How many moles of methane are required to produce `22 g CO_(2)` (g) after combustion?

Answer

To determine how many moles of methane (CH₄) are required to produce 22 g of carbon dioxide (CO₂) after combustion, we can follow these steps:

### Step 1: Write the balanced chemical equation for the combustion of methane.
The balanced equation for the combustion of methane is:
\[ \text{CH}_4 + 2 \text{O}_2 \rightarrow \text{CO}_2 + 2 \text{H}_2\text{O} \]

### Step 2: Determine the molar mass of carbon dioxide (CO₂).
The molar mass of CO₂ can be calculated as follows:
- Carbon (C) has a molar mass of 12 g/mol.
- Oxygen (O) has a molar mass of 16 g/mol.
- Therefore, the molar mass of CO₂ is:
\[ 12 \, \text{g/mol} + 2 \times 16 \, \text{g/mol} = 12 + 32 = 44 \, \text{g/mol} \]

### Step 3: Calculate the number of moles of CO₂ produced.
To find the number of moles of CO₂ produced from 22 g, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
So, for 22 g of CO₂:
\[ \text{Number of moles of CO}_2 = \frac{22 \, \text{g}}{44 \, \text{g/mol}} = 0.5 \, \text{moles} \]

### Step 4: Use the stoichiometry of the reaction to find moles of methane required.
From the balanced equation, we see that 1 mole of methane produces 1 mole of CO₂. Therefore, the moles of methane required to produce 0.5 moles of CO₂ is also 0.5 moles.

### Conclusion:
The number of moles of methane required to produce 22 g of CO₂ is:
\[ \text{0.5 moles of CH}_4 \]

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