Glossary

4.2 The Nernst Equation and Its Applications

2 min read•july 23, 2024

The Nernst equation connects cell potential to concentration and in electrochemical reactions. It's crucial for understanding how these factors affect the energy available in a system, helping predict reaction spontaneity and equilibrium conditions.

This equation bridges thermodynamics and electrochemistry, allowing us to calculate cell potentials under . It's a powerful tool for analyzing real-world electrochemical systems and their behavior in various environments.

Thermodynamic Principles and the Nernst Equation

Derivation of Nernst equation

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  • Relates (ΔG\Delta G) to cell potential (EcellE_{cell}) using ΔG=−nFEcell\Delta G = -nFE_{cell}
    • nn represents number of electrons transferred in redox reaction
    • FF is (96,485 C/mol)
  • Change in Gibbs free energy also depends on standard Gibbs free energy change (ΔG∘\Delta G^{\circ}) and (QQ) via ΔG=ΔG∘+RTln⁡Q\Delta G = \Delta G^{\circ} + RT \ln Q
    • RR is the gas constant (8.314 J/mol·K)
    • TT is the temperature in Kelvin
  • Combining equations and solving for EcellE_{cell} yields Nernst equation Ecell=Ecell∘−RTnFln⁡QE_{cell} = E_{cell}^{\circ} - \frac{RT}{nF} \ln Q
  • At standard temperature (298 K), Nernst equation simplifies to Ecell=Ecell∘−0.0592Vnlog⁡QE_{cell} = E_{cell}^{\circ} - \frac{0.0592V}{n} \log Q

Applications of the Nernst Equation

Application of Nernst equation

  • Calculates cell potentials under non-standard conditions (concentrations ≠ 1 M or gas pressures ≠ 1 atm)
  • Steps to calculate non-standard cell potential:
    1. Determine standard cell potential (Ecell∘E_{cell}^{\circ}) from table of standard reduction potentials
    2. Calculate reaction quotient (QQ) based on concentrations or partial pressures of reactants and products
    3. Substitute values into Nernst equation and solve for EcellE_{cell}
  • Same process applies to calculate potential of individual electrodes under non-standard conditions
    • Use standard reduction potential of electrode instead of standard cell potential

Concentration effects on cell potentials

  • Nernst equation reveals cell potential depends on concentrations of reactants and products
    • Increasing reactant concentration or decreasing product concentration increases cell potential
    • Decreasing reactant concentration or increasing product concentration decreases cell potential
  • Magnitude of change in cell potential depends on reaction stoichiometry
    • For 1:1 stoichiometry, tenfold concentration change results in 0.0592Vn\frac{0.0592V}{n} change in cell potential
    • For other stoichiometries, change in cell potential calculated using Nernst equation

Relationship between Cell Potential, Free Energy, and Equilibrium Constants

Cell potential vs free energy

  • Cell potential and Gibbs free energy related by ΔG=−nFEcell\Delta G = -nFE_{cell}
  • Under standard conditions, becomes ΔG∘=−nFEcell∘\Delta G^{\circ} = -nFE_{cell}^{\circ}
  • Standard Gibbs free energy change related to equilibrium constant (KK) by ΔG∘=−RTln⁡K\Delta G^{\circ} = -RT \ln K
  • Combining equations yields relationship between standard cell potential and equilibrium constant Ecell∘=RTnFln⁡KE_{cell}^{\circ} = \frac{RT}{nF} \ln K
  • These relationships allow:
    1. Calculation of equilibrium constant from standard cell potential
    2. Calculation of standard cell potential from equilibrium constant
    3. Determination of redox reaction spontaneity based on sign of cell potential or Gibbs free energy change

Key Terms to Review (13)

Calculating Equilibrium Concentration: Calculating equilibrium concentration refers to the process of determining the concentrations of reactants and products in a chemical system at equilibrium, where the rate of the forward reaction equals the rate of the reverse reaction. This calculation is essential for understanding chemical reactions and involves applying principles such as the Nernst Equation, which relates concentration to cell potential, especially in electrochemical cells. The ability to calculate these concentrations helps predict how changes in conditions affect the position of equilibrium and the overall behavior of a system.
Determining Cell Potential: Determining cell potential refers to calculating the voltage produced by an electrochemical cell, which indicates the tendency of the cell to perform work in a redox reaction. This potential is crucial for understanding the spontaneity of reactions and can be influenced by factors such as concentration, temperature, and the nature of the reactants involved. The Nernst Equation is a key tool used to relate the cell potential to these factors, allowing for more precise predictions of cell behavior under varying conditions.
Dilute solutions: Dilute solutions are mixtures where a small amount of solute is dissolved in a large amount of solvent, resulting in a low concentration of solute. These solutions play a crucial role in various electrochemical processes, particularly in influencing the behavior of ions and the electrochemical potential, which is critical when applying the Nernst equation to predict cell behavior under different concentrations.
Electrolytic cell: An electrolytic cell is an electrochemical cell that uses electrical energy to drive a non-spontaneous chemical reaction. In this type of cell, an external voltage source forces the flow of electrons through an electrolyte, resulting in chemical changes at the electrodes. This concept is crucial in understanding various electrochemical processes, including the manipulation of electrode potentials, the calculation of cell efficiencies, and the thermodynamic relationships governing these systems.
Enthalpy Change: Enthalpy change refers to the amount of energy absorbed or released during a chemical reaction at constant pressure, usually measured in joules or kilojoules. It plays a crucial role in understanding energy transformations in electrochemical reactions, linking thermodynamics with electrochemistry. The concept helps explain how changes in enthalpy influence cell potentials and reaction spontaneity, especially when considering the Nernst equation and standard state conditions.
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 C/mol. This constant is crucial in electrochemistry because it connects the amount of electric charge to the amount of substance involved in an electrochemical reaction, linking current flow to chemical changes. It plays a significant role in quantifying the relationships between electric charge and reactions, making it essential in various electrochemical equations.
Galvanic cell: A galvanic cell is an electrochemical device that converts chemical energy into electrical energy through spontaneous redox reactions. It consists of two electrodes, an anode and a cathode, immersed in electrolyte solutions, allowing for the flow of electrons and ions, thus generating an electric current.
Gibbs Free Energy: Gibbs free energy (G) is a thermodynamic potential that measures the maximum reversible work obtainable from a system at constant temperature and pressure. It plays a vital role in determining the spontaneity of electrochemical reactions, where a negative change in Gibbs free energy indicates that a reaction can occur spontaneously, influencing electrode processes, cell potentials, and overall electrochemical efficiency.
Logarithmic Scale: A logarithmic scale is a way of displaying numerical data over a wide range of values in a compact manner, where each tick mark on the scale represents a power of a base number, typically 10. This approach allows for easier interpretation of data that spans several orders of magnitude, particularly useful in fields such as electrochemistry where concentrations or voltages can vary dramatically. In the context of electrochemical measurements, the Nernst equation often employs logarithmic scales to relate concentrations of reactants and products to the electric potential.
Nernst Equation Formula: The Nernst Equation Formula is a mathematical expression that relates the reduction potential of an electrochemical reaction to the concentrations of the reactants and products at a given temperature. This equation allows for the calculation of the cell potential under non-standard conditions, highlighting how the electrochemical potential changes with concentration, temperature, and reaction quotient.
Non-standard conditions: Non-standard conditions refer to the specific set of variables under which electrochemical measurements are made, differing from the standard state defined by a temperature of 25°C, a pressure of 1 atm, and concentrations of 1 M for all reactants and products. Understanding non-standard conditions is essential for applying the Nernst Equation, which allows us to calculate cell potentials based on actual experimental conditions rather than theoretical values.
Reaction quotient: The reaction quotient, denoted as Q, is a dimensionless value that represents the ratio of the concentrations of products to the concentrations of reactants at any point in a chemical reaction. It is essential for understanding the direction a reaction will shift to reach equilibrium. By comparing Q to the equilibrium constant, K, one can predict whether the reaction will favor products or reactants as it approaches equilibrium.
Temperature: Temperature is a measure of the average kinetic energy of particles in a substance, influencing various physical and chemical processes. It plays a critical role in electrochemical systems, affecting reaction rates, equilibrium conditions, and the overall performance of electrochemical devices.
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