$4.$ A fuel oil burned in a steam generator has a composition which may be represented by C$14$H$30.$ A dry$-$basis flue$-$gas analysis shows the following volumetric composition:

CO$211\mathrm{.}226\%,$

O$24\mathrm{.}145\%,$

CO $0\mathrm{.}863\%,$ and

N$283\mathrm{.}766\%.$

Write the complete combustion equation for $1$ mol of fuel and calculate:

$($a$)$ the air$-$to$-$fuel ratio by mass,

$($b$)$ the excess air in percent, and

$($c$)$ the mass of water vapor in the flue gases per unit mass of fuel.