Glossary

10.3 Nernst equation and its applications

6 min read•july 30, 2024

The is a crucial tool in electrochemistry, connecting cell potential to concentration and temperature. It helps predict spontaneous reactions and calculate equilibrium constants, bridging the gap between standard and non-standard conditions in electrochemical cells.

Understanding the Nernst equation allows us to analyze real-world electrochemical systems. By applying this equation, we can determine how changes in concentration and temperature affect cell potentials, providing insights into battery performance, corrosion processes, and other electrochemical phenomena.

Nernst equation derivation and significance

Relationship between Gibbs free energy change and cell potential

Top images from around the web for Relationship between Gibbs free energy change and cell potential

1 of 3

Top images from around the web for Relationship between Gibbs free energy change and cell potential

1 of 3
  • The Nernst equation is derived from the relationship between the change (ΔG) and the cell potential (E) in an
  • This relationship is given by the equation ΔG=−nFEΔG = -nFE
    • nn represents the number of electrons transferred in the redox reaction
    • FF is the Faraday constant (96,485 C/mol)

Nernst equation expression and components

  • The Nernst equation relates the cell potential under non-standard conditions (E) to the standard cell potential (E°) and the concentrations of reactants and products
  • It takes into account the (Q), which represents the relative concentrations of products and reactants at a given point in the reaction
  • The Nernst equation is expressed as E=E°−RTnFln⁡QE = E° - \frac{RT}{nF}\ln Q
    • RR is the gas constant (8.314 J/mol·K)
    • TT is the absolute temperature in Kelvin
    • QQ is the reaction quotient, calculated using the concentrations of reactants and products

Significance of the Nernst equation in electrochemistry

  • The Nernst equation allows for the prediction of cell potentials under various conditions, not just standard conditions
  • It enables the determination of the direction of spontaneous by calculating the cell potential and comparing it to zero
  • The Nernst equation can be used to calculate equilibrium constants for redox reactions by setting the cell potential equal to zero and solving for the reaction quotient (Q)
  • It provides a quantitative understanding of how changes in concentration and temperature affect the cell potential and the direction of redox reactions

Cell potential calculation under non-standard conditions

Identifying standard cell potential and reaction quotient

  • To apply the Nernst equation, first identify the standard cell potential (E°) for the given redox reaction
    • E° can be calculated using a table of standard reduction potentials
  • Determine the reaction quotient (Q) by substituting the given concentrations of reactants and products into the expression for Q
    • The expression for Q is based on the balanced redox reaction, with products in the numerator and reactants in the denominator

Substituting values into the Nernst equation

  • Substitute the values of E°, R, T, n, F, and Q into the Nernst equation (E=E°−RTnFln⁡QE = E° - \frac{RT}{nF}\ln Q) to calculate the cell potential (E) under the given non-standard conditions
  • Use appropriate units for temperature (Kelvin) and concentration (typically molarity or mole fraction) when applying the Nernst equation
  • Example: For a redox reaction with E° = 1.23 V, n = 2, T = 298 K, and Q = 0.1, the cell potential would be calculated as:
    • E=1.23 V−(8.314 J/mol⋅K)(298 K)(2)(96,485 C/mol)ln⁡(0.1)=1.29 VE = 1.23\,V - \frac{(8.314\,J/mol·K)(298\,K)}{(2)(96,485\,C/mol)}\ln(0.1) = 1.29\,V

Special case: Cell potential at Q = 1

  • When the concentrations of reactants and products are equal (or the reaction quotient Q equals 1), the cell potential calculated by the Nernst equation will be equal to the standard cell potential (E°)
  • This is because ln⁡(1)=0\ln(1) = 0, so the second term in the Nernst equation becomes zero
  • Example: For a redox reaction with E° = 1.23 V, n = 2, T = 298 K, and Q = 1, the cell potential would be:
    • E=1.23 V−(8.314 J/mol⋅K)(298 K)(2)(96,485 C/mol)ln⁡(1)=1.23 VE = 1.23\,V - \frac{(8.314\,J/mol·K)(298\,K)}{(2)(96,485\,C/mol)}\ln(1) = 1.23\,V

Predicting spontaneous redox reactions

Gibbs free energy change and spontaneity

  • A spontaneous redox reaction occurs when the Gibbs free energy change (ΔG) is negative
  • This corresponds to a positive cell potential (E > 0) as calculated by the Nernst equation, due to the relationship ΔG=−nFEΔG = -nFE
  • Example: If the calculated cell potential for a redox reaction is +0.85 V, the reaction will proceed spontaneously in the forward direction

Direction of spontaneous redox reactions

  • If the calculated cell potential is positive (E > 0), the redox reaction will proceed spontaneously in the forward direction as written
    • Oxidation occurs at the anode and reduction at the cathode
  • If the calculated cell potential is negative (E < 0), the redox reaction will proceed spontaneously in the reverse direction
    • Reduction occurs at the anode and oxidation at the cathode
  • Example: For a redox reaction with E = -0.42 V, the reaction will proceed spontaneously in the reverse direction, with the reduction occurring at the anode and the oxidation at the cathode

Equilibrium conditions

  • When the calculated cell potential is equal to zero (E = 0), the system is at equilibrium, and no net reaction occurs
  • The concentrations of reactants and products at equilibrium are related by the equilibrium constant (K)
  • Example: If the calculated cell potential for a redox reaction is 0 V, the system is at equilibrium, and the concentrations of reactants and products are related by the equilibrium constant (K)

Temperature and concentration effects on cell potential

Temperature effects on cell potential

  • The Nernst equation shows that the cell potential (E) is directly proportional to the absolute temperature (T)
  • Higher temperatures result in larger deviations from the standard cell potential (E°)
  • Increasing the temperature will increase the magnitude of the second term in the Nernst equation, RTnFln⁡Q\frac{RT}{nF}\ln Q, leading to a larger difference between E and E°
  • Example: For a redox reaction with E° = 1.23 V, n = 2, and Q = 0.1, increasing the temperature from 298 K to 323 K will increase the magnitude of the cell potential deviation from E°

Concentration effects on cell potential

  • Changes in reactant and product concentrations affect the cell potential through the reaction quotient (Q) in the Nernst equation
  • Increasing the concentration of reactants or decreasing the concentration of products will decrease the value of Q, leading to an increase in the cell potential (E)
  • Conversely, decreasing the concentration of reactants or increasing the concentration of products will increase the value of Q, leading to a decrease in the cell potential (E)
  • Example: For a redox reaction with E° = 1.23 V, n = 2, and T = 298 K, increasing the concentration of reactants by a factor of 10 (Q changes from 1 to 0.1) will increase the cell potential from 1.23 V to 1.29 V

Equilibrium constant vs standard cell potential

Relationship between equilibrium constant and standard cell potential

  • At equilibrium, the cell potential (E) is equal to zero, and the reaction quotient (Q) is equal to the equilibrium constant (K)
  • By setting E = 0 in the Nernst equation, the relationship between the standard cell potential (E°) and the equilibrium constant (K) can be derived: E°=RTnFln⁡KE° = \frac{RT}{nF}\ln K
  • This equation relates the standard cell potential (E°) to the equilibrium constant (K), the gas constant (R), the absolute temperature (T), the number of electrons transferred (n), and the Faraday constant (F)

Calculating equilibrium constant from standard cell potential

  • To calculate the equilibrium constant (K) from the standard cell potential (E°), substitute the values of E°, R, T, n, and F into the equation E°=RTnFln⁡KE° = \frac{RT}{nF}\ln K and solve for K
  • Example: For a redox reaction with E° = 1.23 V, n = 2, and T = 298 K, the equilibrium constant (K) can be calculated as:
    • 1.23 V=(8.314 J/mol⋅K)(298 K)(2)(96,485 C/mol)ln⁡K1.23\,V = \frac{(8.314\,J/mol·K)(298\,K)}{(2)(96,485\,C/mol)}\ln K
    • K=e(2)(96,485 C/mol)(1.23 V)(8.314 J/mol⋅K)(298 K)=1.6×1041K = e^{\frac{(2)(96,485\,C/mol)(1.23\,V)}{(8.314\,J/mol·K)(298\,K)}} = 1.6 \times 10^{41}

Calculating standard cell potential from equilibrium constant

  • To calculate the standard cell potential (E°) from the equilibrium constant (K), substitute the values of K, R, T, n, and F into the equation E°=RTnFln⁡KE° = \frac{RT}{nF}\ln K and solve for E°
  • Example: For a redox reaction with K = 1.6 × 10^41, n = 2, and T = 298 K, the standard cell potential (E°) can be calculated as:
    • E°=(8.314 J/mol⋅K)(298 K)(2)(96,485 C/mol)ln⁡(1.6×1041)=1.23 VE° = \frac{(8.314\,J/mol·K)(298\,K)}{(2)(96,485\,C/mol)}\ln(1.6 \times 10^{41}) = 1.23\,V

Considerations when using the relationship between E° and K

  • When using the relationship between E° and K, ensure that the equilibrium constant is dimensionless (i.e., based on mole fractions or activities rather than concentrations)
  • The temperature must be in Kelvin when using this equation
  • Example: If the equilibrium constant is given in terms of concentrations, convert it to a dimensionless value using the standard state concentration (1 M) before using the equation relating E° and K

Key Terms to Review (18)

Battery efficiency: Battery efficiency refers to the ratio of useful energy output from a battery to the total energy input during charging, expressed as a percentage. This concept is critical in evaluating how well a battery converts input electrical energy into stored chemical energy and subsequently retrieves it during discharge. High battery efficiency indicates that a battery can store and deliver energy with minimal loss, which is essential for applications ranging from consumer electronics to electric vehicles.
Cell Voltage Determination: Cell voltage determination refers to the process of calculating the electrical potential difference between the anode and cathode in an electrochemical cell. This voltage, also known as cell potential or electromotive force (emf), is crucial for understanding how an electrochemical cell operates and how changes in concentration and temperature can affect its performance. The Nernst equation plays a vital role in this determination by allowing for the calculation of cell potential under non-standard conditions.
Concentration Cell: A concentration cell is a type of electrochemical cell that generates an electromotive force (EMF) due to a difference in concentration of ions in two half-cells, which are connected by a salt bridge. This setup allows for the flow of electrons from the half-cell with higher concentration to the one with lower concentration, ultimately producing electrical energy. Concentration cells serve as a practical illustration of the Nernst equation, demonstrating how potential difference changes with varying ion concentrations.
Corrosion analysis: Corrosion analysis is the study of the mechanisms and factors that lead to the degradation of materials, particularly metals, due to chemical or electrochemical reactions with their environment. Understanding corrosion is essential for predicting material lifespan, improving material selection, and developing effective prevention strategies. This analysis often involves measuring the potential of a metal in relation to a reference electrode, and the Nernst equation can be applied to quantify how environmental changes affect corrosion rates.
Dilution effect: The dilution effect refers to the reduction in the concentration of solutes in a solution when additional solvent is added. This concept is crucial for understanding how the behavior of ions and molecules can change in different concentrations, especially in electrochemical systems, where concentrations affect potential and reaction kinetics.
Electrochemical cell: An electrochemical cell is a device that converts chemical energy into electrical energy through redox reactions or uses electrical energy to drive chemical reactions. These cells consist of two electrodes, an anode and a cathode, separated by an electrolyte, which allows ions to move between them. This fundamental principle is crucial in understanding the Nernst equation and its applications, as it describes how the cell's potential can change based on the concentrations of the reactants and products involved.
Electrode potential calculation: Electrode potential calculation involves determining the voltage (or electric potential) at an electrode in an electrochemical cell under specific conditions. This value is crucial for understanding how a given reaction will occur and is closely related to the concentration of reactants and products, temperature, and the overall cell design, making it essential for predicting the behavior of electrochemical cells using the Nernst equation.
Equilibrium Potential: Equilibrium potential is the electric potential difference across a membrane that exactly balances the concentration gradient for a particular ion, resulting in no net movement of that ion across the membrane. It reflects the tendency of an ion to move in response to its concentration and charge, which is described mathematically by the Nernst equation. Understanding equilibrium potential helps explain how different ions contribute to the overall membrane potential and how cells maintain their ionic balance.
Faraday's Constant: Faraday's Constant is a fundamental physical constant that represents the electric charge carried by one mole of electrons, approximately equal to 96485 coulombs per mole. This value is crucial in electrochemistry as it connects the amount of substance transformed in an electrochemical reaction to the total electric charge passed through the system, playing a key role in understanding the Nernst equation and its applications.
Gibbs Free Energy: Gibbs free energy is a thermodynamic potential that measures the maximum reversible work obtainable from a system at constant temperature and pressure. This concept is vital for predicting the spontaneity of processes, as it combines the system's enthalpy and entropy to determine whether a reaction or process can occur naturally without external input.
Nernst Equation: The Nernst Equation is a mathematical relationship that describes the electrochemical potential of a cell based on the concentrations of reactants and products involved in a redox reaction. This equation is vital in understanding how variations in concentration affect the voltage produced by electrochemical cells, allowing for insights into thermodynamic stability, reaction spontaneity, and performance in energy storage systems.
R (universal gas constant): The universal gas constant, denoted as 'r', is a fundamental constant in physical chemistry that relates the energy scale to the temperature scale in the ideal gas law. It appears in various equations involving gases and plays a crucial role in connecting pressure, volume, temperature, and the number of moles of a gas. Understanding 'r' is essential when applying the Nernst equation, as it helps quantify how changes in temperature and concentration affect electrochemical potentials.
Reaction quotient: The reaction quotient, denoted as Q, is a measure of the relative concentrations of products and reactants in a chemical reaction at any given point, used to determine the direction in which a reaction will proceed to reach equilibrium. It is calculated using the same expression as the equilibrium constant, but with the current concentrations instead of those at equilibrium. Understanding Q helps predict whether a system will shift toward products or reactants based on the comparison between Q and the equilibrium constant K.
Redox Reactions: Redox reactions, or reduction-oxidation reactions, are chemical processes in which the oxidation state of one or more substances changes due to the transfer of electrons. These reactions are fundamental in various chemical processes, including energy production, corrosion, and biological systems, highlighting their essential role in both organic and inorganic chemistry.
Reversible Reaction: A reversible reaction is a chemical process in which the products can react to regenerate the original reactants, allowing the system to reach a state of dynamic equilibrium. This means that both the forward and reverse reactions occur simultaneously, and the concentrations of reactants and products remain constant over time. The concept of reversible reactions is crucial for understanding how changes in conditions can affect the position of equilibrium and the rates of reactions, particularly in electrochemical processes as described by the Nernst equation.
Standard Electrode Potential: Standard electrode potential is the measure of the ability of a half-cell to gain or lose electrons under standard conditions, typically 25°C, 1 M concentration of ions, and 1 atm pressure for gases. This value is expressed in volts and serves as a reference point for comparing the reactivity of different electrodes in electrochemical cells. Understanding this concept is essential for determining the direction of electron flow and the overall cell potential during electrochemical reactions.
Temperature Dependence: Temperature dependence refers to the way in which a physical or chemical property of a substance changes with temperature. This concept is crucial in understanding various processes, such as heat capacity, phase changes, and reaction rates, which all exhibit different behaviors as temperature varies.
Thermodynamic Stability: Thermodynamic stability refers to the condition in which a system is in its lowest energy state and is resistant to changes or disturbances. A thermodynamically stable system will not spontaneously change its state unless an external influence is applied, indicating that it has achieved a balance between enthalpy and entropy. Understanding thermodynamic stability is crucial for evaluating reactions and processes, as it relates to heat capacity, free energy, and electrochemical systems.
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
Back
Practice QuizGlossary
Practice QuizGlossary
Next guide