Bilingual edition: English is preserved and Chinese follows each unit. Terminology uses the confirmed v20260916 glossary; automated semantic review remains traceable.
中英双语版:英文原文完整保留,中文紧随对应单元;术语采用 v20260916 确认表,自动语义审校结果可追溯。

Standard Electrode Potentials

标准电极电势

In an electrochemical cell, an electric potential is created between two dissimilar metals. This potential is a measure of the energy per unit charge which is available from the oxidation/reduction reactions to drive the reaction. It is customary to visualize the cell reaction in terms of two half-reactions, an oxidation half-reaction and a reduction half-reaction.

在电解池中,两种不同金属之间会产生一个电势。这个电势是衡量氧化还原反应中每单位电荷可提供的能量,用于驱动反应。通常,人们会将电池反应视为两个半反应,即氧化半反应和还原半反应。
Reduced species -> oxidized species + ne-
简化物种 -> 氧化物种 + ne⁻
Oxidation at anode
阳极氧化
Oxidized species + ne- -> reduced species
氧化剂 + ne - -> 还原剂
Reduction at cathode
阴极还原

The cell potential (often called the electromotive force or emf) has a contribution from the anode which is a measure of its ability to lose electrons - it will be called its "oxidation potential". The cathode has a contribution based on its ability to gain electeons, its "reduction potential". The cell potential can then be written

电池的电动势(通常称为电动势或emf)包含来自阳极的贡献,这是它失去电子能力的度量——它被称为其‘氧化势’。阴极的贡献基于其获得电子的能力,称为其‘还原势’。电池的电动势可以写成

Ecell = oxidation potential + reduction potential

电池的电动势等于氧化势与还原势之和

If we could tabulate the oxidation and reduction potentials of all available electrodes, then we could predict the cell potentials of voltaic cells created from any pair of electrodes. Actually, tabulating one or the other is sufficient, since the oxidation potential of a half-reaction is the negative of the reduction potential for the reverse of that reaction. Two main hurdles must be overcome to establish such a tabulation

如果我们能列出所有可用电极的氧化和还原电势,那么就可以预测由任意两个电极组成的原电池的电池电势。实际上,列出其中一个即可,因为一个半反应的氧化电势是该反应逆反应的还原电势的负数。要建立这样的列表,必须克服两个主要障碍。
  1. The electrode potential cannot be determined in isolation, but in a reaction with some other electrode.
    电极电势不能孤立确定,而是在与其他电极反应的情况下确定的。
  2. The electrode potential depends upon the concentrations of the substances, the temperature, and the pressure in the case of a gas electrode.
    电极电势取决于物质的浓度、温度以及气体电极中的压力。

In practice, the first of these hurdles is overcome by measuring the potentials with respect to a standard hydrogen electrode. It is the nature of electric potential that the zero of potential is arbitrary; it is the difference in potential which has practical consequence. Tabulating all electrode potentials with respect to the same standard electrode provides a practical working framework for a wide range of calculations and predictions. The standard hydrogen electrode is assigned a potential of zero volts.

实际上,克服这些障碍的第一步是通过相对于标准氢电极测量电势来实现的。电势的性质决定了零点是任意的;只有电势差才有实际意义。将所有电极电势相对于同一标准电极进行整理,为广泛的计算和预测提供了实用的框架。标准氢电极被赋予零伏的电势。

The second hurdle is overcome by choosing standard thermodynamic conditions for the measurement of the potentials. The standard electrode potentials are customarily determined at solute concentrations of 1 Molar, gas pressures of 1 atmosphere, and a standard temperature which is usually 25°C. The standard cell potential is denoted by a degree sign as a superscript.

第二个障碍是通过选择标准热力学条件来测量电势。标准电极电势通常在溶质浓度为1摩尔/升、气体压力为1大气压以及标准温度(通常为25°C)下确定。标准电池电势用上标度数符号表示。
E°Cell
电池电动势
  1. Measured against standard hydroden electrode.
    相对于标准氢电极测量
  2. Concentration 1 Molar
    浓度 1 mol/L
  3. Pressure 1 atmosphere
    压力 1 个大气压
  4. Temperature 25°C
    温度 25°C

The example below shows some of the extreme values for standard cell potentials.

下面的例子展示了一些标准电池电势的极值。
Cathode (Reduction)
Half-Reaction
阴极(还原)半反应
Standard Potential
E° (volts)
标准电势 E ° (伏特)
Li+(aq) + e- -> Li(s)
Li⁺(aq) + e⁻ → Li(s)
-3.04
K+(aq) + e- -> K(s)
K⁺(aq) + e⁻ → K(s)
-2.92
Ca2+(aq) + 2e- -> Ca(s)
Ca²⁺(aq) + 2e⁻ → Ca(s)
-2.76
Na+(aq) + e- -> Na(s)
Na⁺(aq) + e⁻ → Na(s)
-2.71
Zn2+(aq) + 2e- -> Zn(s)
Zn²⁺(aq) + 2e⁻ → Zn(s)
-0.76
Cu2+(aq) + 2e- -> Cu(s)
Cu²⁺(aq) + 2e⁻ → Cu(s)
0.34
O3(g) + 2H+(aq) + 2e- -> O2(g) + H2O(l)
O₃(g)+ 2H⁺(aq)+ 2e⁻ → O₂(g)+ H₂O(l)
2.07
F2(g) + 2e- -> 2F-(aq)
F₂(g) + 2e⁻ → 2F⁻(aq)
2.87

The values for the table entries are reduction potentials, so lithium at the top of the list has the most negative number, indicating that it is the strongest reducing agent. The strongest oxidizing agent is fluorine with the largest positive number for standard electrode potential. The link below takes you to a more extensive table.

表中的数值是还原电势,因此列表顶部的锂具有最负的数值,表明它是最强的还原剂。最强的氧化剂是氟,其标准电极电势具有最大的正数值。下方的链接可带你到更详细的表格。
Table of Standard Electrode Potentials
标准电极电势表

Useful applications of the standard electrode potentials include the following.

标准电极电势的有用应用包括以下内容。
Strengths of oxidizing and reducing agents
氧化剂和还原剂的强度
Electrode potentials under non-standard conditions
非标准条件下的电极电势
Potentials for voltaic cells
伏打电池的电势
Relationship to Gibbs free energy
与吉布斯自由能的关系
Relationship to equilibrium constants
与平衡常数的关系
Index

Oxidation/
Reduction concepts


Electrochemistry concepts

Reference
Hill & Kolb
Ch 8

Ebbing
Ch 19
索引 氧化还原概念 电化学概念 参考 Hill & Kolb 第8章 Ebbing 第19章
 
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Calculation of Voltaic Cell Potentials

伏打电池电势的计算

When an electrochemical cell is arranged with the two half-reactions separated but connected by an electrically conducting path, a voltaic cell is created. The maximum voltage which can be produced between the poles of the cell is determined by the standard electrode potentials under the standard conditions under which those potentials are defined.

当一个电化学电池的两个半反应被分离但通过一个电导路径连接时,就会形成一个伏打电池。该电池两极之间所能产生的最大电压,由标准电极电势在定义这些电势的标准条件下确定。

Consider the historic Daniell cell in which zinc and copper were used as electrodes. The data from the table of standard electrode potentials is

考虑历史上使用的丹尼尔电池,其中锌和铜被用作电极。表中标准电极电势的数据是
Cathode (Reduction)
Half-Reaction
阴极(还原)半反应
Standard Potential
E° (volts)
标准电势 E ° (伏特)
Zn2+(aq) + 2e- -> Zn(s)
Zn²⁺(aq) + 2e⁻ → Zn(s)
-0.76
Cu2+(aq) + 2e- -> Cu(s)
Cu²⁺(aq) + 2e⁻ → Cu(s)
0.34

The cell potential can be written

电池的电动势可以表示为

Ecell = oxidation potential + reduction potential

电池的电动势等于氧化势与还原势之和

Since the tabulated standard electrode potentials are reduction potentials, the one which is most negative will need to be reversed in sign to get its oxidation potential. When that is done, it is clear that the theoretical standard cell potential for the zinc-copper cell is 1.10 volts.

由于表列的标准电极电势是还原电势,最负的电势需要改变符号以得到其氧化电势。当这样做之后,可以清楚地看出锌-铜电池的理论标准电池电势为1.10伏特。

In general, a real voltaic cell will differ from the standard conditions, so we need to be able to adjust the calculated cell potential to account for the differences. This can be done with the application of the Nernst equation.

一般来说,实际的伏打电池会与标准条件有所不同,因此我们需要能够调整计算出的电池电动势以考虑这些差异。这可以通过应用能斯特方程来实现。

Presuming that there are two metal electrodes with their ions, the standard potential for a cell with anode potential volts and cathode potential volts is

假设有两个金属电极,其离子分别为,则标准电动势为伏特的阳极电势和伏特的阴极电势的电池是
中文译文中的待填/计算数值依次对应:1:ea 2:ec。实际数值以上方原输入框为准。

E°cell = volts

电池电动势为伏特
中文译文中的待填/计算数值依次对应:1:es。实际数值以上方原输入框为准。

If the ion concentration at the anode is [A] = M and the concentration at the cathode is [C] = M, then the thermodynamic reaction quotient Q = [A]/[C] =

如果阳极的离子浓度为[A] = M,阴极的离子浓度为[C] = M,则热力学反应商Q = [A]/[C] =
中文译文中的待填/计算数值依次对应:1:ca 2:cc 3:q。实际数值以上方原输入框为准。

For temperature = °C = K and number of electrons exchanged n = , the calculated cell potential is

当温度 = °C = K 且交换的电子数 n = 时,计算得到的电池电势为
中文译文中的待填/计算数值依次对应:1:tc 2:t 3:n。实际数值以上方原输入框为准。

Ecell = volts

电池电压为伏特
中文译文中的待填/计算数值依次对应:1:ecell。实际数值以上方原输入框为准。

By numerically exploring the above calculation, you can confirm that large concentration differences between the anions and the cations can cause the voltage to differ significantly from the standard cell potential, and that such large concentration differences also make the cell potential more temperature dependent.

通过数值探索上述计算,可以确认,阴离子与阳离子之间的大浓度差会使电压显著偏离标准电池电动势,并且这种大浓度差也使电池电动势更依赖温度。
Index

Oxidation/
Reduction concepts


Electrochemistry concepts

Reference
Hill & Kolb
Ch 8

Ebbing
Ch 19
索引 氧化还原概念 电化学概念 参考 Hill & Kolb 第8章 Ebbing 第19章
 
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The Nernst Equation

能斯特方程

The cell potential for a voltaic cell under standard conditions can be calculated from the standard electrode potentials. But real voltaic cells will typically differ from the standard conditions. The Nernst equation relates the cell potential to its standard cell potential.

电池的电动势可以在标准条件下通过标准电极电势计算得出。但实际的原电池通常会与标准条件有所不同。能斯特方程将电池的电动势与其标准电池电动势联系起来。
R = gas constant
T = temperature in Kelvins
Q = thermodynamic reaction quotient
F = Faraday's constant
n = number of electrons transferred
R = 气体常数;T = 华氏温度;Q = 热力学反应商;F = 法拉第常数;n = 转移的电子数

The quantity Q, the thermodynamic reaction constant, is like a dynamic version of the equilibrium constant in which the concentrations and gas pressures are the instantaneous values in the reaction mixture. For a reaction

量Q,热力学反应常数,类似于平衡常数的动态版本,其中浓度和气体压力是反应混合物中的即时值。对于一个反应

the reaction quotient has the form

反应商的形式是

where [C] is understood to be the molar concentration of product C, or the partial pressure in atmospheres if it is a gas.

其中[C]被理解为产物C的摩尔浓度,或若其为气体则理解为大气压下的分压。

Applied to the Daniell cell where zinc and copper form the electrodes, the reaction is

应用于丹尼尔电池,其中锌和铜形成电极,反应为

Zn(s) + Cu2+(aq) <-> Zn2+(aq) + Cu(s)

Zn(s) + Cu²+(aq) ↔ Zn²+(aq) + Cu(s)

the form of Q is

Q 的形式

since the concentrations of the pure metal solids are assigned the value 1. This implies that the departure of the cell potential from its standard value of 1.10 volts will be influenced by the temperature and the ion concentrations.

由于纯金属固体的浓度被赋予值1。这表明,电池电动势偏离其标准值1.10伏将受到温度和离子浓度的影响。

One implication is that the cell potential will be reduced from the standard value if the concentration of Zn2+(aq) is greater than that of Cu2+(aq) at the standard temperature. An excess concentration of Cu2+(aq) will give a higher voltage. The graph at right shows the increase in cell voltage with increasing concentration of the cation. Note that the horizontal axis is logarithmic, and that the straight line variation of the voltage represents an logarithmic variation with Q. Note that the cell potential is equal to the standard value if the concentrations are equal even if they are not equal to the standard value of 1M, since the logarithm gives the value zero.

一个推论是,如果在标准温度下Zn²+ (aq)的浓度大于Cu²+ (aq)的浓度,那么电池的电动势将从标准值降低。Cu²+ (aq)的过量浓度会给出更高的电压。右边的图显示了阳离子浓度增加时电池电压的增加。请注意,横轴是对数的,而电压的直线变化表示与Q呈对数变化。请注意,即使浓度不等于标准值1M,当浓度相等时,电池电动势等于标准值,因为对数给出了零值。

Consider a concentration of 10-5Molar for Zn2+(aq) and 0.1 Molar for Cu2+(aq) as a test case for temperature dependance. We can see that the cell potential tends to increase with temperature, or that a colder cell prodices less voltage - a commonly observed phenomenon with dry cell batteries. The variation with temperature is linear with temperature, but quite small for this cell. The large variations of practical output voltage with temperature for dry cells does not arise from the Nernst equation alone.

考虑锌离子浓度为10⁻⁵摩尔/升,铜离子浓度为0.1摩尔/升的情况作为温度依赖性的测试案例。我们可以看到,电池的电动势随温度升高而增加,或者可以得出一个较冷的电池产生较少电压的结论——这是干电池中常见的现象。温度变化与电动势的变化呈线性关系,但对于这种电池来说,这种变化相当小。干电池在实际使用中温度对输出电压的显著变化并非仅仅源于能斯特方程。

Background for the Nernst equation
能斯特方程的背景
Index

Oxidation/
Reduction concepts


Electrochemistry concepts

Reference
Hill & Kolb
Ch 8

Ebbing
Ch 19
索引 氧化还原概念 电化学概念 参考 Hill & Kolb 第8章 Ebbing 第19章
 
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Background for the Nernst Equation

能斯特方程的背景

The Nernst equation allows us to predict the cell potential for voltaic cells under conditions other than standard conditions of 1M, 1 atmosphere, 25°C. The effects of different temperatures and concentrations may be tracked in terms of the Gibbs free energy change ΔG. This free energy change depends upon the temperature and concentrations according to

能斯特方程允许我们预测在非标准条件下(如浓度不为1M、压力不为1大气压、温度不为25°C)的原电池电势。不同温度和浓度的影响可以通过吉布斯自由能变化ΔG来追踪。这种自由能变化根据温度和浓度按照

where ΔG° is the free energy change under standard conditions and Q is the thermodynamic reaction quotient. The free energy change is related to the cell potential Ecell by

其中ΔG°是在标准条件下自由能的变化,Q是热力学反应商。自由能的变化与电池电势E cell相关。
so for non-standard conditions

or

或者

which is called the Nernst equation.

这被称为能斯特定律。
因此,对于非常规条件
Index

Oxidation/
Reduction concepts


Electrochemistry concepts

Reference
Hill & Kolb
Ch 8

Ebbing
Ch 19
索引 氧化还原概念 电化学概念 参考 Hill & Kolb 第8章 Ebbing 第19章
 
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