Given :
- Oxygen cylinder volume = 30 liters
- Initial gauge pressure = 15 atm
- Temperature = 27°C
- After the withdrawal of oxygen gauge pressure = 11 atm
- Temperature = 17°C .
- R = 8.31 Jmol⁻¹K⁻¹
- The molecular mass of O2 = 32 u
To Find :
- Estimate the mass of oxygen taken out of the cylinder.
Solution :
The volume of oxygen, V1 = 30 liters = 30×10⁻³ m³
Gauge pressure, P₁ = 15 atm = 15×1.013×10₅ Pa
Temperature, T₁ = 27°C = 300K
Universal gas constant, R = 8.314 Jmol⁻¹K⁻¹
Let the initial number of moles of oxygen gas in the cylinder be n₁.
The gas equation is given as:
P₁ V₁ = n₁ RT₁
∴n₁ = P₁ V₁ /RT₁ = (15.195×10⁵х 30× 10⁻³) /(8.314×300) = 18.276
But n₁ = m₁ /M
Where,
m₁ = Initial mass of oxygen
M = Molecular mass of oxygen = 32 g
∴ m₁ = N₁ M = 18.276×32 = 584.84g
After some oxygen is withdrawn from the cylinder, the pressure and temperature reduce.
Volume, V₂ = 30 litres = 30 × 10⁻³m³
Gauge pressure, P₂ = 11 atm = 11×1.013×10⁵ Pa
Temperature, T₂ = 17°C = 290K
Let n₂ be the number of moles of oxygen left in the cylinder.
The gas equation is given as:
P₂V₂ = n₂RT₂
∴ n₂ = P₂V₂ /RT₂
= (11.143 ×10₅ ×30×10⁻³⁰ ) /(8.314×290) = 13.86
But n₂ = m₂ /M
Where,
m₂ is the mass of oxygen remaining in the cylinder
∴m₂ = n₂×M = 13.86×32 = 453.1g
The mass of oxygen taken out of the cylinder is given by the relation:
The initial mass of oxygen in the cylinder – The final mass of oxygen in the cylinder
= m₁−m₂
= 584.84g–453.1g
= 131.74g
= 0.131kg
Therefore, 0.131 kg of oxygen is taken out of the cylinder.
