Lecture Notes on Relating Standard Cell Potential to Equilibrium Constant

Key Equations

• Standard Change in Free Energy:
  • ΔG⁰ = -nF E⁰
  • ΔG⁰ = -RT ln(K)
• Relating Standard Cell Potential (E⁰) to Equilibrium Constant (K):
  • Since both equations are equal to ΔG⁰, set them equal:
    • (-nFE⁰ = -RT \ln(K))

Solving for Standard Cell Potential (E⁰)

• Rearrange to solve for E⁰:
  • (E⁰ = \frac{RT}{nF} \ln(K))

Standard Conditions

• Temperature:
  • Standard conditions: 25°C
  • Convert to Kelvin: 25 + 273.15 = 298.15 K
• Gas Constant (R):
  • R = 8.314 J/(mol·K)
• Faraday's Constant (F):
  • F = 96,500 C/mol

Calculation of RT/F

• (\frac{RT}{F} = 0.0257 \text{ volts})
  • Units derive as Volts (Joules/Coulombs)

Revised Equation

• Equation with Natural Log:
  • (E⁰ = \frac{0.0257 \text{ volts}}{n} \ln(K))

Conversion to Logarithmic Form

• Multiply 0.0257 by ln(10) to switch from natural log to log:
  • (0.0257 \times \ln(10) = 0.0592)
• Equation in Log Form:
  • (E⁰ = \frac{0.0592 \text{ volts}}{n} \log(K))

Summary

• Two forms of the equation relate standard cell potential (E⁰) to equilibrium constant (K):
  • One using natural logarithm (ln)
  • One using base-10 logarithm (log)
• The number of moles of electrons (n) transferred in the redox reaction is a key factor in both equations.