For a generic metal M , the standard reduction potentials for the M³⁺/M and M²⁺/M couples are given as x and y respectively. The standard electrode potential for the M³⁺/M²⁺ half-cell reaction will be:

Step-by-step solution

The given half-cell reactions can be written as: M³⁺ + 3e^- M , E^ ₁ = x G^ ₁ = -n₁FE^ ₁ = -3Fx M²⁺ + 2e^- M , E^ ₂ = y G^ ₂ = -n₂FE^ ₂ = -2Fy The required half-cell reaction is: M³⁺ + e^- M²⁺ This reaction is obtained by subtracting the second reaction from the first reaction: G^ ₃ = G^ ₁ - G^ ₂ -1 F E^ ₃ = -3Fx - (-2Fy) -FE^ ₃ = -3Fx + 2Fy E^ ₃ = 3Fx - 2Fy F = 3x - 2y Answer: 3x - 2y