Final answer:
Statement A and B are true as they accurately reflect the stoichiometry of the balanced equation for the reaction between methane and oxygen. Statement C is false because the mass ratios of reactants to products are not the same as their mole ratios.
Step-by-step explanation:
The reaction between methane (CH₄) and oxygen (O₂) produces carbon dioxide (CO₂) and water (H₂O). The balanced chemical equation for this reaction is CH₄ + 2O₂ → CO₂ + 2H₂O.
Statement A is true: One mole of methane reacts with two moles of oxygen to produce one mole of carbon dioxide and two moles of water. Statement B is also true: One molecule of methane reacts with two molecules of oxygen to produce one molecule of carbon dioxide and two molecules of water. However, Statement C is false: One gram of methane does not react with two grams of oxygen to produce one gram of carbon dioxide and two grams of water because the masses of the molecules involved are not considered in the simple stoichiometric relationships indicated by the balanced equation. The mass relationship depends on the molar masses of the substances involved.
To explain this further, the balanced equation indicates the ratio of reactants to products in moles or molecules, not in grams. One mole of methane has a mass of approximately 16 grams, while one mole of oxygen (as O₂) has a mass of approximately 32 grams, which does not adhere to a 1:2 mass ratio.