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

A zinc-copper galvanic cell at standard conditions has a cell potential of +1.10 V and a &#916;G value of &#8722;212 kJ, indicating that it operates spontaneously. However, as the reactant&#8217;s concentration changes during the cell&#8217;s discharge, it leads to a gradual decrease of cell potential until the reaction stops completely. 
Conditions like these are called nonstandard. Here, the established standard values of cell potential, Gibbs free energy, and the equilibrium constant are no longer valid.
Nonstandard conditions are prevalent in many reactions ranging from redox reactions to ion gradients in neuronal membranes. But how is an accurate cell potential determined in such systems?
If the concentration of a reactant is greater, and the concentration of a product is smaller compared to standard conditions, then Le Ch&#226;telier&#8217;s Principle is used to determine the reaction&#8217;s direction qualitatively; however, it cannot be used for quantifying the deviating cell potential.
Thus, this necessitates establishing a relationship between the cell potentials for cells under standard and nonstandard conditions. Recall that the free energy changes under standard and nonstandard conditions are related. 
Substituting the equation of change in free energy with the cell potential results in a modified equation known as the Nernst equation. The Nernst equation determines how the cell potential differs from its standard value depending on the number of electrons transferred, temperature, and reaction composition. 
The reaction quotient, Q, accounts for the change in free energy due to the difference in the reaction mixtures&#8217; composition. If reactants are solid, Q is omitted.
Under standard state conditions, the value of Q is unity and the concentration of reactants and products is equal. The logarithm of one is zero, so the cell potential equals the standard cell potential. 
A Q value less than one indicates a higher concentration of reactants compared to products, which shifts the equilibrium to the right, increasing the cell potential. 
A Q value greater than one indicates a higher product to reactant concentration, driving the reaction to the left and lowering the cell potential.
At equilibrium, the Q value is equal to K, and the cell potential becomes zero. 
The Nernst equation explains why electrochemical batteries &#8220;die&#8221; post-discharge: as the reactant concentration decreases, the cell approaches equilibrium conditions and its potential decreases to zero

the nernst equation

Nonstandard Reaction Conditions
The interconnection between standard cell potentials and various thermodynamic parameters such as the standard free energy change &#916;G&#176; and equilibrium constant K has been previously explored. For example, a redox reaction involving zinc(II) and tin(II) ions at 1 M concentration with E&#186;cell = +0.291 V and &#916;G&#176; = &#8722;56.2 kJ is spontaneous.
<img alt="Static equilibrium diagram, shows object supported by tension, weight forces; &#931;Fx=0, &#931;Fy=0 principles." src="/files/ftp_upload/11437/11437_Equation_1.png" style="text-align: center; height: 50px;" data-altupdatedat="1754904545000" data-alt="Chemical equilibrium, static equilibrium formula &#931;F=0 diagram; particle forces analyzation system." />
Discharge of this cell, however, results in a change in the reactant concentration and a steady decrease of the cell potential. At such a condition, however, the relationships between the cell potential and the thermodynamic parameters cannot be easily established as they only hold true at standardized conditions of concentration, temperature, and pressure (i.e., 1 M concentration, 298 K or 25 &#176;C and a pressure of 1 atmosphere). Many redox reactions of significant scientific interest occur under nonstandard state conditions, e.g., different reactant concentrations in a galvanic cell or concentration gradients occurring across biological membranes. Hence, it becomes important to calculate the potentials of such systems.
<img alt="Drawing of a woman with detailed anatomical proportions, Leonardo da Vinci style study." src="/files/ftp_upload/11437/11437_Equation_2.png" style="text-align: center; height: 50px;" data-altupdatedat="1754904545000" data-alt="DNA transcription process, RNA polymerase binding to DNA diagram, genetic information flow." />
When the concentration of zinc ions in the reaction is lesser and the concentration of the tin ions greater compared to standard conditions, the spontaneity of the redox reaction can be qualitatively predicted using Le Chatelier&#8217;s Principle. Given the higher concentration of product to reactant, the reaction has a higher tendency to proceed in the direction favoring the generation of the products. This results in a higher cell potential value or Ecell than that of the E&#176;cell value.
<img alt="Static equilibrium, &#931;Fx=0, &#931;Fy=0, force analysis diagram, educational physics use." src="/files/ftp_upload/11437/11437_Equation_3.png" style="text-align: center; height: 50px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium, &#931;Fx=0, &#931;Fy=0 diagram with force vectors and angles for physics analysis." />
This reaction proceeds in the forward direction; however, the quantitative value of this cell potential cannot be easily determined.
Derivation of the Nernst Equation for Redox Reactions Occurring under Nonstandard Conditions
The relationship between Ecell and E&#176;cell values can be derived from the previously established relationship between free energy changes at standard and nonstandard conditions, which is given as follows:
<img alt="Flowchart of static equilibrium, depicting sum of forces &#931;Fx=0, diagram of mechanical system." src="/files/ftp_upload/11437/11437_Equation_4.png" style="text-align: center; height: 50px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium; &#931;Fx=0, &#931;Fy=0 equations; vector diagram; force analysis, physics study." />
&#916;G is the change in free energy, &#916;G&#176; is the standard change in free energy, R is the gas constant (value = 8.314 J/mol&#8729;K), and Q is the reaction quotient, which accounts for the change in free energy due to the difference in the reaction mixtures&#8217; composition. The Q value is omitted if the reactants are solid.
On substitution of the equation relating free energy change to cell potential, a modified equation is obtained, known as the Nernst equation.
<img alt="Induced fit enzyme model diagram showing enzyme-substrate complex and active site interaction." src="/files/ftp_upload/11437/11437_Equation_5.png" style="text-align: center; height:90px;" data-altupdatedat="1754904545000" data-alt="Chemical structure of glutamic acid with functional groups, used in molecular biology studies." />
The Nernst equation describes the variation in the potential of a redox system (such as a galvanic cell) from its standard state value. It is dependent on the number of electrons transferred during the redox reaction, n, the temperature measured in kelvin, T, and the reaction mixture composition given as Q.
A simplified form of the Nernst equation for most work is one in which values for the fundamental constants (R and F) and a factor converting from natural log to base-10 logarithms have been included:
<img alt="Static equilibrium diagram, &#931;Fx=0, &#931;Fy=0, beam supported by cables, forces and angles shown." src="/files/ftp_upload/11437/11437_Equation_6.png" style="text-align: center; height: 70px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium diagram; &#931;Fx=0, &#931;Fy=0; forces on a beam; engineering, physics analysis." />
Under standard state conditions, the value of the reaction quotient Q is unity, whose logarithm is zero. This is due to the equal concentration of reactants and products at standard state conditions. Here, Ecell is equal to E&#176;cell. A Q value less than one indicates a higher concentration of reactants, shifting the reaction equilibrium to the right and, thus, yielding a higher value of cell potential. A Q value greater than one indicates a higher product concentration, driving the reaction to the left, and a lower value of cell potential. At equilibrium, the Q value is equal to K, and the cell potential becomes zero, i.e., the reaction shows no tendency to proceed in either direction. This explains why batteries &#8220;die&#8221; on continuous discharge: the decrease in reactant concentration drives the reaction towards equilibrium and its cell potential steadily decreases to zero.
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>.

The Nernst Equation

Nonstandard Reaction Conditions
The interconnection between standard cell potentials and various thermodynamic parameters such as the standard free energy ...

Education

JoVE Core

Chemistry

Electrochemistry

KEY TERMS AND CONCEPTS

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...

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

JoVE Core Chemistry brings general chemistry concepts to life using concise and easy-to-understand animated video lessons. Plus, in the scientist-in-action videos, we demonstrate classical and original research experiments performed in today's laboratories worldwide.

Cell Potential Under Changing Conditions

Description

Transcript

Tags