Given that the standard potentials (Eᵒ) of Cu²⁺/Cu and Cu⁺/Cu are 0.34 V and 0.522 V respectively, the Eᵒ of Cu²⁺/Cu⁺ :

Solution

Chemistry ma’am · 4 steps

Potentials do not add, but Δ G does: convert each to -nFE first, then combine.

1. Write the half-reactions. (1) Cu²⁺ + 2e⁻ → Cu, E₁° = 0.34 V. (2) Cu⁺ + e⁻ → Cu, E₂° = 0.522 V. The target Cu²⁺ + e⁻ → Cu⁺ is reaction (1) minus reaction (2).
2. Combine free energies. E° is an intensive quantity, so you cannot subtract potentials directly. Use Δ G° = -nFE° for each step, because free energies do add and subtract.

   -1 · F E₃° = (-2F × 0.34) - (-1F × 0.522)

3. Solve. -FE₃° = -0.68F + 0.522F = -0.158F, so E₃° = +0.158 V.
4. So. The standard potential of Cu²⁺/Cu⁺ is +0.158 V, option (d).

The idea to keep. When half-reactions combine into another half-reaction, convert each E° to Δ G° = -nFE°, add or subtract those, then divide by the new n.

Answer from the NTA final answer key. Solution by PrepWiser.