For the galvanic cell reaction involving magnesium and silver: Mg ( s )+2 Ag ⁺( aq ) Mg ²⁺( aq )+2 Ag ( s ) The standard Gibbs energy change ( G ^ ) is -617.6 ~kJ ~mol ⁻¹ . If the standard reduction potential of the Ag ⁺ / Ag electrode is 0.80 ~V , what is the standard reduction potential of the Mg ²⁺ / Mg electrode? (Given 1 ~F =96500 ~C ~mol ⁻¹ )

Step-by-step solution

The given cell reaction is: Mg ( s )+2 Ag ⁺( aq ) Mg ²⁺( aq )+2 Ag ( s ) The number of moles of electrons transferred is n = 2 . The standard Gibbs energy change is: G ^ = -n F E _ cell ^ -617.6 10³ ~J ~mol ⁻¹ = -2 96500 ~C ~mol ⁻¹ E _ cell ^ E _ cell ^ = -617600 -193000 ~V = 3.20 ~V The standard cell potential is also given by the difference in standard reduction potentials of the cathode and anode: E _ cell ^ = E _ cathode ^ - E _ anode ^ Here, silver is reduced (cathode) and magnesium is oxidized (anode). 3.20 ~