Cu ⁺ undergoes disproportionation, according to the equation, 2 Cu ⁺ Cu ²⁺+ Cu The E ^ value for the reaction is: [ E _ Cu ²⁺ / Cu ^ o =0.34 ~V and E _ Cu ²⁺ / Cu ⁺ ^ O =0.15 ~V ]

Step-by-step solution

The given disproportionation reaction is 2 Cu ⁺ Cu ²⁺ + Cu . This reaction can be split into two half-reactions: 1) Oxidation: Cu ⁺ Cu ²⁺ + e⁻ (where E^ _ ox = -E^ _ Cu ²⁺/ Cu ⁺ = -0.15 V ) 2) Reduction: Cu ⁺ + e⁻ Cu (where E^ _ red = E^ _ Cu ⁺/ Cu ) To find E^ _ Cu ⁺/ Cu , we use the Gibbs free energy relation G^ = -nFE^ . For Cu ²⁺ + 2e⁻ Cu , G^ ₁ = -2 F 0.34 = -0.68F . For Cu ²⁺ + e⁻ Cu ⁺ , G^ ₂ = -1 F 0.15 = -0.15F . Subtracting the second from the first gives Cu ⁺ + e⁻ Cu , with G^ ₃ = G^ ₁ - G^ ₂ = -0.68F - (