components of a voltaic cell include:

伏打电池的关键组成部分包括：

Anode (negative electrode): oxidation occurs here; electrons are released and flow through the external circuit.
阳极（负极）：发生氧化反应；电子释放并通过外部电路流动。
Cathode (positive electrode): reduction occurs here; electrons are accepted from the external circuit.
阴极（正极）：发生还原反应；从外部电路接受电子。
Salt bridge: typically a strip of filter paper soaked in an inert electrolyte such as KNO₃ or KCl; it completes the circuit and prevents accumulation of charge.
盐桥：通常为浸有KNO₃或KCl等惰性电解质的滤纸条；它闭合电路并防止电荷积累。
External circuit: the wire connecting the two electrodes, through which electrons flow from anode to cathode.
外部电路：连接两个电极的导线，电子经此从阳极流向阴极。

For the Daniell cell (zinc–copper cell), the overall reaction is spontaneous, and the measured potential difference is approximately 1.10 V under standard conditions.

对于丹尼尔电池（锌–铜电池），总反应是自发的，在标准条件下测得电势差约为1.10 V。

4. Standard Hydrogen Electrode (SHE) | 标准氢电极

To measure electrode potentials, a reference electrode is required. The standard hydrogen electrode (SHE) is the universal reference, assigned a potential of exactly 0.00 V under standard conditions (298 K, 1 atm H₂ pressure, 1 mol dm⁻³ H⁺ concentration).

要测量电极电位，需要一个参比电极。标准氢电极（SHE）是通用参比电极，在标准条件下（298 K、1 atm H₂压力、1 mol dm⁻³ H⁺浓度）其电位被规定为恰好0.00 V。

The half-reaction for the SHE is:

SHE的半反应为：

2H⁺(aq) + 2e⁻ ⇌ H₂(g) E° = 0.00 V

Platinum is used as the electrode because it is inert, conducts electricity well, and provides a catalytically active surface for the H₂/H⁺ equilibrium to establish rapidly.

铂用作电极是因为它是惰性的、导电性好，并且能为H₂/H⁺平衡提供催化活性表面，使平衡快速建立。

To measure the standard electrode potential (E°) of a half-cell, it is connected to the SHE and the potential difference is measured using a high-resistance voltmeter.

要测量某半电池的标准电极电位（E°），将其与SHE连接，用高电阻电压表测量电势差。

5. Standard Electrode Potentials | 标准电极电位

The standard electrode potential (E°) of a half-cell is the voltage measured when a half-cell is connected to the SHE under standard conditions. It is a measure of the tendency of a species to be reduced: the more positive the E° value, the greater the tendency to gain electrons and undergo reduction.

半电池的标准电极电位（E°）是在标准条件下将半电池连接到SHE时测得的电压。它衡量物质被还原的趋势：E°值越正，获得电子并被还原的趋势越大。

Standard conditions are: 298 K temperature, 1 mol dm⁻³ concentration for all aqueous species, and 100 kPa (1 atm) pressure for any gases involved.

标准条件为：温度298 K，所有水溶液物种浓度为1 mol dm⁻³，涉及气体压力为100 kPa（1 atm）。

A selection of common standard electrode potentials is shown below:

下表列出了一些常见的标准电极电位：

Half-reaction	E° / V
F₂(g) + 2e⁻ → 2F⁻(aq)	+2.87
Cu²⁺(aq) + 2e⁻ → Cu(s)	+0.34
2H⁺(aq) + 2e⁻ → H₂(g)	0.00
Zn²⁺(aq) + 2e⁻ → Zn(s)	−0.76
Li⁺(aq) + e⁻ → Li(s)	−3.04

6. The Electrochemical Series | 电化学系列

The electrochemical series is a list of half-reactions arranged in order of decreasing (more positive to more negative) standard electrode potential. Species at the bottom of the E° table (most negative) are strong reducing agents and are easily oxidised, while species at the top (most positive) are strong oxidising agents and are easily reduced.

电化学系列是按标准电极电位递减（从更正到更负）排列的半反应列表。E°表底部的物质（最负）是强还原剂，容易被氧化；表顶部的物质（最正）是强氧化剂，容易被还原。

This series allows us to predict the spontaneity of redox reactions: a reaction is spontaneous when the species with the more positive E° acts as the oxidising agent and the species with the more negative E° acts as the reducing agent.

该系列使我们能够预测氧化还原反应的自发性：当E°更正的物质充当氧化剂，E°更负的物质充当还原剂时，反应是自发的。

Higher E° (more positive): species are more readily reduced; they are better oxidising agents.
越高E°（更正）：物种更容易被还原；它们是更好的氧化剂。
Lower E° (more negative): species are more readily oxidised; they are better reducing agents.
越低E°（更负）：物种更容易被氧化；它们是更好的还原剂。

For example, since E°(F₂/F⁻) = +2.87 V is much greater than E°(Cl₂/Cl⁻) = +1.36 V, fluorine will oxidise chloride ions to chlorine gas. In general, any species on the higher E° half-reaction will oxidise the reduced form of any species lower in the series.

例如，由于E°(F₂/F⁻) = +2.87 V远大于E°(Cl₂/Cl⁻) = +1.36 V，氟会将氯离子氧化成氯气。一般而言，E°较高的氧化态物种能将系列中位置更低的还原态物种氧化。

7. Cell Notation and Conventions | 电池表示法与惯例

Electrochemical cells are conveniently represented using cell (line) notation. The anode (oxidation half-cell) is written on the left, the cathode (reduction half-cell) on the right, and a double vertical line (||) represents the salt bridge. A single vertical line (|) separates phases within a half-cell.

电化学电池用电池（线式）表示法可以简便地表达。阳极（氧化半电池）写在左边，阴极（还原半电池）写在右边，双竖线（||）表示盐桥。单竖线（|）分隔半电池内的不同相态。

For the Daniell cell, the cell notation is:

对于丹尼尔电池，电池表示式为：

Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s)

Key conventions to remember:

需要记住的关键惯例：

The anode and its ion are on the left; the cathode and its ion are on the right.
阳极及其离子在左边；阴极及其离子在右边。
Gases and non-metallic electrodes require an inert electrode (e.g. Pt) in the notation, written adjacent to the gas: Pt(s) | H₂(g) | H⁺(aq).
气体和非金属电极需要用惰性电极（如Pt），标注在气体旁边：Pt(s) | H₂(g) | H⁺(aq)。
Commas separate species in the same phase, e.g. Fe²⁺(aq), Fe³⁺(aq) | Pt(s).
同相中的物种用逗号分隔，如Fe²⁺(aq), Fe³⁺(aq) | Pt(s)。

8. Calculating Cell Potential | 计算电池电位

The standard cell potential (E°cell) is the potential difference between the two half-cells under standard conditions. It can be calculated from the standard electrode potentials of the two half-reactions using:

标准电池电位（E°cell）是标准条件下两个半电池之间的电势差。可以由两个半反应的标准电极电位计算：

E°cell = E°(cathode) − E°(anode)

Alternatively, if using reduction potentials:

或者使用还原电位时：

E°cell = E°(reduction at cathode) − E°(reduction at anode)

A positive E°cell indicates a spontaneous reaction (ΔG° < 0), while a negative E°cell corresponds to a non-spontaneous reaction (ΔG° > 0).

E°cell为正表示反应自发进行（ΔG° < 0），E°cell为负则对应非自发反应（ΔG° > 0）。

Worked example: For the Daniell cell, Zn is oxidised (E° = −0.76 V) and Cu²⁺ is reduced (E° = +0.34 V). Therefore:

示例：对于丹尼尔电池，Zn被氧化（E° = −0.76 V），Cu²⁺被还原（E° = +0.34 V）。因此：

E°cell = +0.34 V − (−0.76 V) = +1.10 V

Because E°cell is positive, the reaction is spontaneous and the cell can deliver electrical work.

由于E°cell为正，该反应自发放热，电池能够输出电功。

9. The Nernst Equation | 能斯特方程

The Nernst equation relates the actual cell potential (E) to the standard cell potential (E°), the temperature, and the reaction quotient (Q):

能斯特方程将实际电池电位（E）与标准电池电位（E°）、温度和反应商（Q）联系起来：

E = E° − (RT/nF) × lnQ

At 298 K, using base-10 logarithms, this simplifies to:

在298 K时，使用以10为底的对数，可简化为：

E = E° − (0.0592/n) × log₁₀Q

Here, R is the gas constant (8.314 J mol⁻¹ K⁻¹), T is the absolute temperature, n is the number of electrons transferred, F is the Faraday constant (96,485 C mol⁻¹), and Q is the reaction quotient.

其中，R是气体常数（8.314 J mol⁻¹ K⁻¹），T是绝对温度，n是转移电子数，F是法拉第常数（96,485 C mol⁻¹），Q是反应商。

The Nernst equation is essential for predicting how cell potential changes with concentration. For the Daniell cell:

能斯特方程对于预测电池电位随浓度如何变化至关重要。对于丹尼尔电池：

E = E° − (0.0592/2) × log₁₀( [Zn²⁺] / [Cu²⁺] )

Increasing [Cu²⁺] relative to [Zn²⁺] makes Q smaller, which makes E larger. Conversely, as the cell discharges, [Zn²⁺] increases and [Cu²⁺] decreases, Q increases, and E gradually drops until the cell “runs flat” at E = 0.

增大[Cu²⁺]相对于[Zn²⁺]的比值会使Q变小，从而使E更大。反之，当电池放电时，[Zn²⁺]增大而[Cu²⁺]减小，Q增大，E逐渐降低，直至E = 0时电池”耗尽”。

10. Electrolytic Cells | 电解电池

Unlike voltaic cells, electrolytic cells use electrical energy to drive non-spontaneous chemical reactions. A direct current (DC) supply is connected to two electrodes immersed in an electrolyte (a molten ionic compound or an aqueous ionic solution).

与伏打电池不同，电解电池利用电能驱动非自发化学反应。将直流电源连接到浸入电解质（熔融离子化合物或水溶液体系）中的两个电极上。

Key features of electrolytic cells:

电解电池的关键特征：

Anode (positive electrode): connected to the positive terminal of the power supply; oxidation occurs here.
阳极（正极）：连接到电源正极；在此发生氧化反应。
Cathode (negative electrode): connected to the negative terminal; reduction occurs here.
阴极（负极）：连接到电源负极；在此发生还原反应。
Electrolyte: the substance that conducts electricity through mobile ions; it undergoes decomposition during electrolysis.
电解质：通过可移动离子导电的物质；在电解过程中发生分解。

In the electrolysis of molten NaCl, sodium ions migrate to the cathode and are reduced to sodium metal, while chloride ions migrate to the anode and are oxidised to chlorine gas.

在熔融NaCl的电解中，钠离子迁移到阴极并被还原为钠金属，氯离子迁移到阳极并被氧化为氯气。

Cathode: Na⁺ + e⁻ → Na Anode: 2Cl⁻ → Cl₂ + 2e⁻

When electrolysing aqueous solutions, competition arises between water and the ionic species. The product is determined by the relative electrode potentials and the overpotentials (kinetic effects). For example, in the electrolysis of aqueous NaCl, H₂ is evolved at the cathode rather than Na, because water is more easily reduced than Na⁺.

电解水溶液时，水与离子物种之间存在竞争。产物由相对电极电位和过电位（动力学效应）决定。例如，在电解NaCl水溶液时，阴极放出H₂而不是Na，因为水比Na⁺更容易被还原。

11. Faraday’s Laws of Electrolysis | 法拉第电解定律

Faraday’s laws quantify the relationship between the amount of substance produced or consumed at an electrode and the charge passed through the cell.

法拉第定律定量描述了电极上产生或消耗物质的量与通过电池电量之间的关系。

First law: The mass of a substance deposited or liberated at an electrode is directly proportional to the quantity of electric charge passed.

第一定律：电极上析出或沉积的物质质量与通过的电量成正比。

m ∝ Q where Q = I × t

Second law: The mass of substance deposited or liberated is directly proportional to its molar mass and inversely proportional to the number of electrons transferred per ion (n).

第二定律：沉积或析出物质的质量与其摩尔质量成正比，与每个离子转移的电子数（n）成反比。

Combining both laws gives the key expression:

结合两条定律得到关键表达式：

m = (M × I × t) / (n × F)

where m is the mass in grams, M is the molar mass in g mol⁻¹, I is the current in amperes, t is time in seconds, n is the number of electrons transferred per ion, and F is the Faraday constant = 96,485 C mol⁻¹ (the charge on one mole of electrons).

其中m是质量（克），M是摩尔质量（g mol⁻¹），I是电流（安培），t是时间（秒），n是每个离子转移的电子数，F是法拉第常数 = 96,485 C mol⁻¹（一摩尔电子的电荷量）。

Worked example: How many grams of copper are deposited when a current of 2.00 A flows through a CuSO₄ solution for 30.0 minutes? (M(Cu) = 63.5 g mol⁻¹, n = 2)

示例：当2.00 A的电流通过CuSO₄溶液30.0分钟时，沉积多少克铜？（M(Cu) = 63.5 g mol⁻¹, n = 2）

Q = I × t = 2.00 × (30.0 × 60) = 3,600 C

m = (63.5 × 3,600) / (2 × 96,485) = 1.18 g

The number of moles of electrons can also be found directly: n(e⁻) = Q / F, which is often useful for determining stoichiometry in electrolysis problems.

电子的摩尔数也可以直接求出：n(e⁻) = Q / F，这在解决电解问题的化学计量时往往非常有用。

12. Practical Applications | 实际应用

Electrochemical principles underpin many technologies we rely on daily, from portable power sources to industrial processes and corrosion protection.

电化学原理支撑着我们日常依赖的许多技术，从便携式电源到工业生产和腐蚀防护。

Primary (non-rechargeable) batteries: e.g. alkaline batteries and zinc–carbon cells, in which the redox reaction proceeds spontaneously until the reactants are consumed.
一次电池（不可充电）：如碱性电池和锌–碳电池，氧化还原反应自发进行直至反应物消耗殆尽。
Secondary (rechargeable) batteries: e.g. lead-acid batteries and lithium-ion batteries, where the cell reaction is reversed by applying an external voltage during charging.
二次电池（可充电）：如铅酸电池和锂离子电池，充电时通过施加外部电压将电池反应逆转。
Fuel cells: a continuous supply of fuel (e.g. H₂) and oxidant (O₂) produces electricity and water as the only product, making them highly efficient and environmentally friendly.
燃料电池：持续供应燃料（如H₂）和氧化剂（O₂）产生电能，唯一产物是水，因此效率高且环保。
Electroplating: an electrolytic cell is used to coat one metal onto another (e.g. chrome plating) for corrosion resistance or aesthetic purposes.
电镀：利用电解电池将一种金属镀到另一种金属表面（如镀铬），用于防腐或美观。
Corrosion prevention: sacrificial (cathodic) protection connects a more reactive metal (e.g. zinc or magnesium) to iron or steel; the sacrificial metal oxidises preferentially, protecting the structure.
腐蚀防护：牺牲阳极（阴极保护）将更活泼的金属（如锌或镁）连接到铁或钢铁上；牺牲金属优先被氧化，从而保护结构件。

Understanding the principles of electrochemical cells not only helps master IB Chemistry examinations but also builds a foundation for appreciating energy storage and sustainability challenges in the modern world.

理解电化学电池的原理不仅有助于掌握IB化学考试内容，也为认识现代世界的储能与可持续发展挑战奠定了基础。

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Principles of Electrochemical Cells | 电化学电池原理