To determine how many moles of methane (CH₄) are required to produce 22 grams of carbon dioxide (CO₂), we can follow these steps:
1. Determine the molar mass of CO₂:
- Carbon (C) has an atomic mass of 12 g/mol.
- Oxygen (O) has an atomic mass of 16 g/mol.
- Therefore, the molar mass of CO₂:
[tex]\( \text{Molar mass of CO₂} = 12 \, \text{g/mol (C)} + 2 \times 16 \, \text{g/mol (O)} = 12 + 32 = 44 \, \text{g/mol} \)[/tex]
2. Calculate the moles of CO₂ produced:
- Given mass of CO₂ is 22 grams.
- Using the formula:
[tex]\( \text{moles of CO₂} = \frac{\text{mass of CO₂}}{\text{molar mass of CO₂}} \)[/tex]
[tex]\[
\text{moles of CO₂} = \frac{22 \, \text{grams}}{44 \, \text{g/mol}} = 0.5 \, \text{moles}
\][/tex]
3. Using the balanced chemical equation:
- The equation is: [tex]\( \text{CH}_4 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} \)[/tex]
- From the equation, we see that the molar ratio of CH₄ to CO₂ is 1:1. This means that 1 mole of CH₄ produces 1 mole of CO₂.
4. Determine the moles of CH₄ required:
- Since the required moles of CO₂ are 0.5 moles, and the molar ratio of CH₄ to CO₂ is 1:1:
[tex]\[
\text{moles of CH₄} = \text{moles of CO₂} = 0.5 \, \text{moles}
\][/tex]
Hence, 0.5 moles of methane (CH₄) are required to produce 22 grams of carbon dioxide (CO₂).
