Each gas does its own share
When gases mix without reacting, each one behaves as if it were alone in the container. John Dalton noticed this in 1801 while studying the atmosphere: the total pressure of a mixture is simply the sum of the pressures of its parts. This idea is used in chemistry labs, diving, anesthesia, mountaineering and the study of breathing.
Dalton’s law
P_total = P₁ + P₂ + P₃ + …
and each partial pressure equals the mole fraction of that gas times the total pressure:
Pᵢ = xᵢ × P_total, where xᵢ = nᵢ ÷ n_total
Because only proportions matter, you can describe the mixture in moles, in percent by volume or in any consistent amounts.
Example: dry air at sea level
Using 78% nitrogen, 21% oxygen and 1% argon at 1 atm:
- Nitrogen: 0.78 atm (593 mmHg)
- Oxygen: 0.21 atm (160 mmHg)
- Argon: 0.01 atm (7.6 mmHg)
At the summit of a high mountain, the oxygen percentage is the same, but the total pressure is lower, so each breath delivers less oxygen.
Gas collected over water
In school labs, gases such as hydrogen or oxygen are often collected by displacing water in an inverted bottle. The gas inside is saturated with water vapor, so:
P_dry gas = P_total − P_water vapor
Water vapor pressure depends only on temperature: about 17.5 mmHg at 68 °F (20 °C), 23.8 mmHg at 77 °F (25 °C) and 760 mmHg at the boiling point. The calculator estimates it with the Antoine equation, valid from 1 to 100 °C.
If the barometer reads 1 atm and the water is at 25 °C, the dry gas pressure is 1 − 0.031 = 0.969 atm. Use this value in the ideal gas law to find the moles of gas collected.
Why it matters for breathing and diving
- Diving: at 33 ft (10 m) underwater, the total pressure doubles to 2 atm, and so does the oxygen partial pressure. Above about 1.4 to 1.6 atm of oxygen, the risk of oxygen toxicity rises, which limits how deep each gas mix can be used.
- Medicine: arterial blood gases report the partial pressures of oxygen and carbon dioxide, not percentages.
- Altitude: aircraft cabins are pressurized to the equivalent of 6,000 to 8,000 ft to keep the oxygen partial pressure comfortable for passengers.
Limits
Dalton’s law assumes ideal gases. At very high pressures, or with gases that interact strongly, such as ammonia and water vapor, real partial pressures differ slightly.