Name: redox cell potential, Δg°, and k
Uploaded: 2020-09-24T15:06:52.000Z
Duration: 2 min 58 s
Channel: JoVE

标准电池电位表明氧化还原反应的 自发性，反应的标准吉布斯自由能的变化 也是如此。既然这两个术语都是反应自发性的量度，它们之间有联系吗？在锌铜原电池中，1.10 伏 的电池电位会引起电子流，这是 电池所做的最大电气功。w_max 以焦耳为单位，表示为 以库仑为单位转移的总电荷与 以伏特为单位的电池电位的乘积。总电荷 q 取决于 n，即反应过程中转移的 电子的摩尔数。在锌铜原电池中，有 2 摩尔电子 从锌转移到铜，因此 n 等于 2。为了获得总电荷，将 N 乘以法拉第常数，法拉第常数是 1 摩尔电子 中存在的电荷量：96, 485 库仑。因此，锌铜原电池所做的 最大电功 由电子摩尔数、法拉第常数和 电池电位决定。这里，所有用于电功的能量 都由电池本身提供，导致 系统对周围环境做功，用负号表示。回想一下，吉布斯自由能 与反应做功的能量有关。在标准状态下，吉布斯自由能的变化 是反应中产生的最大功 的量度。因此，可以用ΔG 代替最大功，从而可以确定电化学反应的 自由能变化。对于锌铜反应，ΔG 为 212 千焦耳，表明它是自发过程。相比之下，标准电池电位 为 0.93 伏的镍锰氧化还原反应 产生的值为 179 千焦耳，表明它是非自发过程。标准自由能变化也与 平衡常数 K 有关。较大的平衡常数 表示反应发生在生成物一侧，与之相关的ΔG 值为负，反之亦然。考虑到它们与ΔG 的关系，标准电池电位 和平衡常数也相关。用气体常数、温度和 K 的自然对数代替ΔG，通过求解电池电位方程，可以得出这个关系式。

电池电势和自由能

Cell Potential and Free Energy

氧化还原反应的热力学 
 热力学是物理的分支，它处理热量和其他形式的能量之间的关系。 在一个电化学单元中，化学能量被转换为电气能量。 
 因此，可以预测电池电势，自由能变化和反应的平衡常数之间的关系。 电池电势也可以测量为氧化物或还原强度，类似的 酸-碱 强度度量值会反映在平衡常量中。 
 Gibbs ’自由能以及 E°细胞 和 ΔG° 细胞之间的关系 
 吉布斯自由能是一种用于计算热动力系统在恒定温度和压力条件下执行的可逆工作的最大数量的数量。 它以符号 G 表示，其变化以 ∆G 表示 系统的标准自由能更改 (ΔG°) 定义为系统执行的最大工作 (wmax)。 对于在标准条件下在原电池（伽凡尼电池）内发生的氧化还原反应，所做的所有工作都与从还原剂到氧化剂 (电子) 的电子转移有关。 因此， 
 <img alt="Eq1" src="/files/ftp_upload/11436/11436_Equation_1.png" style="text-align: center; height: 50px;" />
 但是，与电子传输相关的任何工作都取决于库伦和电池电势中传输的电荷： 
 <img alt="Eq2" src="/files/ftp_upload/11436/11436_Equation_2.png" style="text-align: center; height: 50px;" />
 其中 n = 传输电子的摩尔数， F 是法拉迪的常数，表示 1 摩尔电子的库仑电荷， E°细胞是标准电池电势。 ΔG° 和 ΔE°之间的关系确认了反应自发性的标志约定和标准。 自发氧化还原反应具有自由能的正电位和负值。 
 E°单元格和 K 之间的关系 
 标准自由能变化 ΔG° 与氧化还原反应的平衡常数 K 相关，如下所示： 
 <img alt="Eq3" src="/files/ftp_upload/11436/11436_Equation_3.png" style="text-align: center; height: 50px;" />
 将 ΔG° 和 K 以及与 ΔG° 和 E°单元格相关的方程之间先前导出的关系组合在一起，可以得出以下结果： 
 <img alt="Eq4" src="/files/ftp_upload/11436/11436_Equation_4.png" style="text-align: center; height: 50px;" />
 因此， 
 <img alt="Eq5" src="/files/ftp_upload/11436/11436_Equation_5.png" style="text-align: center; height: 75px;" />
 该方程指示，使用大或正标准电池电势的氧化还原反应将接近完成，当大多数反应物转换为生成物时，将达到平衡。 
 反向进行的非自发反应或反应表现为负电池电势，正自由能值和小于 One 的平衡常数。 一个平衡常数以及等于零的电池电势和自由能值与标准条件下的平衡反应相关联。 
 标准条件下的电池电势与热力学常量 ΔG° 和 K 之间的关系可以通过下图来解释： 
 <img alt="Image1" src="/files/ftp_upload/11436/11436_Image_1.png" style="text-align: center; height: 250px;" />
 图 1 ：描绘三个重要热力学性质之间关系的图形。 
 本文改编自 <a href="https://openstax.org/books/chemistry-2e/pages/17-4-potential-free-energy-and-equilibrium">Openstax, 化学 2e, 第17.4节： 势能、自由能，与平衡</a>。

氧化还原反应的热力学
热力学是物理学的一个分支，研究热量与其他形式能量之间的关系。在……

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KEY TERMS AND CONCEPTS

关键术语与概念

redox cell potential, Δg°, and k

Redox cell potential connects chemical energy, free energy change, and the equilibrium constant in an electrochemical cell. In these reactions, chemical energy is converted into electrical energy. That link helps predict whether a reaction is spontaneous and how far it may proceed.

Thermodynamics is the study of how heat and other forms of energy are related. In an electrochemical cell, cell potential can also reflect oxidizing strength or reducing strength. A similar idea appears in acid-base chemistry, where equilibrium constants help compare strength.

Gibbs free energy, written as G, is used to describe the maximum reversible work a system can perform at constant temperature and pressure. Its change is written as ΔG, and the standard free energy change, ΔG°, is the maximum work performed by the system under standard conditions. For a redox reaction in a galvanic cell, the work is tied to electron transfer from the reducing agent to the oxidizing agent.

The work from electron transfer depends on the charge moved in coulombs and the cell potential. In the equation, n is the number of moles of transferred electrons, F is Faraday’s constant, and E°cell is the standard cell potential. This relationship shows the sign pattern for spontaneity. Spontaneous redox reactions have positive cell potential and negative free energy change.

The standard free energy change is also related to the equilibrium constant K. When the equation for ΔG° is combined with the relation between ΔG° and E°cell, a direct link between E°cell and K appears. Reactions with large or positive standard cell potentials tend to move toward completion, so most reactants are converted to products before equilibrium is reached.

Nonspontaneous reactions, or reactions that proceed in the reverse direction, have negative cell potential, positive free energy change, and an equilibrium constant less than 1. If a reaction is at equilibrium under standard conditions, then K equals 1 and both cell potential and free energy change are 0. The relationship between E°cell, ΔG°, and K shows how thermodynamic values describe the same redox system from different angles.

Redox Cell Potential, ΔG°, and K

balancing redox equations

Redox Reactions and Half-Reaction Balancing

Redox reactions involve electron transfer and changes in oxidation number. In electrochemistry, these reactions connect chemical changes with electrical energy. They also power technologies such as industrial metal processing and rechargeable batteries used in electric vehicles. Oxidation number is a way to track how an atom's electronic environment changes compared with the pure element, where the oxidation number is zero. For a simple ionic compound, the oxidation number matches the ion...

electromotive force

Cell Voltage and Electron Flow

Electric current is the flow of electric charge through a conducting medium or a solution. In wires, that charge is carried by electrons. In some solutions, ions can also move and carry charge. When electrons move through a wire, they produce an electric current. This idea connects to redox reactions, where electrons are lost and gained. In the spontaneous reaction between zinc and copper ions, zinc is oxidized to zinc ions. Copper ions are reduced to solid copper. Even so, this direct...

voltaic/galvanic cells

Galvanic Cells and Battery Reactions

Galvanic cells use spontaneous redox reactions to produce electric current. A common example is a disposable AA battery, which powers devices by turning chemical energy into electrical energy. Another example is a copper wire placed in silver nitrate solution, where the solution slowly turns bright blue and a grey solid forms on the wire. In the copper and silver reaction, copper is oxidized and silver ions are reduced. Copper forms cuprous ions, which give the solution its blue color. At the...

standard electrode potentials

Using Electrode Potentials to Predict Reactions

Electrode potentials help predict whether a redox reaction will happen on its own. A redox reaction involves electron transfer. In electrochemistry, the measured value is called cell potential or cell voltage. It shows the energy linked to charge transfer and is measured in volts, where 1 volt equals 1 joule per coulomb. A single half-cell cannot be measured by itself because electron transfer needs both a donor and a receiver. For that reason, scientists measure the difference between two...

cell potential and free energy

Redox cell potential connects chemical energy, free energy change, and the equilibrium constant in an electrochemical cell. In these reactions, chemical energy is converted into electrical energy. That link helps predict whether a reaction is spontaneous and how far it may proceed. Thermodynamics is the study of how heat and other forms of energy are related. In an electrochemical cell, cell potential can also reflect oxidizing strength or reducing strength. A similar idea appears in acid-base...

the nernst equation

Cell Potential Under Changing Conditions

Cell potential changes when a redox reaction does not run at standard conditions. Standard cell potentials connect with standard free energy change, ΔG°, and the equilibrium constant K, but those relationships only hold at 1 M concentration, 298 K, and 1 atmosphere. A zinc(II) and tin(II) redox cell with E°cell = +0.291 V and ΔG° = −56.2 kJ is spontaneous under those standard conditions. As a cell discharges, the reactant concentration changes and the cell potential steadily drops. Many redox...

concentration cells

Cell Potential from Concentration Differences

Concentration cells are voltaic cells that use two almost identical half-cells. The half-cells use the same electrode and the same half-reaction. They differ only in the concentration of one redox species, so the cell potential depends on that concentration difference. In a concentration cell, the Nernst equation can be used to find the cell potential. For the zinc example shown, the calculated cell potential is positive. A positive cell potential means the overall reaction is spontaneous. <br...

batteries and fuel cells

Primary, Rechargeable Batteries and Fuel Cells

Batteries and fuel cells are galvanic cells that supply electrical power for many applications. They range from tiny button batteries in wristwatches to large systems that can provide backup energy to municipal power grids. Some are primary cells, which are single-use and cannot be recharged. Others are secondary cells, which use reversible reactions and can be charged again by an external power source. A common primary battery is the dry cell. It uses zinc as both the container and the anode,...

corrosion

Rusting and Metal Protection

Corrosion is the natural breakdown of metals through electrochemical reactions. It can appear as rust on iron, tarnish on silver, or a blue-green patina on copper. In each case, the metal is oxidized. Some corrosion products can protect the surface, while others keep damaging the metal. Rusting is the harmful type of corrosion seen in iron. It happens when iron is exposed to oxygen and water. A galvanic cell forms on the iron surface, and this drives oxidation at the anodic region and...

electrolysis

Electrolysis in Batteries and Metal Production

Electrolysis uses electrical energy to drive a nonspontaneous redox reaction. In a galvanic cell, a spontaneous redox reaction does electrical work on the surroundings by sending electrons through an external circuit. In electrolysis, an external circuit does work on the redox system by applying a voltage large enough to force the reaction in the opposite direction. This process is used in several real-world settings. Recharging a battery is one example, because an outside power source drives...

key terms and concepts

Explore how redox cell potential relates to Gibbs free energy and the equilibrium constant. Learn which reactions are spontaneous and how E°cell predicts direction.

Redox Cell Potential, ΔG°, and K | JoVE K12

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Redox Cell Potential, ΔG°, and K

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