Question

Equal masses of O₂, H₂ and CH₄ are kept under identical conditions of temperature and pressure. The ratio of the volumes occupied by them is:

• A. 2:16:2
• B. 2:16:1
• C. 1:16:2
• D. 1:1:1

Hint:

For equal mass, moles and hence volume are inversely proportional to molar mass.

Answer 1

The Correct Option is C

Step 1: Under identical conditions of temperature and pressure, the ideal gas equation PV = nRT shows that for fixed P and T, volume is directly proportional to the number of moles, so V is proportional to n.

Step 2: For a fixed mass w of gas, the number of moles is n = w/M, where M is the molar mass. So volume is proportional to w/M, meaning gases with equal mass but different molar mass occupy volumes in inverse proportion to their molar masses.

Step 3: Take a common mass, say w grams, of each gas. Molar masses are O₂ = 32 g/mol, H₂ = 2 g/mol, CH₄ = 16 g/mol. Moles are then w/32, w/2 and w/16 respectively.

Step 4: The ratio of volumes is the same as the ratio of moles: \( \frac{w}{32} : \frac{w}{2} : \frac{w}{16} \). Cancel w and multiply every term by 32 to clear denominators: \( 1 : 16 : 2 \).

Step 5: So the volume ratio of O₂ : H₂ : CH₄ is 1 : 16 : 2, which is option C.