The minimum number of moles of $O_2$ required for complete combustion of $1$ mole of propane and $2$moles of butane is

Step 1 : Given data

$1$mole propane combustion $5$mole $O_2$ combustion required

$\underset{\text{1 mole}}{{\mathrm{C}}_3{\mathrm{H}}_8}+\underset{5\text{mole}}{{\mathrm{SO}}_2}\to 3C{O}_2+4{\mathrm{H}}_2\mathrm{O}$

${\mathrm{C}}_4{\mathrm{H}}_{10}+\frac{13}{2}{\mathrm{O}}_2\to 4C{O}_2+5{\mathrm{H}}_2\mathrm{O}$

Step 2 : For $2$moles of butane $13$ mole of $O_2$

$\begin{array}{ll}1\text{mole}& 6.5\text{mole}\\ 2\text{mole}& 13\text{mole}\end{array}$

Then total moles for For $2$moles of butane $13$ mole of $O_2$ as 13+5=18