Oxygen cylinder duration for an overnight ventilator
A rural clinic in Shan State keeps a 40.0 L oxygen cylinder for a ventilator. The cylinder gauge reads 150 atm at 30°C. The ventilator consumes 6.0 L of oxygen per minute measured at 1.0 atm and 30°C. The clinic's safety rule says the cylinder must be replaced when the absolute pressure falls to 3.0 atm, because the regulator becomes unreliable below that. The clinic needs to support one patient overnight for 14 hours. A nurse calculates that 40 L × 150 = 6000 L, so at 6 L min⁻¹ the cylinder will last 1000 min (16.7 h) and concludes it is sufficient. The nurse has not subtracted the unusable residual gas. The cylinder is stored in a warm room, and the flow meter is calibrated at 1 atm.
1. Calculate the usable volume of oxygen at 1 atm and the duration at 6.0 L min⁻¹. Decide whether one cylinder is sufficient for 14 hours.
Read the worked answer
The gas that can be used is the gas above the safety residual pressure:
P_usable = 150 − 3 = 147 atm.
At constant temperature, P₁V₁ = P₂V₂, so usable volume at 1 atm is
V = 147 × 40.0 = 5880 L.
At 6.0 L min⁻¹: t = 5880 / 6.0 = 980 min = 16.3 h.
This is just enough for 14 h, with about 2.3 h margin. The nurse's 16.7 h value is slightly too optimistic because it ignores the 3 atm residual gas. One cylinder is sufficient only if the flow remains at 6.0 L min⁻¹ and there is no leak or extra use.
2. If the ventilator is instead set to 8.0 L min⁻¹, determine whether the cylinder lasts 14 hours and state a practical recommendation.
Read the worked answer
At 8.0 L min⁻¹: t = 5880 / 8.0 = 735 min = 12.25 h.
This is less than 14 h, so one cylinder would run out before the night is over. The clinic should arrange a second full cylinder, reduce the flow if clinically acceptable, or plan a cylinder changeover with a reliable alarm. The calculation must use usable volume, not the full 6000 L, because the regulator must not be run below 3 atm.
3. Explain why the cylinder pressure falls as oxygen is used and why the clinic should not use the cylinder below 3 atm.
Read the worked answer
At constant volume and temperature, pressure is proportional to the number of moles of gas (P = nRT/V). As oxygen leaves the cylinder, n decreases, so the pressure falls.
Below 3 atm the regulator may not deliver a stable flow, and the remaining gas is difficult to use safely. A residual pressure also helps prevent contamination or ingress of air into the cylinder. The safety rule is therefore a practical control, not a suggestion that the last 3 atm contain no oxygen.