Name: cell potential under changing conditions
Uploaded: 2020-09-24T15:06:52.000Z
Duration: 2 min 59 s
Channel: JoVE

在标准状态下，锌铜原电池的电池电位 为 1.10 伏，ΔG 值为 212 千焦耳，表明它是自发运行的。然而，随着电池放电过程中 反应物浓度的变化，会导致电池电位逐渐降低，直到反应完全停止。诸如此类的情况称为非标态。这里，电池电位、吉布斯自由能和平衡常数的 既定标准值不再有效。非标准状态普遍存在于许多反应中，从氧化还原反应到 神经元膜中的离子梯度。但是，在这样的系统中如何确定 准确的电池电位呢？如果与标准状态相比，反应物的浓度更大，而生成物的浓度更小，则可以使用勒夏特列原理 定性确定反应的方向；然而，它不能用于定量偏离的 电池电位。因此，这就需要在标准和非标准状态下 建立电池的 电池电位之间的关系。回想一下，在标准和非标准状态下，自由能的变化是相关的。将电池电位代入自由能变化方程，得到一个修正方程，称为能斯特方程。能斯特方程根据 转移的电子数、温度和反应组成 确定电池电位 与其标准值之间的差异。反应商 Q 解释了 由于反应混合物组成不同 而引起的自由能变化。如果反应物为固体，则省略 Q。在标准状态下，Q 值为一，反应物和生成物的浓度 相等。1 的对数为零，因此电池电位 等于标准电池电位。Q 值小于 1 表示 反应物浓度高于生成物浓度，这将使平衡向右移动，电池电位增加。Q 值大于 1 表示 生成物浓度高于反应物浓度，促使反应向左移动，电池电位降低。平衡时，Q 值等于 K，电池电位变为零。能斯特方程解释了电化学电池放电后"死亡"的原因：随着反应物浓度的降低，电池接近平衡状态，其电位降至零。

能斯特方程（nernst equation）

非标准反应条件 
 标准电池电势与各种热力学参数 (如标准自由能变化 G° 和平衡常数 K) 之间的互联之前已经过探讨。 例如，在 Eºcell = +0.291 V 和 ΔG° = −56.2 kJ 的情况下，在 1 M 浓度下发生的氧化还原反应 (含锌 (II) 和锡 (II) 离子) 是自发的。 
 <img alt="Eq1" src="/files/ftp_upload/11437/11437_Equation_1.png" style="text-align: center; height: 50px;" />
 但是，释放此单元格会导致反应物浓度发生变化，电池电势也会稳步下降。 但是，在这种情况下，电池电势和热动力参数之间的关系不容易建立，因为它们只在浓度，温度和压力 (即 1 M 浓度， 298 K 或 25 °C 以及 1 个大气压力) 的标准化条件下才是真实的。 许多具有重大科学意义的氧化还原反应发生在非标准状态下，例如，在原电池（伽凡尼电池）或浓度梯度中，生物膜出现不同的反应物浓度。 因此，必须计算这种系统的潜力。 
 <img alt="Eq2" src="/files/ftp_upload/11437/11437_Equation_2.png" style="text-align: center; height: 50px;" />
 当反应中的锌离子浓度较小，锡离子的浓度比标准条件大时，氧化还原反应的自发性可以通过 勒夏特列原理（Le Chatelier's Principle） 进行定性的预测。 鉴于生成物对反应物的浓度越高，反应就越倾向于朝着有利于生成物代人的方向前进。 这会导致电池电势值或 Ecell 高于 E°单元格值。 
 <img alt="Eq3" src="/files/ftp_upload/11437/11437_Equation_3.png" style="text-align: center; height: 50px;" />
 这种反应朝着前进的方向发展；但是，无法轻易确定此电池电势的定量的值。 
 在下发生的氧化还原反应的 能斯特方程（Nernst equation） 派生 非标准条件 
 Ecell 和 E°单元格值之间的关系可以从自由能变化在标准和非标准条件下之前建立的关系中导出，具体如下： 
 <img alt="Eq4" src="/files/ftp_upload/11437/11437_Equation_4.png" style="text-align: center; height: 50px;" />
 ΔG 是自由能的变化， ΔG° 是自由能的标准变化， R 是气体常数 (值 = 8.314 焦耳 / 摩尔∙K) ， Q 是反应商，这是由于反应混合物成分的差异，自由能的变化。 如果反应物为实心，则忽略 Q 值。 
 替换与自由能电池电势更改相关的方程时，将获得一个已修改的方程，称为 能斯特方程（Nernst equation）。 
 <img alt="Eq5" src="/files/ftp_upload/11437/11437_Equation_5.png" style="text-align: center; height:90px;" />
 能斯特方程（Nernst equation） 描述了氧化还原系统 (如原电池（伽凡尼电池）) 与其标准状态值之间的电位变化。 它取决于氧化还原反应过程中传输的电子数量， n ，以开氏， T 为单位测得的温度以及以 Q 为单位给出的反应混合物成分 
 对于大多数工作， 能斯特方程（Nernst equation） 的简化形式是包含基本常量 (R 和 F) 的值以及从自然日志转换为基 -10 对数的系数： 
 <img alt="Eq6" src="/files/ftp_upload/11437/11437_Equation_6.png" style="text-align: center; height: 70px;" />
 在标准状态条件下，反应商 Q 的值为单位，其对数为零。 这是由于在标准状态条件下反应物和生成物的浓度相等。 此处， Ecell 等于 E°cell。 Q 值小于 One 表示反应物的浓度较高，将反作用平衡向右移动，从而产生较高的电池电势值。 Q 值大于 1 表示生成物浓度越高，左侧的反应越大，电池电势的值越低。 在平衡， Q 值等于 K ，电池电势变为零，即，反应表明没有朝任何一个方向继续的趋势。 这解释了电池在连续放电时“没电”的原因：反应物浓度的下降推动了对平衡的反应，而其电池电势稳步下降到零。 
 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>。

能斯特方程（Nernst equation）

非标准反应条件
标准电池电位与各种热力学参数（如标准自由能）之间的互连 ...

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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 reactions of scientific interest also occur under nonstandard conditions. These include cells with different ion concentrations and concentration gradients across biological membranes. When zinc ion concentration is lower and tin ion concentration is higher than standard conditions, Le Chatelier’s Principle predicts that the reaction is more likely to move toward products, so the cell potential is higher than E°cell. The reaction still moves forward, but the exact value of the cell potential is not easy to calculate by simple comparison alone.

The Nernst equation gives that value for redox systems under nonstandard conditions. It is derived from the link between free energy under standard and nonstandard conditions. In that relationship, ΔG is the free energy change, ΔG° is the standard free energy change, R is the gas constant, and Q is the reaction quotient, which describes how the mixture composition affects free energy. The Q term is left out when reactants are solids. After combining this idea with the equation relating free energy to cell potential, the Nernst equation is obtained.

The Nernst equation shows how cell potential depends on the number of electrons transferred, n, the temperature in kelvin, T, and the reaction quotient, Q. A common simplified form includes the constants R and F and converts natural logs to base-10 logs. Under standard conditions, Q equals 1, so its logarithm is zero and Ecell equals E°cell. If Q is less than 1, reactants are relatively higher in concentration, the equilibrium shifts right, and the cell potential increases. If Q is greater than 1, products are relatively higher, the equilibrium shifts left, and the cell potential decreases.

At equilibrium, Q equals K and the cell potential becomes zero. That means the reaction has no tendency to proceed in either direction. This is why batteries die during continuous discharge. As reactants are used up, the reaction moves toward equilibrium and the cell potential falls to zero.

Cell Potential Under Changing Conditions

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, 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...

the nernst equation

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

Learn how the Nernst equation predicts cell potential in nonstandard conditions, including changing ion concentrations, reaction quotient Q, and battery discharge.

Cell Potential Under Changing Conditions | JoVE K12

chemistry

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Cell Potential Under Changing Conditions

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