To balance the chemical equation given the following reaction:
[tex]\[ \text{CH}_4 + 2 \text{O}_2 \rightarrow \text{H}_2\text{O} + \text{CO}_2 \][/tex]
we need to ensure that the number of atoms of each element is the same on both sides of the equation. Let's go through the process step by step.
1. Count the atoms on the left (reactants) side:
- Carbon (C): 1 atom in [tex]\(\text{CH}_4\)[/tex]
- Hydrogen (H): 4 atoms in [tex]\(\text{CH}_4\)[/tex]
- Oxygen (O): 4 atoms in [tex]\(2 \text{O}_2\)[/tex] (each [tex]\(\text{O}_2\)[/tex] molecule has 2 oxygen atoms).
2. Count the atoms on the right (products) side:
- Carbon (C): 1 atom in [tex]\(\text{CO}_2\)[/tex]
- Hydrogen (H): 2 atoms in [tex]\(\text{H}_2\text{O}\)[/tex]
- Oxygen (O): 1 atom in [tex]\(\text{H}_2\text{O}\)[/tex] + 2 atoms in [tex]\(\text{CO}_2\)[/tex] (total 3 oxygen atoms).
3. Notice that the number of hydrogen and oxygen atoms are not balanced between the reactants and products. We need 4 hydrogen atoms on the products side to match the 4 hydrogen atoms on the reactants side, and we need to balance the oxygen atoms accordingly.
4. Adjust coefficients to balance hydrogen:
- On the left side, we have [tex]\(4\ \text{H}\)[/tex] atoms; on the right side, there is [tex]\(2\ \text{H}\)[/tex] atoms in [tex]\(\text{H}_2\text{O}\)[/tex]. Hence, we need [tex]\(2\ \text{H}_2\text{O}\)[/tex] molecules to have [tex]\(4\ \text{H}\)[/tex] atoms.
- So the equation now becomes:
[tex]\[
\text{CH}_4 + 2 \text{O}_2 \rightarrow 2 \text{H}_2\text{O} + \text{CO}_2
\][/tex]
5. Recheck the balancing:
- Left side:
- Carbon: [tex]\(1\)[/tex]
- Hydrogen: [tex]\(4\)[/tex]
- Oxygen: [tex]\(2 \times 2 = 4\)[/tex]
- Right side:
- Carbon: [tex]\(1\)[/tex]
- Hydrogen: [tex]\(2 \times 2 = 4\)[/tex]
- Oxygen: [tex]\(2 \text{(from 2 H}_2\text{O)} + 2 \text{(from CO}_2) = 4\)[/tex]
The number of atoms on both sides of the equation is now balanced.
The balanced chemical equation is:
[tex]\[
\text{CH}_4 + 2 \text{O}_2 \rightarrow 2 \text{H}_2\text{O} + \text{CO}_2
\][/tex]
