Lecture on Nernst Equation and Cell Potentials

Introduction

• Nernst Equation: Used to calculate cell potentials.
• Example: Zinc-Copper cell.
• Conditions: Concentration of zinc and copper ions at 1 M, 25°C.

Standard Cell Potentials

• Redox Reactions:
  • Copper ions (Cu²⁺) are reduced to form solid copper (Cu).
  • Solid zinc (Zn) is oxidized to form zinc ions (Zn²⁺).
• Overall Reaction: Electrons lost by zinc are gained by copper.
• Standard Cell Potential:
  • Calculated as 1.10 volts by adding reduction and oxidation potentials.
  • Standard conditions: 1 M concentrations, 25°C.

Nernst Equation

• Formula: E = E₀ - (0.0592 V / n) * log Q
  • E₀: Standard cell potential (1.10 volts).
  • n: Number of moles of electrons transferred (n = 2).
  • Q: Reaction quotient, similar to K but for non-equilibrium concentrations.*

Reaction Quotient (Q)

• Expression: Product concentration over reactant concentration, ignoring solids.
• Example: Zinc ion concentration = 1 M; Copper ion concentration = 1 M.
• Q = 1: Log(1) = 0, so E = E₀ = 1.10 volts under standard conditions.

Non-Standard Conditions

• Zinc ion concentration = 10 M; Copper ion concentration = 1 M.
• Q = 10: Log(10) = 1.
• Calculation:
  • E = 1.10 - 0.030 = 1.07 volts.

Changes in Cell Potential

• Reaction Progression:
  • Products increase, reactants decrease, thus Q increases.
  • Example: Q = 100, E = 1.04 volts.

Equilibrium

• At equilibrium, Q = K, and cell potential E = 0.
• Thermodynamics: ΔG = 0, hence E = 0 at equilibrium.
• Nernst Equation at Equilibrium:
  • Relates standard cell potential to equilibrium constant: E₀ = (0.0592 V / n) * log K.*

Conclusion

• Usefulness of Nernst Equation:
  • Calculates cell potentials under various concentrations.
  • Essential for understanding cell behavior over time.