A city gas has the following composition by volume:

CO$2=3\%,$ C$1\mathrm{.}13$H$4\mathrm{.}52=9\mathrm{.}4\%,$

O$2=0\mathrm{.}6\%,$ C$2\mathrm{.}14$ H$6\mathrm{.}28=13\mathrm{.}6\%,$

H$2=34\%,$ CO$=35\%,$ N$2=4\mathrm{.}4\%$

$($a$)$ Calculate the theoretical number of cubic meters of air, $($at S$.$T$.$P$.),$ that must be supplied for the

combustion of one mole of the gas $($Assuming air contains $21\%$ by volume oxygen$).$

$($b$)$ Calculate the heating value of the gas in calories per gm$.$mole. $($Heats of combustion $($Hoc$)$: H$2=$

$68317$ cal$/$mol$,$ CO$=67636$ cal$/$mol $).$