Given the standard electrode potentials for the following half-reactions of a hypothetical metal M : M³⁺ + e^- M²⁺ E^ = 1.50 V M²⁺ + 2e^- M E^ = -0.30 V The magnitude of the standard electrode potential for M³⁺ / M is x 10⁻² V . The value of x is ________ (Nearest integer)

Step-by-step solution

The standard Gibbs free energy change for a half-reaction is given by G^ = -nFE^ . For the first half-reaction: M³⁺ + e^- M²⁺ G^ ₁ = -1 F (1.50) = -1.50F For the second half-reaction: M²⁺ + 2e^- M G^ ₂ = -2 F (-0.30) = +0.60F Adding the two half-reactions gives the target half-reaction: M³⁺ + 3e^- M G^ ₃ = G^ ₁ + G^ ₂ = -1.50F + 0.60F = -0.90F The standard electrode potential for the target half-reaction is: E^ ₃ = - G^ ₃ nF = -(-0.90F) 3F = 0.30 V The magnitude is 0.30 V = 30 10⁻² V . Thus, x = 30 . Answer: 30