To balance the chemical equation for the combustion of methane, we start with the unbalanced form:
[tex]\[ CH_4 + O_2 \rightarrow CO_2 + H_2O \][/tex]
Let's go through the process of balancing the equation step by step:
1. Identify the number of atoms of each element on both sides of the equation:
- Left side: [tex]\( 1 \)[/tex] carbon (C), [tex]\( 4 \)[/tex] hydrogen (H), [tex]\( 2 \)[/tex] oxygen (O)
- Right side: [tex]\( 1 \)[/tex] carbon (C), [tex]\( 2 \)[/tex] hydrogen (H), [tex]\( 2 \)[/tex] oxygen (O)
2. Balance atoms that appear in only one reactant and one product first.
- Carbon (C) is already balanced (1 C on each side).
- Hydrogen (H) can be balanced by putting a coefficient of 2 in front of H₂O:
[tex]\[ CH_4 + O_2 \rightarrow CO_2 + 2 H_2O \][/tex]
- Now, the number of hydrogen atoms on the right side is 4 (2 H₂O), which matches the 4 hydrogen atoms on the left side.
3. Balance oxygen atoms last since oxygen appears in [tex]\( O_2 \)[/tex] which can adjust more easily.
- Currently, we have:
- Left side: [tex]\( 2 \)[/tex] oxygen (O)
- Right side: [tex]\( 4 \)[/tex] oxygen (2 from CO₂ + 2x1 from each H₂O)
- To balance oxygen, we need to have [tex]\( 4 \)[/tex] oxygen atoms on the left side as well. This can be achieved by putting a coefficient of 2 in front of O₂:
[tex]\[ CH_4 + 2 O_2 \rightarrow CO_2 + 2 H_2O \][/tex]
4. Double-check the balance:
- Carbons: [tex]\( 1 \)[/tex] on the left, [tex]\( 1 \)[/tex] on the right.
- Hydrogens: [tex]\( 4 \)[/tex] on the left, [tex]\( 4 \)[/tex] on the right.
- Oxygens: [tex]\( 4 \)[/tex] on the left (2 molecules of [tex]\( O_2 \)[/tex]), [tex]\( 4 \)[/tex] on the right (2 from CO₂ + 2x1 from each H₂O).
The equation is now balanced:
[tex]\[ CH_4 + 2 O_2 \rightarrow CO_2 + 2 H_2O \][/tex]
The coefficients for each substance are:
- Methane (CH₄): [tex]\(1\)[/tex]
- Oxygen (O₂): [tex]\(2\)[/tex]
- Carbon dioxide (CO₂): [tex]\(1\)[/tex]
- Water (H₂O): [tex]\(2\)[/tex]
The missing coefficient for oxygen and water, both in reactants and products, is:
[tex]\[ 2 \][/tex]
Therefore, the correct answer is C. 2.
