The number of moles of methane required to produce 11g \(CO_2\) (g) after complete combustion is:
(Given molar mass of methane in g mol–1 : 16)
(Given molar mass of methane in g mol–1 : 16)
- 0.75
- 0.25
- 0.35
- 0.5
The Correct Option is B
Approach Solution - 1
The general combustion reaction of alkanes is:
\[\text{C}_n\text{H}_{2n+2} + \frac{3n+1}{2}\text{O}_2 \rightarrow n\text{CO}_2 + (n+1)\text{H}_2\text{O}.\]
For methane (\(\text{CH}_4\)), the specific balanced equation is:
\[\text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}.\]
Step 1: Molar mass of \(\text{CO}_2\)
The molar mass of \(\text{CO}_2\) is:
\[\text{Molar mass of } \text{CO}_2 = 12 + (2 \times 16) = 44 \, \text{g/mol}.\]
Step 2: Calculate moles of \(\text{CO}_2\)
The number of moles of \(\text{CO}_2\) in \(11 \, \text{g}\) is:
\[\text{Moles of } \text{CO}_2 = \frac{\text{Mass of } \text{CO}_2}{\text{Molar mass of } \text{CO}_2} = \frac{11}{44} = 0.25 \, \text{mol}.\]
Step 3: Relate \(\text{CH}_4\) to \(\text{CO}_2\)
From the balanced reaction:
\[1 \, \text{mole of } \text{CH}_4 \, \text{produces } 1 \, \text{mole of } \text{CO}_2.\]
Therefore, to produce \(0.25 \, \text{moles of } \text{CO}_2\), the moles of \(\text{CH}_4\) required are:
\[\text{Moles of } \text{CH}_4 = 0.25 \, \text{mol}.\]Step 4: Mass of \(\text{CH}_4\)
The mass of \(0.25 \, \text{moles of } \text{CH}_4\) can be verified as:
\[\text{Mass of } \text{CH}_4 = \text{Moles of } \text{CH}_4 \times \text{Molar mass of } \text{CH}_4 = 0.25 \times 16 = 4 \, \text{g}.\]
Conclusion:
The number of moles of methane required to produce \(11 \, \text{g of } \text{CO}_2\) is \(0.25 \, \text{mol}\).
Final Answer: (2).
Approach Solution -2
For complete combustion of methane:
\[ CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O \]
From the equation, 1 mole of CH₄ produces 1 mole of CO₂.
Step 2: Calculate moles of CO₂ produced.
Given mass of CO₂ = 11 g
Molar mass of CO₂ = 44 g/mol
\[ \text{Moles of CO₂} = \frac{11}{44} = 0.25 \, \text{mol} \]
Step 3: Relate moles of CH₄ to CO₂.
From the balanced equation, 1 mole CH₄ → 1 mole CO₂
Hence, moles of CH₄ required = moles of CO₂ produced = 0.25 mol
Step 4: Final Answer.
The number of moles of methane required = 0.25 mol
Final Answer: 0.25
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