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A cylinder contains hydrogen gas at pressure of 249 kPa and temperature 27°C. Its density is : (R = 8.3 J mol⁻¹ K⁻¹)

1. 0.2 kg/m³
2. 0.1 kg/m³
3. 0.02 kg/m³
4. 0.5 kg/m³

Correct answer: 0.2 kg/m³

Solution

Using the ideal gas equation, PV = nRT, and substituting n = m/M (where m is mass, M is molar mass), we derive the density formula: ρ = PM/RT. Substituting P = 249000 Pa, M = 2 g/mol = 0.002 kg/mol, R = 8.3 J/mol·K, and T = 300 K, we get ρ = (249000 × 0.002) / (8.3 × 300) = 0.2 kg/m³.

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