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

The standard cell potential indicates a redox reaction&#8217;s spontaneity, so does the change in standard Gibbs free energy for a reaction. As both terms are a measure of reaction spontaneity, are they related to each other?
In a zinc-copper galvanic cell, the cell potential of 1.10 volts causes an electron flow, which is the maximum electrical work done by the cell. wmax is measured in joules and is expressed as the product of the total charge transferred in coulombs and the cell potential in volts.
The total charge, q, depends on n, the number of moles of electrons transferred during the reaction. In the zinc-copper galvanic cell, 2 moles of electrons are transferred from zinc to copper, so n = 2. To get the total charge, N is multiplied by Faraday&#8217;s constant, which is the magnitude of electric charge present in 1 mole of electrons: 96,485 coulombs.
Thus, the maximum electrical work performed by the zinc-copper galvanic cell is determined from the moles of electrons, Faraday&#8217;s constant, and the cell potential.
Here, all the energy for the electrical work is supplied by the cell itself, resulting in the system performing work on the surroundings which is denoted by a negative sign. 
Recall that Gibbs free energy is associated with a reaction&#8217;s energy available to perform work. Under standard-state conditions, the change in Gibbs free energy is a measure of the highest amount of work generated in a reaction.
Thus, the maximum work can be substituted with &#916;G, allowing the free energy change of an electrochemical reaction to be determined. 
For the zinc-copper reaction, &#916;G is &#8722;212 kilojoules, indicating that it is spontaneous. In comparison, a nickel-manganese redox reaction with a standard cell potential of &#8722;0.93 volts yields a value of +179 kilojoules, indicating that it is nonspontaneous.
The standard free energy change is also related to the equilibrium constant, K. A large equilibrium constant indicates that the reaction lies to the product side correlating with a negative &#916;G value, and vice versa. 
Given their relation to &#916;G, the standard cell potential and equilibrium constant are also related. This relationship is derived by solving this equation for the cell potential and substituting &#916;G with the gas constant, temperature, and the natural log of K.

cell potential and free energy

Thermodynamics of a Redox Reaction
Thermodynamics is the branch of physics dealing with the relationship between heat and other forms of energy. In an electrochemical cell, chemical energy is converted into electrical energy.
Thus, a link can be predicted between cell potential, free energy change, and the equilibrium constant for the reaction. Cell potential can also be measured as the oxidant or the reducing strength, and similar acid-base strength measures are reflected in equilibrium constants.
Gibbs&#8217; Free Energy and the Relationship Between E&#176;cell and &#916;G&#176;
The Gibbs free energy is a quantity used to calculate the maximum amount of reversible work performed by a thermodynamic system maintained at constant temperature and pressure conditions. It is denoted by the symbol G, and its change is represented as &#8710;G. The standard free energy change of a system, &#916;G&#176;, is defined as the maximum work performed by a system, wmax. For a redox reaction occurring within a galvanic cell under standard conditions, all the work done is associated with electron transferring from the reducing agent to the oxidizing agent, welec. Thus,
<img alt="Chemical reaction mechanism diagram with intermediate product process and electron movement arrows." src="/files/ftp_upload/11436/11436_Equation_1.png" style="text-align: center; height: 50px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium diagram; &#931;Fx=0 equation; educational physics concept." />
However, any work associated with electron transfer depends on the charge transferred in Coulombs as well as the cell potential:
<img alt="Microscope optics diagram showing light path through lenses and objectives for magnification." src="/files/ftp_upload/11436/11436_Equation_2.png" style="text-align: center; height: 50px;" data-altupdatedat="1754904545000" data-alt="Microwave chromatography apparatus diagram; includes power supply, waveguide, column, detector." />
where n = the number of moles of transferred electrons, F is Faraday&#8217;s constant, which represents the coulombic charge of 1 mole of electrons, and E&#176;cell is the standard cell potential. The relation between &#916;G&#176; and &#916;E&#176;cell confirms the sign conventions and the criteria for reaction spontaneity. Spontaneous redox reactions have positive potential and negative values of free energy.
Relationship between E&#176;cell and K
The standard free energy change &#916;G&#176; is related to the equilibrium constant K of a redox reaction as follows:
<img alt="Electrochemical cell diagram, showing redox reaction with electrolysis process and electron flow." src="/files/ftp_upload/11436/11436_Equation_3.png" style="text-align: center; height: 50px;" data-altupdatedat="1754904545000" data-alt="Ballistic pendulum physics diagram, equations &#931;Fx=0, MA=0 illustrate collision momentum analysis." />
Combining a previously derived relation between &#916;G&#176; and K and the equation relating to &#916;G&#176; and E&#176;cell yields the following:
<img alt="Chemical equilibrium, ammonia synthesis reaction formula, diagram; involves N&#8322;, H&#8322;, NH&#8323;." src="/files/ftp_upload/11436/11436_Equation_4.png" style="text-align: center; height: 50px;" data-altupdatedat="1754904545000" data-alt='"Free body diagram of inclined plane with weight, normal force, friction, showing &#931;Fx=0, &#931;Fy=0 concepts."' />
Therefore,
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This equation indicates that redox reactions with large or positive standard cell potentials will proceed towards completion, reaching equilibrium when most reactants have been converted to product.
Nonspontaneous reactions or reactions proceeding in reverse directions exhibit negative cell potentials, positive free energy values, and an equilibrium constant of less than one. An equilibrium constant of one and cell potential and free energy values equal to zero is associated with a reaction under equilibrium at standard conditions.
The relationship between the cell potential under standard conditions and the thermodynamic constants &#916;G&#176; and K can be explained by the figure given below:
<img alt="Gibbs energy equation diagram; &#916;G, K, E&#176;cell relations; thermodynamics, electrochemistry, formula." src="/files/ftp_upload/11436/11436_Image_1.png" style="text-align: center; height: 250px;" data-altupdatedat="1754904545000" data-alt="Nernst equation diagram; &#916;G&#176;, K, E&#176;cell relationship, electrochemical processes, thermodynamics formula." />
Figure 1: Graphic depicting the relation between three important thermodynamic properties.
This text is adapted from <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>.

Cell Potential and Free Energy

Thermodynamics of a Redox Reaction
Thermodynamics is the branch of physics dealing with the relationship between heat and other forms of energy. In an ...

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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...

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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...

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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