Chapter 5.1, Problem 5P

Consider a fuel cell that uses methane (“natural gas”) as fuel. The reaction is ${\text{CH}}_{\text{4}}{\text{+2O}}_{\text{2}}\to {\text{2H}}_{\text{2}}\text{O}+{\text{CO}}_{\text{2}}$.

(a) Use the data at the back of this book to determine the values of $△H$ and $△G$ for this reaction, for one mole of methane. Assume that the reaction takes place at room temperature and atmospheric pressure.

(b) Assuming ideal performance, how much electrical work can you get out of the cell, for each mole of methane fuel?

(c) How much waste heat is produced, for each mole of methane fuel?

(d) The steps of this reaction are $\text{at}-\text{electrode}:{\text{CH}}_{\text{4}}+{\text{2H}}_{\text{2}}\text{O}\to {\text{CO}}_{\text{2}}+{\text{8H}}^{\text{+}}+{\text{8e}}^{-}$; $\text{at}-\text{electrode}:{\text{2O}}_2+8{\text{H}}^{+}+{\text{8e}}^{-}\to 4{\text{H}}_{\text{2}}\text{O}$.

What is the voltage of the cell?