A gasoline is composed of $85\%$ octane C$8$H$18$ and $15\%$ ethanol C$2$H$5$OH at $298$ k and combusts with air at the same temperature. The volumetric analysis of the combustion products at $1$ bar on a dry basis is: $14\mathrm{.}5\%$ CO$2,1\mathrm{.}5\%$ CO$,4\mathrm{.}5\%$ O$2$ and $79\mathrm{.}5\%$ N$2.$ Determine:

$1)$ Balance of the combustion reaction

$2)$ Air$-$Fuel Ratio $($AF$)$ on a mass basis

$3)$ Percentage of theoretical air used

$4)$ Stoichiometric flue gas temperature

$5)$ Upper and lower heating value of the fuel