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Electrochemistry

Question
CBSEENCH12006127

Calculate the standard electrode potential of the Mg2+ / Mg electrode for a cell in which the cell reaction is
Mg(s) + 2Ag+(aq) → Mg2+(aq) + 2Ag(s)
Given that, [Mg2+] = 0.1 M, [Ag+] = 0.01 M
Ag/Ag = + 0.80, Ecell = + 2.90 V

Solution

The cell is
Mg(s) | Mg2+ (aq) (0.1 M) || Ag+ (aq) (0.01 M) | Ag(s)
and the Ecell is given by

Ecell = E°cell - 0.0592log Mg2+Ag+22.90 = E°cell - 0.0592log(0.1)(0.01)22.90 = E°cell - 0.0592×3

                        2.90 = E°cell - 0.0885E°cell = 2.988 V

But               E°cell = E°Ag+/Ag - E°Mg2+/Mg
              E°Mg2+/Mg = + 0.80 - 2.988E°Mg2+/Mg = -2.188 V