Equilibrium constant from E°cell

Worked example

Find K at 298 K for a redox reaction with E°cell = 0.361 V and n = 2.

1. 1. Gibbs energy and cell potential: solve for ΔG°

   $\Delta G^\circ = -nFE^\circ$

   = −69.66 kJ mol⁻¹

2. 2. Standard Gibbs energy and K: solve for K

   $K = \exp\!\left(-\dfrac{\Delta G^\circ}{RT}\right)$

   = 1.624 × 10¹²

Answer: K = 1.62 × 10¹²

Method

ΔG° = −nFE°, then K = exp(−ΔG°/RT). Combined: ln K = nFE°/RT, so even a few tenths of a volt give a very large K.

Common mistakes

• ΔG° = −nFE°: include the number of electrons transferred in the balanced equation.

Formulas used

• Gibbs energy and cell potential

  $\Delta G^\circ = -nFE^\circ$

• Standard Gibbs energy and K

  $\Delta G^\circ = -RT\ln K$

More electrochemistry questions

• ΔG° from E°
• Nernst equation
• Mass deposited by electrolysis
• E°cell from reduction potentials
• Electrode potential away from standard conditions
• Latimer diagram: skipping an oxidation state
• Disproportionation constant from a Latimer diagram
• Daniell cell away from standard conditions