Question

A gaseous mixture of O$_2$ and CH$_4$ are in the ratio 1 : 4 by mass. Find the ratio of their molecules.

• A. 1 : 4
• B. 2 : 3
• C. 1 : 8
• D. 3 : 2

Hint:

Mole ratio = Molecule ratio. Divide mass ratio by molar masses to get the answer.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
According to Avogadro's law, the ratio of molecules in gaseous samples is equal to the ratio of their number of moles.
Step 2: Key Formula or Approach:
Number of moles (\(n\)) = \(\frac{\text{Mass}}{\text{Molar mass}}\).
Ratio of molecules = Ratio of moles = \(\frac{n_{\text{O}_2}}{n_{\text{CH}_4}}\).
Step 3: Detailed Explanation:
1. Let mass of \(\text{O}_2 = 1 \text{ g}\) and mass of \(\text{CH}_4 = 4 \text{ g}\).
2. Molar mass of \(\text{O}_2 = 32 \text{ g/mol}\).
3. Molar mass of \(\text{CH}_4 = 16 \text{ g/mol}\).
4. \(n_{\text{O}_2} = \frac{1}{32} \text{ moles}\).
5. \(n_{\text{CH}_4} = \frac{4}{16} = \frac{1}{4} \text{ moles}\).
6. Ratio \(n_{\text{O}_2} : n_{\text{CH}_4} = \frac{1/32}{1/4} = \frac{4}{32} = \frac{1}{8}\).
Step 4: Final Answer:
The ratio of their molecules is 1 : 8.