Concept:According to Graham's Law of Diffusion, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
Formula:$$ \frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}} $$
Solution:- Identify the molar masses: \( M_{\text{H}_2} = 2 \text{ g/mol} \) and \( M_{\text{O}_2} = 32 \text{ g/mol} \).
- Set up the ratio comparing Hydrogen (gas 1) to Oxygen (gas 2): \( \frac{r_{\text{H}_2}}{r_{\text{O}_2}} = \sqrt{\frac{M_{\text{O}_2}}{M_{\text{H}_2}}} \).
- Substitute the values: \( \sqrt{\frac{32}{2}} = \sqrt{16} \).
- Calculate the square root: \( \sqrt{16} = 4 \), which translates to a ratio of 4:1.
- This means hydrogen diffuses 4 times faster than oxygen.
Why other options are incorrect:- Option A (2:1): This would only be true if \( M_{\text{O}_2} \) was 8.
- Option B (1:4): This is the inverted ratio (Rate of \( \text{O}_2 \) to Rate of \( \text{H}_2 \)). The question asks for \( \text{H}_2 \) to \( \text{O}_2 \).
- Option C (3:2): Mathematically unrelated to the molar masses 32 and 2.
Quality & Fidelity Assurance:
Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.