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

G1 Physics · Accepted Answer

Step 1: Start with PV = nRT and n = m/M. Step 2: Therefore P = (m/V)(RT/M) = ρRT/M, giving ρ = PM/(RT). Step 3: For hydrogen H₂, M = 2 × 10⁻³ kg mol⁻¹; T = 27 + 273 = 300 K; P = 249 × 10³ Pa. Step 4: ρ = (249 × 10³ × 2 × 10⁻³)/(8.3 × 300) = 498/2490 = 0.20 kg m⁻³. Final answer: (B) 0.2 kg m⁻³.