Partial Pressure from Mole Fraction

John Dalton realised in 1801 that gas molecules in a mixture ignore one another: each exerts the pressure it would exert alone, and the total is their sum. Divide through by the total and you get the form everyone actually uses — a component's partial pressure is its mole fraction times the total pressure. Dry air is 20.9% oxygen by mole, so at 101.325 kPa the oxygen partial pressure is 0.209 × 101.325 = 21.2 kPa, and that number, not the percentage, is what drives oxygen across the alveolar membrane.

This is why altitude matters and composition does not: the air on top of Everest is still 20.9% oxygen, but at 33 kPa total pressure the oxygen partial pressure falls to about 7 kPa, roughly a third of sea-level value. Divers meet the same arithmetic in reverse — at 40 m the ambient pressure is 5 atm, so ordinary air delivers an oxygen partial pressure above 1 atm and a nitrogen partial pressure near 4 atm, which is where oxygen toxicity and nitrogen narcosis begin. The trap is mixing up mole fraction with mass fraction or volume percent; only mole fraction goes into this equation, though for ideal gases volume percent happens to equal it.