the balanced equation for the reaction between methane and oxygen is as follows;
CH₄ + 2O₂ ---> CO₂ + 2H₂O
molar ratio of methane to oxygen is 1:2
at constant temperature and pressure, volume of gas is directly proportional to number of moles of gas present.
Therefore molar ratio of reactants are equivalent to volume ratio of reactants.
then volume ratio of methane to oxygen is 1:2
2 L of oxygen reacts with 1 L of methane
therefore 0.660 L of oxygen reacts with - 1/2 x 0.660 = 0.330 L of methane
volume of methane gas required is 0.330 L