Number of moles of methane required to produce 22g CO _ 2 ( g )...

${CH}_{4} + 2{O}_{2} \to {CO}_{2} + 2{H}_{2}O$

Gram molecular mass of ${CO}_{2} = 12 + 2 ( 16 ) = 44g / mol$

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

Therefore moles of ${CH}_{4}$ required to produce $22g$ of ${CO}_{2}$ are:

$= \dfrac{1}{44} \times 22 = 0 . 5mol = 50 \times {10}^{- 2}mol$

Hence, $m = 50$