Question

How many moles of methane are required to produce $11\ \text{g}$ $CO_{2(g)}$ after combustion? (Molar mass of $CO_{2}=44\ \text{g mol}^{-1}$)

• A. 0.25
• B. 0.5
• C. 1.5
• D. 2.0
• E. 2.5

Hint:

In a 1:1 molar ratio reaction, the moles of product required equal the moles of reactant used.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a stoichiometry problem. We need to use the balanced chemical equation for the combustion of methane to find the molar relationship between methane (CH\(_4\)) and carbon dioxide (CO\(_2\)) and then use this relationship to calculate the required moles of methane.
Step 2: Key Formula or Approach:
1. Write and balance the chemical equation for the complete combustion of methane. 2. Convert the given mass of the product (CO\(_2\)) to moles. \[ \text{moles} = \frac{\text{mass}}{\text{Molar mass}} \] 3. Use the mole ratio from the balanced equation to find the moles of the reactant (methane). Step 3: Detailed Explanation:
1. Balanced Chemical Equation:
The combustion of methane (CH\(_4\)) in oxygen (O\(_2\)) produces carbon dioxide (CO\(_2\)) and water (H\(_2\)O). \[ \text{CH}_4 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} \] To balance the equation: - Balance C: 1 C on the left, 1 C on the right. (Balanced) - Balance H: 4 H on the left, 2 H on the right. We need 2 H\(_2\)O. \[ \text{CH}_4 + \text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \] - Balance O: 2 O on the left, 2 O in CO\(_2\) + 2 O in 2H\(_2\)O = 4 O on the right. We need 2 O\(_2\). \[ \text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(g) \] The balanced equation shows that 1 mole of CH\(_4\) produces 1 mole of CO\(_2\). The mole ratio is 1:1. 2. Calculate Moles of CO\(_2\):
We are given: - Mass of CO\(_2\) produced = 11 g - Molar mass of CO\(_2\) = 44 g/mol \[ \text{moles of CO}_2 = \frac{11 \text{ g}}{44 \text{ g/mol}} = \frac{1}{4} = 0.25 \text{ mol} \] 3. Calculate Moles of Methane:
Since the mole ratio of CH\(_4\) to CO\(_2\) is 1:1, the number of moles of methane required is the same as the number of moles of carbon dioxide produced. \[ \text{moles of CH}_4 = \text{moles of CO}_2 = 0.25 \text{ mol} \] Step 4: Final Answer:
0.25 moles of methane are required.