Question 3 of 9intermediate🔧 ApplyNumerical3 marks

An oxygen cylinder of volume 30 litre has an initial gauge pressure of 15 atm and a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm and its temperature drops to 17 °C. Estimate the mass of oxygen taken out of the cylinder (R = 8.31 J mol⁻¹ K⁻¹, molecular mass of O₂ = 32 u).

Correct Answer

The mass of oxygen taken out of the cylinder is approximately 0.14 kg (or 140 g).

Exercise: EXERCISES | Q: 12.4
For More Understanding

Explanation

This problem applies the ideal gas equation PV = nRT to find the number of moles before and after gas withdrawal. The key insight is that gauge pressure must be converted to absolute pressure by adding atmospheric pressure (1 atm). The difference in moles multiplied by molecular mass gives the mass withdrawn.

Solution Steps

  1. Step 1: Convert given values to SI units Volume, V = 30 litre = 30×1030 \times 10⁻³ m³ = 0.03 m³ Initial temperature, T₁ = 27 °C = 27 + 273 = 300 K Final temperature, T₂ = 17 °C = 17 + 273 = 290 K Molecular mass of O₂, M = 32 g/mol = 0.032 kg/mol

  2. Step 2: Convert gauge pressure to absolute pressure Initial absolute pressure, P₁ = 15 + 1 = 16 atm = 16×1.0116 \times 1.01 × 10⁵ Pa Final absolute pressure, P₂ = 11 + 1 = 12 atm = 12×1.0112 \times 1.01 × 10⁵ Pa

  3. Step 3: Calculate initial number of moles using PV = nRT n₁ = P₁V/(RT₁) = (16×1.0116 \times 1.01 × 10⁵ × 30×1030 \times 10⁻³)/(8.31×3008.31 \times 300) n₁ = 19.45 mol

  4. Step 4: Calculate final number of moles n₂ = P₂V/(RT₂) = (12×1.0112 \times 1.01 × 10⁵ × 30×1030 \times 10⁻³)/(8.31×2908.31 \times 290) n₂ = 15.09 mol

  5. Step 5: Calculate mass of oxygen withdrawn Number of moles withdrawn, Δn = n₁ - n₂ = 19.45 - 15.09 = 4.36 mol Mass withdrawn = Δn × M = 4.36×324.36 \times 32 = 139.5 g ≈\approx 0.14 kg

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