Given the standard electrode potentials for gold at 298 K: E^ ( Au ³⁺/ Au ) = +1.40 V E^ ( Au ^+/ Au ) = +1.69 V What is the standard cell potential ( E^ _ cell ) for the disproportionation reaction of Au ^+ ? 3 Au ^+ Au ³⁺ + 2 Au

Step-by-step solution

The disproportionation reaction is 3 Au ^+ Au ³⁺ + 2 Au . This involves two half-reactions: Oxidation: Au ^+ Au ³⁺ + 2e^- Reduction: Au ^+ + e^- Au First, calculate the standard reduction potential for Au ³⁺/ Au ^+ : Au ³⁺ + 3e^- Au , E^ ₁ = +1.40 V, G^ ₁ = -3F(1.40) = -4.20F Au ^+ + e^- Au , E^ ₂ = +1.69 V, G^ ₂ = -1F(1.69) = -1.69F The target half-reaction is Au ³⁺ + 2e^- Au ^+ . This is obtained by subtracting the second reaction from the first: G^ ₃ = G^ ₁ - G^ ₂ = -4.20F - (-1.69F) = -2.51F -2FE^ ₃ = -2.51F E^