Number of moles of methane required to produce $22\mathrm{g} {\mathrm{CO}}_{2\left(\mathrm{g}\right)}$ after combustion is $\mathrm{x}\times {10}^{–2}$ moles. The value of $\mathrm{x}$ is

${\mathrm{CH}}_4+2{\mathrm{O}}_2\to {\mathrm{CO}}_2+2{\mathrm{H}}_2\mathrm{O}$

Gram molecular mass of ${\mathrm{CO}}_2=12+2\left(16\right)=44 \mathrm{g}/\mathrm{mol}$

From the reaction, it is clear that $1$ mole of methane on complete combustion produces $44 \mathrm{g}$ ($1$ mole) of carbon dioxide.

Therefore moles of ${\mathrm{CH}}_4$ required to produce $22 \mathrm{g}$ of ${\mathrm{CO}}_2$ are:

$=\frac{1}{44}\times 22=0.5 \mathrm{mol} =50\times {10}^{-2} \mathrm{mol}$

Hence, $\mathrm{m}=50$