To balance the chemical equation representing the burning of methane, we need to determine the correct coefficients for each compound. The equation we are starting with is:
[tex]\[
CH_4 + O_2 \rightarrow CO_2 + H_2O
\][/tex]
Let's follow the systematic steps to balance this equation by looking at the number of each type of atom on both sides of the equation.
### Step 1: Balance Carbon Atoms
1. Methane (CH_4) has 1 Carbon (C) atom.
2. Carbon dioxide (CO_2) has 1 Carbon (C) atom.
Since there's one carbon atom on both sides, the carbon atoms are already balanced.
### Step 2: Balance Hydrogen Atoms
1. Methane (CH_4) has 4 Hydrogen (H) atoms.
2. Water (H_2O) has 2 Hydrogen (H) atoms.
To balance the hydrogen atoms, we need 2 water molecules (H_2O) on the product side because [tex]\(4 \text{ H} \div 2 \text{ H per } H_2O = 2\)[/tex]:
[tex]\[
CH_4 + O_2 \rightarrow CO_2 + 2H_2O
\][/tex]
### Step 3: Balance Oxygen Atoms
1. On the reactant side, there are [tex]\(O_2\)[/tex] molecules, each providing 2 Oxygen (O) atoms.
2. On the product side, we now have 1 CO_2 (providing 2 Oxygen atoms) and 2 H_2O (each providing 1 Oxygen atom, for a total of 2 Oxygen atoms).
Adding these up on the product side:
[tex]\[
2 \text{ (from CO}_2) + 2 \text{ (from 2 H}_2O) = 4 \text{ Oxygen (O)}
\][/tex]
We need to have the same amount of oxygen atoms on both sides. Therefore, we need 2 [tex]\(O_2\)[/tex] molecules (each providing 2 Oxygen atoms; thus, [tex]\(2 \times 2 = 4\)[/tex] Oxygen atoms):
[tex]\[
CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O
\][/tex]
### Conclusion:
The missing coefficient in both the reactants (for [tex]\(O_2\)[/tex]) and the products (for [tex]\(H_2O\)[/tex]) is 2. Thus, the correct answer is:
[tex]\[
\boxed{2}
\][/tex]
