Given the standard electrode potentials at 298 K: E^ ( Cu ²⁺/ Cu ) = +0.34 V E^ ( Cu ^+/ Cu ) = +0.52 V The standard electrode potential ( E^ ) for the half-cell reaction Cu ²⁺ + e^- Cu ^+ is:

Step-by-step solution

The given half-cell reactions are: Cu ²⁺ + 2e^- Cu , E^ ₁ = +0.34 V G^ ₁ = -n₁FE^ ₁ = -2 F (0.34) = -0.68F Cu ^+ + e^- Cu , E^ ₂ = +0.52 V G^ ₂ = -n₂FE^ ₂ = -1 F (0.52) = -0.52F The required half-cell reaction is: Cu ²⁺ + e^- Cu ^+ This reaction is obtained by subtracting the second reaction from the first reaction: G^ ₃ = G^ ₁ - G^ ₂ -1 F E^ ₃ = -0.68F - (-0.52F) -FE^ ₃ = -0.16F E^ ₃ = +0.16 V Answer: +0.16 V