Chapter 17, Problem 17.121CHP

Consider the addition of the following half-reactions:

 (1) ${\text{Fe}}^{3+}\left(aq\right)+3{\text{ e}}^{-}\to \text{Fe}\left(s\right)E^{\circ }{}_1=-0.04\text{ V}$

 (2) $\text{Fe}\left(s\right)\to {\text{Fe}}^{2+}\left(aq\right)+2{\text{ e}}^{-}{E}^{\circ }{}_2=0.45\text{ V}$

 (3) ${\text{Fe}}^3\left(aq\right){\text{+e}}^{-}\to {\text{Fe}}^{2+}\left(aq\right)E^{\circ }{}_3=?$

 Because half-reactions (1) and (2) contain a different number of electrons, the net reaction (3) is another half-reaction, and E°₃ can’t be obtained simply by adding E°₁ and E°₂. The free-energy changes, however, are additive because G is a state function:

     $\Delta G^{\circ }{}_3=\Delta G^{\circ }{}_1+\Delta G^{\circ }{}_2$

1. (a) Starting with the relationship between Δ G° and E°, derive a general equation that relates the E° values for half-reactions (1), (2), and (3).
2. (b) Calculate the value of E°₃ for the Fe³⁺/Fe²⁺ half-reaction.
3. (c) Explain why the E° values would be additive (E°₃ = E°₁ + E°₂) if reaction (3) were an overall cell reaction rather than a half-reaction.