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

標準細胞電位は酸化還元反応の自発性を示しており、反応の標準ギブス自由エネルギーの変化も同様です。どちらの用語も反応自発性の尺度であるため、それらは互いに関連していますか?
亜鉛-銅ガルバニックセルでは、1.10ボルトのセル電位が電子の流れを引き起こし、これはセルによって行われる最大の電気的仕事です。WMaxはジュールで測定され、クーロンで転送された総電荷とボルト単位のセル電位の積として表されます。
総電荷qは、反応中に転送される電子のモル数であるnに依存します。亜鉛-銅ガルバニ電池では、2モルの電子が亜鉛から銅に移動するため、n = 2です。総電荷を求めるには、Nにファラデー定数(1モルの電子に存在する電荷の大きさである96,485クーロン)を掛けます。
したがって、亜鉛-銅ガルバニックセルによって実行される最大電気仕事は、電子のモル、ファラデー定数、およびセル電位から決定されます。
ここでは、電気工事のすべてのエネルギーはセル自体によって供給されるため、システムは負の符号で示される周囲で作業を行います。 
ギブスの自由エネルギーは、仕事を実行するために利用可能な反応のエネルギーに関連付けられていることを思い出してください。標準状態の条件下では、ギブス自由エネルギーの変化は、反応で生成される最大仕事量の尺度です。
したがって、最大仕事量をΔGに置き換えることができ、電気化学反応の自由エネルギー変化を決定することができます。 
亜鉛-銅反応の場合、ΔGは-212キロジュールであり、自発的であることを示しています。これに対し、標準セル電位が-0.93ボルトのニッケル-マンガン酸化還元反応は、+179キロジュールの値をもたらし、非自発的であることを示しています。
標準自由エネルギー変化は、平衡定数Kにも関連しています。平衡定数が大きい場合は、反応が負のΔG値と相関する製品側にあり、その逆も同様であることを示しています。 
ΔGとの関係を考えると、標準セル電位と平衡定数も関連しています。この関係は、セル電位についてこの方程式を解き、ΔGをガス定数、温度、およびKの自然対数に代入することによって導き出されます。

電極電位と自由エネルギー

Cell Potential and Free Energy

酸化還元反応の熱力学
 熱力学とは、熱とその他のエネルギーの関係を扱う物理学の一分野です。電気化学反応系では、化学エネルギーが電気エネルギーに変換されます。
 したがって、電極電位、自由エネルギー変化、反応の平衡定数の間には関連性が予測されます。また、電極電位は酸化力や還元力として測定することができ、同様に酸塩基の強さも平衡定数に反映されます。
 ギブズ自由エネルギーG°とE°cell  との関係。
 ギブズ自由エネルギーとは、一定の温度と圧力に保たれた熱力学系が行う可逆的な仕事の最大量を計算するために用いられる量です。自由エネルギーはGという記号で示され、その変化は ∆Gと表されます。系の標準的な自由エネルギー変化であるΔG°は、系が行う最大の仕事であるwmaxとして定義されます。標準条件でガルバニ電池内で起こる酸化還元反応では、すべての仕事は還元剤から酸化剤への電子移動に関連しており、welecとなります。このように、
 <img alt="Eq1" src="/files/ftp_upload/11436/11436_Equation_1.png" style="text-align: center; height: 50px;" />
 一方で、電子移動に伴う仕事は、移動した電荷（クーロン）と各電極の電位に依存します。
 <img alt="Eq2" src="/files/ftp_upload/11436/11436_Equation_2.png" style="text-align: center; height: 50px;" />
 ここで、nは移動した電子のモル数、Fは1 molの電子のクーロン電荷を表すファラデー定数、E°cellは標準電極電位です。ΔG°とΔE°cellの関係から、符号と反応の自発性の対応を確認できます。自発的な酸化還元反応は、正の標準電極電位と負の自由エネルギーの値を持ちます。
 E°cellとKの関係
 標準的な自由エネルギー変化 ΔG°は、酸化還元反応の平衡定数Kと次のような関係です。
 <img alt="Eq3" src="/files/ftp_upload/11436/11436_Equation_3.png" style="text-align: center; height: 50px;" />
 先に導き出した ΔG°とKの関係と、 ΔG°とE°cellの関係式を組み合わせると、次のようになります。
 <img alt="Eq4" src="/files/ftp_upload/11436/11436_Equation_4.png" style="text-align: center; height: 50px;" />
 Therefore,
 <img alt="Eq5" src="/files/ftp_upload/11436/11436_Equation_5.png" style="text-align: center; height: 75px;" />
 この式は、酸化還元反応の標準電極電位が正である場合に反応が進行し、ほとんどの反応物が生成物に変換されたときに平衡に達することを示しています。
 非自発的な反応や逆方向に進む反応は、負の電極電位あるいは正の自由エネルギー値を示し、平衡定数は1より小さいです。平衡定数が1で、電極電位と自由エネルギーの値が0に等しいものは、標準条件で平衡状態です。
 標準状態での電極電位と熱力学な値である ΔG°およびKとの関係は、以下の図で説明できます。
 <img alt="Image1" src="/files/ftp_upload/11436/11436_Image_1.png" style="text-align: center; height: 250px;" />
 Figure 1: 3つの重要な熱力学的値の関係
 上記の文章は以下から引用しました。 <a href="https://openstax.org/books/chemistry-2e/pages/17-4-potential-free-energy-and-equilibrium">Openstax,Chemistry 2e, Section 17.4: Potential, Free Energy, and Equilibrium</a>.

酸化還元反応の熱力学
熱力学は、熱と他の形態のエネルギーとの関係を扱う物理学の一分野です。で...

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Chemistry

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Electrochemistry

電気化学

KEY TERMS AND CONCEPTS

主要用語と概念

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

chemistry

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Redox Cell Potential, ΔG°, and K

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