Consider the standard electrode potentials for the following half-reactions of a metal X : X³⁺ + 3e^- X E^ = -0.10 V X^+ + e^- X E^ = 0.50 V A galvanic cell is constructed by coupling the X³⁺/X^+ half-cell with a Y²⁺/Y half-cell ( E^ = 0.60 V ). The magnitude of the standard Gibbs free energy change ( G^ ) for the spontaneous overall cell reaction is ________ kJ mol ⁻¹ . (Nearest integer) [Given: Faraday's constant F

Step-by-step solution

First, calculate the standard electrode potential for the X³⁺/X^+ half-cell. Given: (i) X³⁺ + 3e^- X G^ ₁ = -3 F (-0.10) = +0.30F (ii) X^+ + e^- X G^ ₂ = -1 F (0.50) = -0.50F Subtracting equation (ii) from (i) gives the target half-reaction: X³⁺ + 2e^- X^+ G^ ₃ = G^ ₁ - G^ ₂ = 0.30F - (-0.50F) = +0.80F The standard electrode potential for X³⁺/X^+ is: E^ _ X³⁺/X^+ = - G^ ₃ nF = -0.80F 2F = -0.40 V For the galvanic cell, the two half-cells are X³⁺/X^+ ( E^ = -0.40 V ) and Y²⁺/Y ( E^ = 0.60 V ). For a spontaneous reac