To balance the chemical equation representing the burning of methane ([tex]\( \text{CH}_4 \)[/tex]), we need to ensure that the number of each type of atom on the reactants side equals the number of each type of atom on the products side.
The given incomplete equation is:
[tex]\[ \text{CH}_4 + \text{O}_2 \rightarrow \text{CO}_2 + \ldots \text{H}_2\text{O} \][/tex]
We begin by balancing each type of atom one step at a time.
1. Carbon (C) atoms:
There is 1 carbon (C) atom in [tex]\(\text{CH}_4\)[/tex] on the reactants side. Thus, we need 1 carbon atom in [tex]\(\text{CO}_2\)[/tex] on the products side. Therefore, the coefficient in front of [tex]\(\text{CO}_2\)[/tex] is 1.
2. Hydrogen (H) atoms:
There are 4 hydrogen (H) atoms in [tex]\(\text{CH}_4\)[/tex] on the reactants side. Since each [tex]\(\text{H}_2\text{O}\)[/tex] molecule has 2 hydrogen atoms, we need 2 molecules of [tex]\(\text{H}_2\text{O}\)[/tex] to balance the 4 hydrogen atoms. Therefore, the coefficient in front of [tex]\(\text{H}_2\text{O}\)[/tex] is 2.
3. Oxygen (O) atoms:
We have balanced carbon and hydrogen, so now let's balance oxygen. On the products side, we have:
- 2 oxygen atoms from the 1 molecule of [tex]\(\text{CO}_2\)[/tex]
- 2 oxygen atoms from the 2 molecules of [tex]\(\text{H}_2\text{O}\)[/tex] (since each molecule has 1 oxygen atom)
This gives a total of [tex]\(2 + 2 = 4\)[/tex] oxygen atoms needed on the reactants side. Each molecule of [tex]\(\text{O}_2\)[/tex] contains 2 oxygen atoms, so we need 2 molecules of [tex]\(\text{O}_2\)[/tex] to get the 4 oxygen atoms. Therefore, the coefficient in front of [tex]\(\text{O}_2\)[/tex] is 2.
Putting it all together, the balanced equation is:
[tex]\[ \text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \][/tex]
The missing coefficient in both the reactants ([tex]\(\text{O}_2\)[/tex]) and the products ([tex]\(\text{H}_2\text{O}\)[/tex]) is 2. Thus, the correct answer is:
C. 2
