Lecture Notes: Nernst Equation and Free Energy

Free Energy and Cell Potential

• Delta G (ΔG): Change in free energy
  • Related to cell potential E by an equation.
• Standard State Conditions:
  • ΔG°: Standard change in free energy
  • Related to standard cell potential E°.

Thermodynamic Equation

• Equation:
  • (-NFE = -NFE° + RT \ln Q)
  • Q: Reaction quotient
  • Divide by (-NF) to simplify and derive the Nernst equation.

Nernst Equation

• Nernst Equation:
  • (E = E° - \frac{RT}{NF} \ln Q)
  • E: Cell potential
  • E°: Standard cell potential
  • T: Temperature in Kelvin
  • N: Number of moles of electrons in redox reaction
• Importance: Allows calculation of cell potential under non-standard conditions.

Derivation for 25 Degrees Celsius

• Temperature Conversion:
  • 25°C = 298.15 K
• Constants:
  • R (gas constant): 8.314 J/mol·K
  • F (Faraday's constant): 96,500 C/mol
• Calculate (\frac{RT}{F}):
  • Equals 0.0257 V
  • Units: Joules/Coulombs = Volts
• Simplified Nernst Equation at 25°C:
  • (E = E° - \frac{0.0257}{N} \ln Q)

Conversion to Base 10 Logarithm

• Conversion:
  • Multiply 0.0257 by ln(10) to convert to base 10
  • Result: 0.0592
• Final Form of Nernst Equation:
  • (E = E° - \frac{0.0592}{N} \log Q)

Importance of the Nernst Equation

• Utility: Calculates cell potential in non-standard conditions.
• Instantaneous Cell Potential: Relates to reaction progress.
• Concentration Changes:
  • Q changes with concentration changes, affecting cell potential.

Conclusion

• Understanding the Nernst equation improves with practice and problem-solving.
• Allows better grasp of its implications in real-world reactions.