Final answer:
The coefficients that balance the chemical equation CH4 + O2 -> 2 CO2 + 2 H2O are 1 and 2 because we need four oxygen atoms in the reactants to balance the four oxygen atoms in the products. This corresponds to option B, 1,3O for the coefficients of methane and oxygen, respectively.
Step-by-step explanation:
The question asks which set of coefficients will balance the chemical equation CH4 + O2 -> 2 CO2 + 2 H2O. We start by balancing carbon and hydrogen, which are already balanced with 1 carbon atom in methane and in carbon dioxide, and 4 hydrogen atoms in methane and in the water molecules. Next, we balance oxygen. There are 4 oxygen atoms in the products (2 in CO2 and 2 in H2O) so we need 4 oxygen atoms in the reactants. This requires us to put a 2 in front of O2 to balance the equation, resulting in CH4 + 2O2 -> 2 CO2 + 2 H2O. The correct set of coefficients to balance the given chemical equation is therefore 1 methane molecule to 2 oxygen molecules, which corresponds to option B, 1,3O (ignoring the typographical error). Using the smallest possible whole-number coefficients in a chemical equation is common practice. For the methane combustion reaction, the smallest whole-number ratio that satisfies the stoichiometry of the reactants and products is 1:2:1:2. No further steps are needed once the balanced equation is achieved with proper whole numbers.