$2.$ Consider a fuel cell that uses methane $($natural gas"$)$ as fuel. The reaction is C$*$H$\_\{4\}+2$O$\_\{2\}->2$H$\_\{2\}*$O $+$ C$*$O$\_\{2\}$

$C{H}_4+2O_{2}2H_{2}O+C{O}_2$

$($a$)$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

$At-$ electrode: $C{H}_4+2H_{2}OC{O}_2+8H^{+}+8e^{-}$

$At+$ electrode: $2O_2+8H^{+}+8e^{-}4H_{2}O$

What is the voltage of the cell?