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No air to breathe

Air and fluids · level 4, lesson 4 of 6

A question to start

Climbers on Mount Everest often carry bottled oxygen, even though a fifth of the air there is still oxygen. If that is too little, how much oxygen is there to breathe on Mars?

The idea

What your lungs care about is how hard the oxygen alone pushes. Each gas in a mixture pushes with its share of the total pressure:

\[\text{oxygen's push} = \text{oxygen's share} \times \text{total pressure}.\]

Scientists call this the partial pressure of oxygen.

Oxygen's push Mars Earth, sea level
Total pressure 636 Pa 101,400 Pa
Oxygen's share 0.16% 20.95%
Oxygen's push about 1 Pa about 21,200 Pa

On the top of Everest, oxygen's push is about \(0.21 \times 33{,}000 \approx 6{,}900\) Pa, a third of sea level. On Mars it is about 1 Pa: about 21,000 times less than at sea level.

sea levelEverestMarsabout 1 Pa

Worked examples

1. Sea level. \(0.2095 \times 101{,}400 \approx 21{,}200\) Pa.

2. Mars. \(0.0016 \times 636 \approx 1.0\) Pa.

3. How many times less? \(21{,}200 \div 1.0 \approx 21{,}000\) times.

Try it

  1. What is the partial pressure of a gas?
  2. Find oxygen's push in air at 50,000 Pa that is 21% oxygen.
  3. In a Mars base, the air is at 70,000 Pa and 30% oxygen. Find oxygen's push. Is it more or less than at sea level?
  4. Why could a person not breathe Mars air, even with a pump to squeeze it?
Answers
  1. The push of that gas alone: its share times the total pressure.
  2. \(0.21 \times 50{,}000 = 10{,}500\) Pa.
  3. \(0.30 \times 70{,}000 = 21{,}000\) Pa, about the same as at sea level.
  4. Squeezed up to Earth pressure, it would still be 95% carbon dioxide and only 0.16% oxygen. The oxygen would first have to be made, by splitting the carbon dioxide.

Common mistake

"If the air is a fifth oxygen, there is plenty." It depends on the total pressure too. On Everest the share is the same as at sea level, but the push is a third.

Where it leads