What is the standard electrode potential at 298 K for the reaction: Cu ²⁺+1 e - Cu ⁺¹ ? Given: E ₀ Cu ⁺¹ / Cu =0.5 ~V & E ₀ Cu ⁺² / Cu =0.335 ~V

Step-by-step solution

The standard electrode potential for the reaction Cu ²⁺ + e ⁻ Cu ⁺ can be determined using the Gibbs free energy change G^ = -nFE^ . For the reaction Cu ²⁺ + 2 e ⁻ Cu , G^ ₁ = -2 F 0.335 = -0.67F . For the reaction Cu ⁺ + e ⁻ Cu , G^ ₂ = -1 F 0.5 = -0.5F . The target reaction is Cu ²⁺ + e ⁻ Cu ⁺ , which is obtained by subtracting the second reaction from the first: G^ ₃ = G^ ₁ - G^ ₂ = -0.67F - (-0.5F) = -0.17F . Since G^ ₃ = -nFE^ ₃ with n=1 , we have -1 F E^ ₃ = -0.17F . Therefore, E^ ₃ = 0.17 V . Answer: 0.17 V