What is the value of ΔG o in kJ at 25 oC for the reaction between the pair

Question

What is the value of ΔG ^o in kJ at 25 ^oC for the reaction between the pair:

Ag(s) and Mn²⁺(aq) to give Mn(s) and Ag⁺(aq)

Use the reduction potential values for Ag⁺(aq) of +0.80 V and for Mn²⁺(aq) of -1.18 V

The correct answer is 3.8*10²

Answer 1

Ag⁺ +e- ==> Ag(s) Eº = +0.80 V (x2)

Mn²⁺ + 2e- ==> Mn(s) Eº = -1.18 V

Since reduction potential for Ag+ is greater, it will be reduced and Mn will be oxidized.

Ag⁺ + e- ==> Ag(s) (reduction) x2

Mn(s) ===> Mn²⁺ + 2e- (oxidation)

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2Ag⁺ + Mn(s) ==> 2Ag(s) + Mn²⁺ overall reaction

Eºcell = 0.80 - (-1.18) = 1.98 V

∆Gº = -nF x Eºcell

∆Gº = -(2)(96,495)(1.98) = -382,086 J x 1 kJ/1000 J = -382 kJ = -3.8x10² kJ for the reaction as written.

Since the question asks for the reverse, i.e. Mn²⁺ + 2Ag(s) ==> 2Ag⁺ + Mn(s), it will be non spontaneous with a ∆Gº = + 3.8x102 kJ