To solve this problem, we need to use the stoichiometry of the given chemical reaction:
[tex]\[ \text{CH}_4 + 2 \text{O}_2 \rightarrow \text{CO}_2 + 2 \text{H}_2\text{O} \][/tex]
According to the balanced equation:
- One mole of methane (CH₄) reacts with two moles of oxygen (O₂) to produce one mole of carbon dioxide (CO₂) and two moles of water (H₂O).
This tells us that for every 2 moles of water (H₂O) produced, there is 1 mole of carbon dioxide (CO₂) produced.
Given that 10 moles of water (H₂O) are produced, we can find the corresponding amount of carbon dioxide (CO₂) produced using the stoichiometric ratio:
[tex]\[ 2 \, \text{moles of H}_2\text{O} \rightarrow 1 \, \text{mole of CO}_2 \][/tex]
If 10 moles of H₂O are produced:
[tex]\[ \frac{10 \, \text{moles of H}_2\text{O}}{2} = 5 \, \text{moles of CO}_2 \][/tex]
Thus:
If 10 moles of [tex]\( \text{H}_2 \text{O} \)[/tex] are produced, 5 moles of [tex]\( \text{CO}_2 \)[/tex] are also produced.
