The atmospheric pressure on the top of Mt Everest, an altitude of 29,035 ft, is only 259.9 mm Hg. What is the partial pressure of oxygen in the lungs at this altitude (assuming that the % O2 is the same as in dry air, 20.88%)? Report the pressure to the tenths of a mm Hg without units. ÂÂ
The atmospheric pressure on the top of Mt. Everest, an altitude of 29,035 ft, is only 259.9 mm Hg. What is the partial pressure of oxygen in the lungs at this altitude (assuming that the % O2 is the same as in dry air, 20.88%)? Report the pressure to the tenths of a mm Hg without units. ÂÂ
The Correct Answer and Explanation is :
To calculate the partial pressure of oxygen at the top of Mt. Everest, we use the equation:
[
P_{O_2} = (\text{fraction of } O_2) \times (\text{total atmospheric pressure})
]
Given:
- Atmospheric pressure at Everest’s summit = 259.9 mm Hg
- Oxygen percentage in dry air = 20.88% = 0.2088
[
P_{O_2} = 0.2088 \times 259.9
]
[
P_{O_2} \approx 54.3
]
Answer: 54.3
Explanation:
Partial pressure refers to the individual contribution of a specific gas in a mixture to the total pressure. Since oxygen makes up about 20.88% of dry atmospheric air, its partial pressure is determined by multiplying this fraction by the total atmospheric pressure.
At sea level, where atmospheric pressure is 760 mm Hg, the partial pressure of oxygen is:
[
P_{O_2} = 0.2088 \times 760 = 158.8 \text{ mm Hg}
]
However, at high altitudes, the atmospheric pressure drops due to lower air density. At 29,035 feet, the pressure on Everest is 259.9 mm Hg, meaning significantly less oxygen is available. The calculation above shows that the partial pressure of oxygen drops to 54.3 mm Hg, which is about one-third of the sea level value.
This drastic reduction in oxygen availability is why climbers experience hypoxia (oxygen deprivation), leading to altitude sickness, confusion, weakness, and even life-threatening conditions if unacclimatized. This also explains why most climbers use supplemental oxygen to maintain adequate oxygen levels.
The human body compensates by increasing breathing rate (hyperventilation), heart rate, and producing more red blood cells over time. However, immediate exposure to such low oxygen levels can cause severe altitude sickness, leading to impaired judgment, dizziness, and even death if untreated.
This calculation is essential in high-altitude medicine and mountaineering physiology, as it helps predict the risks associated with extreme altitudes and the importance of oxygen supplementation.