To identify the balanced chemical equation for the combustion 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 on the products side.
The combustion of methane involves methane ([tex]\( \text{CH}_4 \)[/tex]) reacting with oxygen ([tex]\( \text{O}_2 \)[/tex]) to produce carbon dioxide ([tex]\( \text{CO}_2 \)[/tex]) and water ([tex]\( \text{H}_2 \text{O} \)[/tex]).
Let's examine each option:
A. [tex]\( \text{CH}_4 (g) + 2 \text{O}_2 (g) \rightarrow \text{CO}_2 (g) + \text{H}_2 \text{O} (g) \)[/tex]
- Reactants:
- Carbon: 1
- Hydrogen: 4
- Oxygen: 4
- Products:
- Carbon: 1
- Hydrogen: 2
- Oxygen: 3
In this equation, the number of hydrogen and oxygen atoms are not balanced.
B. [tex]\( \text{CH}_4 (g) + 2 \text{O}_2 (g) \rightarrow 2 \text{CO}_2 (g) + 2 \text{H}_2 \text{O} (g) \)[/tex]
- Reactants:
- Carbon: 1
- Hydrogen: 4
- Oxygen: 4
- Products:
- Carbon: 2
- Hydrogen: 4
- Oxygen: 6
In this equation, the number of carbon and oxygen atoms are not balanced.
C. [tex]\( 2 \text{CH}_4 (g) + \text{O}_2 (g) \rightarrow 2 \text{CO}_2 (g) + \text{H}_2 \text{O} (g) \)[/tex]
- Reactants:
- Carbon: 2
- Hydrogen: 8
- Oxygen: 2
- Products:
- Carbon: 2
- Hydrogen: 2
- Oxygen: 3
Again, the number of hydrogen and oxygen atoms are not balanced in this equation.
D. [tex]\( \text{CH}_4 (g) + 2 \text{O}_2 (g) \rightarrow \text{CO}_2 (g) + 2 \text{H}_2 \text{O} (g) \)[/tex]
- Reactants:
- Carbon: 1
- Hydrogen: 4
- Oxygen: 4
- Products:
- Carbon: 1
- Hydrogen: 4
- Oxygen: 4
In this equation, the number of carbon, hydrogen, and oxygen atoms are balanced.
Therefore, the correct balanced chemical equation for the combustion of methane is:
D. [tex]\( \text{CH}_4(g) + 2 \text{O}_2(g) \rightarrow \text{CO}_2(g) + 2 \text{H}_2\text{O}(g) \)[/tex]
