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: Formula
Number of moles ($n$) $= \frac{\text{Mass}}{\text{Molar Mass}}$. Ratio of molecules is the same as the ratio of moles.
Step 2: Moles Calculation
Let mass of $\text{O}_2 = 1 \text{ g}$ and mass of $\text{CH}_4 = 4 \text{ g}$.
Molar mass: $\text{O}_2 = 32$, $\text{CH}_4 = 16$.
$n_{\text{O}_2} = \frac{1}{32}$
$n_{\text{CH}_4} = \frac{4}{16} = \frac{1}{4}$
Step 3: Ratio
Ratio $= \frac{1}{32} : \frac{1}{4} = \frac{1}{32} \times 4 = \frac{1}{8}$
Final Answer: (C)