A 30 L oxygen cylinder initially contains 18.20 mol of O₂. After some gas is withdrawn, its gauge pressure is 11 atm at 27°C. Calculate the mass withdrawn. Take R = 100/12 J·mol⁻¹·K⁻¹, M(O₂) = 32 g/mol, and 1 atm = 1.01 × 10⁵ Pa.
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Question

A 30 L oxygen cylinder initially contains 18.20 mol of O₂. After some gas is withdrawn, its gauge pressure is 11 atm at 27°C. Calculate the mass withdrawn. Take R = 100/12 J·mol⁻¹·K⁻¹, M(O₂) = 32 g/mol, and 1 atm = 1.01 × 10⁵ Pa.

Options

G1 Physics · Accepted Answer

Step 1: Absolute pressure = gauge pressure + atmospheric pressure = 11 + 1 = 12 atm. Step 2: Convert units: V = 30 × 10⁻³ m³, T = 27 + 273 = 300 K, P = 12 × 1.01 × 10⁵ Pa. Step 3: Use PV = nRT. Remaining moles: n𝒇 = PV/(RT) = [12 × 1.01 × 10⁵ × 0.030]/[(100/12) × 300] = 14.544 mol. Step 4: Moles removed = 18.20 − 14.544 = 3.656 mol. Step 5: Mass removed = 3.656 × 32 g = 116.992 g ≈ 0.117 kg (source rounds to 0.116 kg). Final answer: Nearest listed value 0.116 kg, Option C.