📚 Measuring Standard Electrode Potentials | 测量标准电极电势
Standard electrode potentials provide a quantitative measure of the tendency of a chemical species to be reduced. By comparing half-cells under precisely defined conditions against the universal reference – the standard hydrogen electrode – chemists can build up a table of redox strengths. This article explains the experimental setup, essential components, and procedural details required to measure these potentials accurately, as specified by the Cambridge A‑Level Chemistry syllabus.
标准电极电势定量描述了化学物质被还原的趋势。在严格定义的条件下，将半电池与通用参照——标准氢电极——进行对比，化学家便能建立起一张氧化还原能力的表格。本文依据剑桥 A‑Level 化学大纲，详细解释测量这些电势所需的实验装置、关键组件与操作步骤。
1. Introduction to Standard Electrode Potentials | 标准电极电势简介
An electrode potential (E) is the voltage developed when a metal is dipped into a solution of its own ions. Since an isolated half‑cell potential cannot be measured directly, it is always determined by connecting two half‑cells to form a complete electrochemical cell. The measured cell potential (Ecell) is then the difference between the two electrode potentials.
电极电势（E）是金属浸入其自身离子溶液时产生的电压。由于无法直接测量孤立的半电池电势，总是通过连接两个半电池构成一个完整的电化学电池来测定。测得的电池电势（Ecell）即为两个电极电势之差。
By convention, the standard hydrogen electrode (SHE) is assigned a potential of exactly 0 V under standard conditions. All other standard electrode potentials (E°) are measured relative to the SHE, giving a consistent scale of reducing and oxidising power.
根据约定，标准氢电极（SHE）在标准条件下被指定为 0 V。所有其他标准电极电势（E°）均以 SHE 为基准进行测量，从而获得一套衡量还原能力与氧化能力的统一标度。
2. The Standard Hydrogen Electrode (SHE) | 标准氢电极
The standard hydrogen electrode is the primary reference for all electrode‑potential measurements. It consists of a platinum electrode coated with finely divided platinum black (to catalyse the surface reaction), immersed in a solution of 1 mol dm⁻³ H⁺ (e.g. 1 mol dm⁻³ HCl or ½ H₂SO₄). Hydrogen gas at 100 kPa pressure is bubbled over the platinum surface, and the equilibrium established is:
2H⁺(aq) + 2e⁻ ⇌ H₂(g) E° = 0.00 V
标准氢电极是所有电极电势测量的基准。它由一根表面镀有铂黑（以催化表面反应）的铂电极浸入 1 mol dm⁻³ H⁺ 溶液中构成（例如 1 mol dm⁻³ 盐酸或 ½ 硫酸）。在 100 kPa 压力下向铂表面通入氢气，建立的平衡为：
2H⁺(aq) + 2e⁻ ⇌ H₂(g) E° = 0.00 V
The SHE is reversible and non‑polarisable, meaning its potential remains extremely stable. The half‑cell is normally written as:
Pt(s) | H₂(g) | H⁺(aq)
SHE 可逆且不易极化，因此其电势非常稳定。该半电池通常表示为：
Pt(s) | H₂(g) | H⁺(aq)
3. Construction and Setup of the SHE | SHE的构造与装置
The platinum electrode is usually a small foil or wire platinised to increase its active surface area. It is sealed into a glass tube that allows hydrogen gas to enter and bubble out of a small hole near the Pt surface. The tube is submerged so that the platinum is in contact with both the hydrogen gas and the acid solution. A steady stream of H₂ is bubbled through to keep the gas pressure constant and to saturate the solution.
铂电极通常是一片小铂箔或铂丝，经过镀铂处理以增大有效表面积。它封接在玻璃管中，氢气可通入并在铂表面附近的小孔处冒出。玻璃管浸入溶液中，使铂同时接触氢气和酸液。持续通入稳定的氢气流可以保持气体压力恒定并使溶液饱和。
To maintain standard conditions, the temperature must be 298 K (25 °C) and the pressure of H₂ gas exactly 100 kPa. If dilute sulfuric acid is used, the concentration of H⁺ must still be 1 mol dm⁻³; the anion (SO₄²⁻) does not participate in the electrode reaction.
为维持标准状态，温度必须为 298 K（25 °C），氢气压力必须恰好为 100 kPa。若使用稀硫酸，H⁺ 浓度仍需为 1 mol dm⁻³；阴离子（SO₄²⁻）不参与电极反应。
4. Measuring an Electrode Potential: The Half‑Cell Connection | 测量电极电势：半电池的连接
To measure the standard electrode potential of, say, a Zn²⁺/Zn half‑cell, the zinc electrode (a piece of pure zinc) is immersed in a 1 mol dm⁻³ Zn²⁺ solution (e.g. ZnSO₄). This half‑cell is connected to the SHE via a salt bridge and an external circuit containing a high‑resistance voltmeter. The complete cell is represented as:
Zn(s) | Zn²⁺(aq) ║ H⁺(aq) | H₂(g) | Pt(s)
为测量诸如 Zn²⁺/Zn 半电池的标准电极电势，需将锌电极（一片纯锌）浸入 1 mol dm⁻³ Zn²⁺ 溶液中（如 ZnSO₄）。该半电池通过盐桥和含有高阻抗电压表的外电路与 SHE 相连。整个电池可表示为：
Zn(s) | Zn²⁺(aq) ║ H⁺(aq) | H₂(g) | Pt(s)
The voltmeter reading gives the standard cell potential. If zinc is the negative electrode (anode), electrons flow from Zn to the SHE, and the measured E°cell is +0.76 V. By definition, E°cell = E°cathode – E°anode. Since the SHE is the cathode here (reduction occurs: 2H⁺ + 2e⁻ → H₂), E° for Zn²⁺/Zn is –0.76 V.
电压表的读数即为标准电池电势。若锌为负极（阳极），电子从 Zn 流向 SHE，测得 E°cell 为 +0.76 V。根据定义，E°cell = E°阴极 – E°阳极。此时 SHE 为阴极（发生还原：2H⁺ + 2e⁻ → H₂），因此 Zn²⁺/Zn 的 E° 为 –0.76 V。
5. The Salt Bridge and Its Function | 盐桥及其功能
A salt bridge completes the electrical circuit by allowing ions to migrate between the two half‑cell solutions while preventing them from mixing. Typically, it is a U‑shaped tube filled with a saturated solution of an inert electrolyte (often KNO₃ or NH₄NO₃) set in agar jelly. The ends are plugged with glass wool to minimise diffusion.
盐桥允许离子在两半电池溶液间迁移，从而构成完整回路，同时防止溶液混合。它通常是一个 U 形管，内充浸有琼脂的惰性电解质饱和溶液（常用 KNO₃ 或 NH₄NO₃），两端用玻璃棉塞住以减少扩散。
The salt bridge maintains electrical neutrality: as electrons flow through the external wire, positive ions move from the salt bridge into the cathode compartment (or negative ions into the anode compartment) to balance the charges generated by the electrode reactions. Without a salt bridge, the cell potential would rapidly drop to zero.
盐桥维持了电中性：当电子通过外电路流动时，阳离子从盐桥迁移至阴极区（或阴离子迁移至阳极区），以平衡电极反应产生的电荷。没有盐桥，电池电势会迅速降至零。
6. Using a High‑Resistance Voltmeter | 使用高阻抗电压表
A crucial requirement is to measure the cell potential under virtually zero‑current conditions. If appreciable current flows, the concentrations at the electrode surfaces change (polarisation), causing the potential to drift from the true equilibrium value. A high‑resistance voltmeter (digital multimeter with an input impedance > 10¹² Ω) draws negligible current, so the measured EMF approximates the reversible cell potential.
一项关键要求是在近乎零电流的条件下测量电池电势。若有明显电流通过，电极表面的浓度会发生变化（极化），导致电势偏离真实的平衡值。高阻抗电压表（输入阻抗 > 10¹² Ω 的数字万用表）吸取的电流可忽略不计，因此测得的电动势近似等于可逆电池电势。
Alternatively, a potentiometer (or null‑balance method) can be used, where the cell potential is balanced against a known voltage from a standard cell such that no current flows at the point of balance. This classical technique eliminates any current drain altogether.
亦可用电位差计（或零点平衡法），将待测电池电势与已知标准电池的电压相平衡，在平衡点无电流流过。这一经典方法可彻底消除任何电流汲取。
7. Standard Conditions for Measurement | 测量的标准条件
To ensure reproducibility and allow comparison, standard electrode potentials are always reported under strictly defined standard conditions:
- All solutions have an ion concentration of 1 mol dm⁻³ (strictly, unit activity).
- Temperature is 298 K (25 °C).
- Pressure of any gas involved is 100 kPa (1 bar).
- The electrode surface must be clean and the metallic contact purely made of that metal.
为保证重复性和可比性，标准电极电势总是在严格定义的标准条件下报告：
- 所有溶液的离子浓度为 1 mol dm⁻³（严格而言，活度为单位值）。
- 温度为 298 K（25 °C）。
- 涉及任何气体的压力为 100 kPa（1 bar）。
- 电极表面必须洁净，且金属接触部分由该纯金属制成。
If any condition deviates, the measured potential changes, and the value is no longer the standard E°. For example, a lower Zn²⁺ concentration would make the Zn²⁺/Zn half‑cell more negative (Le Chatelier’s principle applied to the equilibrium: Zn²⁺ + 2e⁻ ⇌ Zn).
若任一条件发生偏离，测量到的电势便会改变，所得数值不再是标准 E°。例如，降低 Zn²⁺ 浓度会使 Zn²⁺/Zn 半电池的电势变得更负（根据平衡 Zn²⁺ + 2e⁻ ⇌ Zn 应用勒夏特列原理）。
8. Procedure for Determining E° of a Metal/Metal Ion Half‑Cell | 测定金属/金属离子半电池E°的步骤
Step‑by‑step, to determine E° for Cu²⁺/Cu:
- Prepare the SHE exactly as described: platinised Pt, 1 mol dm⁻³ H⁺, H₂ at 100 kPa, 298 K.
- Prepare a copper electrode (a strip of pure copper foil cleaned with emery paper) and 1 mol dm⁻³ CuSO₄ solution.
- Connect the two half‑cells with a salt bridge (saturated KNO₃‑agar).
- Connect the electrodes to a high‑resistance voltmeter and record the reading with the polarity.
- Write the cell notation and deduce the half‑cell E°.
测定 Cu²⁺/Cu 标准电势的步骤：
- 按照描述准确制备 SHE：镀铂黑的铂电极，1 mol dm⁻³ H⁺，H₂ 压力 100 kPa，298 K。
- 准备铜电极（用砂纸打磨干净的纯铜片）和 1 mol dm⁻³ CuSO₄ 溶液。
- 用盐桥（饱和 KNO₃‑琼脂）连接两个半电池。
- 将电极与高阻电压表相连，记录读数及正负极性。
- 写出电池表示式，推算出半电池 E°。
electrode positive (copper ions are reduced: Cu²⁺ + 2e⁻ → Cu). Thus E°(Cu²⁺/Cu) = +0.34 V.
实际中，电压表读数约为 +0.34 V，且 Cu 电极为正极（铜离子被还原：Cu²⁺ + 2e⁻ → Cu）。因此 E°(Cu²⁺/Cu) = +0.34 V。
9. Procedure for Determining E° of a Non‑Metal/Non‑Metal Ion Half‑Cell | 测定非金属/非金属离子半电池E°的步骤
Many half‑cells involve two aqueous ions, such as Fe³⁺/Fe²⁺, MnO₄⁻/Mn²⁺, or Cl₂/Cl⁻. In these cases, an inert platinum electrode is used as the electron transfer surface because there is no solid metal to participate directly. The half‑cell is set up with a platinum wire or foil dipping into a solution containing both ions at 1 mol dm⁻³ each (if applicable), or in the case of a gas/ion electrode, the gas is bubbled around a Pt electrode immersed in the ion solution.
许多半电池涉及两种水合离子，例如 Fe³⁺/Fe²⁺、MnO₄⁻/Mn²⁺ 或 Cl₂/Cl⁻。此时需使用惰性铂电极作为电子传递表面，因为没有固态金属直接参与。半电池由一根铂丝或铂箔浸入含两种离子均为 1 mol dm⁻³ 的溶液构成（若适用），若为气体/离子电极，则将气体通入浸在离子溶液中的铂电极周围。
Example: For the Fe³⁺/Fe²⁺ half‑cell, place a clean Pt electrode in a solution containing 1 mol dm⁻³ Fe³⁺ and 1 mol dm⁻³ Fe²⁺ (e.g. FeCl₃ and FeCl₂ mixture). Connect to SHE via salt bridge. The measured E° will be +0.77 V. The standard hydrogen electrode again acts as the reference.
示例：对于 Fe³⁺/Fe²⁺ 半电池，将洁净的铂电极置于含 1 mol dm⁻³ Fe³⁺ 和 1 mol dm⁻³ Fe²⁺ 的溶液中（如 FeCl₃ 与 FeCl₂ 混合液）。通过盐桥与 SHE 连接。测得的 E° 将为 +0.77 V。标准氢电极再次作为参比。
For a gas electrode like Cl₂/Cl⁻, chlorine gas at 100 kPa is bubbled over a Pt electrode in 1 mol dm⁻³ Cl⁻. The measured standard electrode potential is +1.36 V.
对于 Cl₂/Cl⁻ 这样的气体电极，在 100 kPa 下将氯气通入 1 mol dm⁻³ Cl⁻ 溶液中的铂电极周围。测得的该标准电极电势为 +1.36 V。
10. Calculating Standard Cell Potential from Half‑Cell Potentials | 从半电池电势计算标准电池电势
Once the standard electrode potentials are determined, they can be used to calculate the EMF of any cell composed of two half‑cells by applying:
E°cell = E°cathode – E°anode
where the cathode is the half‑cell with the more positive (less negative) E° – reduction occurs there.
一旦测定了标准电极电势，便可利用下式计算由任意两个半电池组成的电池电动势：
E°cell = E°阴极 – E°阳极
其中阴极是 E° 更正（或负值更小）的半电池——还原在此发生。
For instance, using Zn²⁺/Zn (–0.76 V) and Cu²⁺/Cu (+0.34 V), the spontaneous cell has copper as cathode and zinc as anode. Thus, E°cell = (+0.34 V) – (– itive value confirms the reaction is thermodynamically feasible under standard conditions.
例如，使用 Zn²⁺/Zn (–0.76 V) 和 Cu²⁺/Cu (+0.34 V)，自发的电池中铜为阴极、锌为阳极。因此，E°cell = (+0.34 V) – (–0.76 V) = +1.10 V。正值证实该反应在标准条件下热力学可行。
11. Factors Affecting the Measured Electrode Potential | 影响测量电极电势的因素
Several experimental factors can shift the measured potential away from the true standard value:
- Concentration: E° + (RT/nF) ln([oxidised]/[reduced]). If the ion concentration is not exactly 1 mol dm⁻³, the measured E deviates logarithmically.
- Temperature: Both the E° itself and the RT/nF term depend on temperature. Measurements must occur at 298 K.
- Pressure: For gas electrodes, pressure changes alter the electrode potential. For SHE, 100 kPa is essential.
- Cleanliness of electrodes: Traces of oxide or contaminant layers can create additional potential barriers or mixed potentials.
- Current flow: If the voltmeter draws significant current, concentration polarisation or activation polarisation will distort the reading.
若干实验因素会使测得的电势偏离真正的标准值：
- 浓度：根据能斯特方程，E = E° + (RT/nF) ln([氧化型]/[还原型])。若离子浓度并非恰好 1 mol dm⁻³，测得的 E 会呈对数式偏离。
- 温度：E° 本身以及 RT/nF 项均与温度有关。测量必须在 298 K 下进行。
- 压力：对于气体电极，压力变化会改变电极电势。对于 SHE，100 kPa 至关重要。
- 电极清洁度：微量氧化物或污染物层会产生额外的电势壁垒或混合电势。
- 电流流动：若电压表吸取显著电流，浓差极化或活化极化会使读数失真。
To mitigate these issues, freshly prepared solutions, polished electrodes, thermostatic control, and high‑impedance measuring devices are used.
为减少这些影响，应使用新配制的溶液、抛光的电极、恒温控制以及高阻抗测量设备。
12. Summary and Key Points | 总结与要点
Measuring standard electrode potentials is a foundational skill in electrochemistry. The standard hydrogen electrode provides the universal zero reference. By connecting the unknown half‑cell to the SHE through a salt bridge and measuring the potential difference with a high‑resistance voltmeter under strict standard conditions (298 K, 1 mol dm⁻³, 100 kPa), the standard electrode potential can be accurately determined. This value reveals the relative reducing or oxidising strength of the redox couple and allows the calculation of any cell EMF. Careful control of experimental variables and avoidance of current flow are critical for reliable data.
测量标准电极电势是电化学的一项基本技能。标准氢电极提供了通用的零点参照。将未知半电池通过盐桥与 SHE 连接，在严格的标准条件（298 K、1 mol dm⁻³、100 kPa）下用高阻抗电压表测量电势差，即可准确测定标准电极电势。该数值揭示了氧化还原电对相对的失电子或得电子能力，并能计算出任意电池的电动势。严格控制实验变量并避免电流通过是获得可靠数据的关键。
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