Question

300 mL of a gas \(X\) of molar mass \(32\ \text{g mol}^{-1}\) is effused in 25 seconds. What volume of methane would effuse in the same time?

• A. 624 mL
• B. 524 mL
• C. 32 mL
• D. 424 mL

Hint:

According to Graham's law, the rate of effusion is inversely proportional to the square root of molar mass: \[ r\propto \frac{1}{\sqrt{M}} \] Lighter gases effuse faster than heavier gases.

Answer 1

The Correct Option is D

Step 1: Apply Graham's law inversely for volume.
At constant time, V ∝ 1/√M. So V_CH₄/V_X = √(M_X/M_CH₄) = √(32/16) = √2. V_CH₄ = 300 × 1.414 ≈ 424 mL.

Step 2: Final Answer:
≈ 424 mL (option 4).