This assignment will use reaction thermodynamics to predict the amount of carbon dioxide produced per unit energy for three different types of fuels:

$$ Natural gas $($assumed here to be methane in the gas state$)$

$$ Gasoline $($assumed here to be n$-$octane in the liquid state$)$

$$ Coal $($assumed here to be elemental carbon in the solid state$)$

First, provide balanced equations for the complete combustion of $1$ mole of each of the above fuel molecules with oxygen $($O$2)$ to produce H$2$O and CO$2,$ both in the vapor state.