Chapter 18, Problem 18.165MP

The half-reactions that occur in ordinary alkaline batteries can be written as

Cathode: ${\text{MnO}}_2\left(s\right)+{\text{H}}_2\text{O}\left(l\right)+{\text{e}}^{-}\to \text{MnO}\left(\text{OH}\right)\left(s\right)+{\text{OH}}^{-}\left(aq\right)$

Anode: $\text{Zn}\left(s\right)+2{\text{OH}}^{-}\left(aq\right)\to \text{Zn}{\left(\text{OH}\right)}_2\left(s\right)+2{\text{e}}^{-}$

In 1999, researchers in Israel reported a new type of alkaline battery, called a "super-iron" battery. This battery uses the same anode reaction as an ordinary alkaline battery but involves the reduction of FeO₄²− — ion (from K₂FeO₄) to solid Fe(OH)₃ at the cathode.

(a) Use the following standard reduction potential and any data from Appendixes C and D to calculate the standard cell potential expected for an ordinary alkaline battery:

$\text{MnO}\left(\text{OH}\right)\left(s\right)+{\text{H}}_2\text{O}\left(l\right)+{\text{e}}^{-}\to \text{Mn}{\left(\text{OH}\right)}_2\left(s\right)+{\text{OH}}^{-}\left(aq\right)E°=-0.380\text{V}$

(b) Write a balanced equation for the cathode half-reaction in a super-iron battery. The half-reaction occurs in a basic environment.

(c) A super-iron battery should last longer than an ordinary alkaline battery of the same size and weight because its cathode can provide more charge per unit mass. Quantitatively compare the number Of coulombs Of charge released by the reduction Of 10.0 g Of K₂FeO₄ to Fe(OH)₃with the number of coulombs of charge released by the reduction of 10.0 g of MnO₂ to MnO(OH).