To balance the chemical equation for the burning of methane, we need to ensure that the number of atoms of each element on the reactant side is equal to the number of atoms on the product side. The chemical equation for the combustion of methane is:
[tex]\[ \text{CH}_4 + O_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} \][/tex]
Step-by-step, we balance this equation:
1. Balance Carbon (C):
- There is 1 carbon atom in CH[tex]\(_4\)[/tex].
- There is 1 carbon atom in CO[tex]\(_2\)[/tex].
- Therefore, the coefficient for CO[tex]\(_2\)[/tex] is already balanced (1 molecule).
2. Balance Hydrogen (H):
- There are 4 hydrogen atoms in CH[tex]\(_4\)[/tex] (since each CH[tex]\(_4\)[/tex] has 4 H atoms).
- There are 2 hydrogen atoms in each H[tex]\(_2\)[/tex]O molecule.
- To balance the 4 hydrogen atoms from CH[tex]\(_4\)[/tex], we need 2 H[tex]\(_2\)[/tex]O molecules because [tex]\(2 \times 2 = 4\)[/tex] hydrogen atoms.
- So, the coefficient for H[tex]\(_2\)[/tex]O is 2.
3. Balance Oxygen (O):
- On the product side, there are:
- 2 oxygen atoms in CO[tex]\(_2\)[/tex],
- And [tex]\(2 \times 1 = 2\)[/tex] oxygen atoms in 2 H[tex]\(_2\)[/tex]O molecules.
- So, in total, there are [tex]\(2 + 2 = 4\)[/tex] oxygen atoms on the product side.
- To balance the 4 oxygen atoms on the reactant side, we need 2 O[tex]\(_2\)[/tex] molecules because each O[tex]\(_2\)[/tex] contains 2 oxygen atoms.
- Therefore, the coefficient for O[tex]\(_2\)[/tex] is 2.
The balanced equation is:
[tex]\[ \text{CH}_4 + 2 \text{O}_2 \rightarrow \text{CO}_2 + 2 \text{H}_2\text{O} \][/tex]
Therefore, the missing coefficients for both O[tex]\(_2\)[/tex] and H[tex]\(_2\)[/tex]O are 2.
Given the choices:
A. 0
B. 1
C. 2
D. 3
E. 4
The correct answer is:
C. 2
