A gas at 2.5 atm and 500 K has a density of 0.96 kg m⁻³. What is its molecular mass? (R = 8.31 J mol⁻¹ K⁻¹, 1 atm = 1.01
**Ideal gas law** P V = n R T governs gas laws, at constant pressure V ∝ T, so temperature increase 300 K→600 K doubles volume 24→48 L. Charles' law quantitative prediction V₂ = V₁×(T₂/T₁), illustrating direct proportionality, absolute temperature must be in kelvin. P = (ρ R T)/(M), M = (ρ R T)/(P).P = 2.5 × 1.01 × 10⁵ = 2.525 × 10⁵ Pa.M = (0.96 × 8.31 × 500)/(2.525 × 10⁵) = 0.0158 kg/mol ≈ 15.8 g/mol ≈ 16 g/mol. Substituting values gives 16 g/mol, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²), ideal gas
Ref: NCERT > Physics Book > Behaviour of Perfect Gas and Kinetic Theory > Gas Laws and Volume-Temperature Relations