A silver concentration cell at 298 K is constructed by connecting two silver electrodes. The anode compartment consists of a silver wire dipped in a saturated aqueous solution of AgCl . The cathode compartment consists of a silver wire dipped in a 0.1 M aqueous solution of AgNO ₃ . The magnitude of the Gibbs free energy change for this cell is _____ J mol ⁻¹ . [Given: K_ sp ( AgCl ) = 10⁻¹⁰ , F = 96500 C mol ⁻¹ , 2.3

Step-by-step solution

For a concentration cell, E^ _ cell = 0 V and n = 1 . At anode (saturated AgCl solution): [ Ag ^+]_ anode = K_ sp = 10⁻¹⁰ = 10⁻⁵ M At cathode ( 0.1 M AgNO ₃ solution): [ Ag ^+]_ cathode = 0.1 = 10⁻¹ M Using Nernst equation: E_ cell = E^ _ cell - 0.06 1 [ Ag ^+]_ anode [ Ag ^+]_ cathode E_ cell = 0 - 0.06 10⁻⁵ 10⁻¹ E_ cell = -0.06 10⁻⁴ = -0.06 (-4) = 0.24 V Gibbs free energy change: G = -nFE_ cell G = -1 96500 0.24 = -23160 J mol ⁻¹ The magnitude of the Gibbs free energy change is 23160 J mol ⁻¹ . Answer: 23160