Question

3.68 g of hydrogen at 17°C occupies the same volume as 58.0 g of another gas X at 95°C. The molar mass of gas X is (g mol\(^{-1}\)):

• A. 20
• B. 40
• C. 44
• D. 56

Hint:

For equal volumes at different temperatures, use \(nT = \text{constant}\) when pressure is constant.

Answer 1

The Correct Option is B

Step 1: Equal volume gas relation.
At same pressure, n₁T₁ = n₂T₂ for identical volumes.

Step 2: Moles of hydrogen.
n(H₂) = 3.68 g / 2 g/mol = 1.84 mol.

Step 3: Kelvin temperatures.
T₁ = 17 + 273 = 290 K; T₂ = 95 + 273 = 368 K.

Step 4: Determining moles of gas X.
n₂ = n₁T₁/T₂ = 1.84×290/368 ≈ 1.45 mol.

Step 5: Molar mass calculation.
M = mass/moles = 58.0/1.45 ≈ 40 g/mol.

Step 6: Conclusion.
The molar mass of gas X is 40 g/mol.