Question

Explain why the sum of the potentials for the half-reactions Sn2+(aq) + 2e− → Sn(s) and Sn4+(aq) + 2e− → Sn2+(aq) does not equal the potential for the reaction Sn4+(aq) + 4e−→ Sn(s). What is the net cell potential? Compare the values of ΔG° for the sum of the potentials and the actual net cell potential.

Answer 1

The given two half-reactions are:

Sn²⁺(aq) + 2e− → Sn(s)             E^o₁ = -0.14 V

Sn⁴⁺(aq) + 2e− → Sn²⁺(aq)        E^o₂ = 0.13 V

by adding the above two half reactions gives the overall half reaction:

Sn⁴⁺(aq) + 4e− → Sn(s)        E^o = -0.01 V

The sum of two half-reactions gives the desired overall half-reaction but we cannot simply add the potentials of two reductive half-reactions to obtain the potential of overall half-reaction because E° is not a state function. While, ΔG° is a state function, therefore by adding the values of ΔG° for the individual reactions provides ΔG° for the overall reaction. To determine the value of E° for the overall half reaction, first add the values of ΔG° (= −nFE°) for each half-reaction to obtain ΔG° for the overall half reaction.

                 ΔG° = −nFE°

In both half reactions n = 2, E°1 = -0.14, E°2 = 0.13

ΔG° = −2F(-0.14V)

ΔG° = −2F(0.13V)

Solving ΔG° for overall reaction

Sn⁴⁺(aq) + 4e− → Sn(s)   

ΔG° = [−2F(-0.14) ]+ [−2F(0.13)]

ΔG° = F[(0.28) ]+ [(−0.26)] = F( 0.02V)

Four electrons are transferred in overall half reaction then

ΔG° = −4FE°

F( 0.02V) = -4F E°

E°l = -0.02V/4 = -0.005 V

The value -0.005 V is different from the value -0.01 V (net cell potential) which is obtained by simply adding E°1 and E°2 for the two half reactions.