Question

Number of moles of methane required to produce 22g \(CO_{2​(g)}\) after combustion is \(x × 10^{−2}\) moles. The value of x is

Answer 1

Correct Answer: 50

To determine the number of moles \(x\) of methane required to produce 22g of \(CO_{2}\), we follow these steps:

1. Balanced Chemical Equation:
CH₄ + 2O₂ → CO₂ + 2H₂O
From the equation, 1 mole of CH₄ produces 1 mole of CO₂.

2. Molar Mass Calculation:
Molar mass of \(CO_{2}\) = 12 (C) + 2×16 (O) = 44 g/mol

3. Moles of CO₂ Produced:
Moles of \(CO_{2} = \frac{22 \text{ g}}{44 \text{ g/mol}} = 0.5 \text{ moles}\)

4. Moles of Methane Required:
Since the ratio is 1:1, moles of CH₄ = moles of CO₂ = 0.5

5. Determine x:
Given \(x \times 10^{-2}\) moles, hence \(x = 0.5 \times 100 = 50\)

6. Validation:
The computed value of \(x\) is 50.
 

Answer 2

\[ \text{CH}_4\,(g) + 2\text{O}_2\,(g) \rightarrow \text{CO}_2\,(g) + 2\text{H}_2\text{O}\,(l) \]
\[ n_{\text{CO}_2} = \frac{22}{44} = 0.5 \, \text{moles} \]
\[ \text{So moles of CH}_4 \text{ required} = 0.5 \, \text{moles} \]
\[ \text{i.e., } 50 \times 10^{-2} \, \text{mole} \]
\[ x = 50 \]