Dalton's law: each gas contributes its share of the total pressure
A gas mixture's total pressure is split among its gases in proportion to how many molecules of each are present. Multiply a gas's mole fraction (its share of the molecules, 0 to 1) by the total pressure to get its partial pressure. The partial pressures always add back up to the total.
What each gas in dry air pushes at sea level
At 1 atm (760 mmHg), air breaks down like this. The partial pressure column is simply each fraction times 760 mmHg.
| Gas | Mole fraction | Partial pressure (atm) | mmHg |
|---|---|---|---|
| Nitrogen (N₂) | 0.7809 | 0.781 atm | 593.7 |
| Oxygen (O₂) | 0.2095 | 0.209 atm | 159.2 |
| Argon (Ar) | 0.0093 | 0.0093 atm | 7.1 |
| Carbon dioxide (CO₂) | 0.0004 | 0.0004 atm | 0.3 |
1 atm = 101.325 kPa = 760 mmHg = 1.013 bar = 14.7 psi, so you can read the answer in whatever unit the problem uses.
The two things people mix up
- Mole fraction is not partial pressure. Oxygen's fraction is 0.21 anywhere; its partial pressure is 0.21 atm only when total pressure is 1 atm. Change the total and the pressure changes with it.
- Add pressures, not fractions blindly. Total pressure is the sum of every partial pressure. If a two-gas mix is 32% oxygen, the rest (68%) is the other gas, and each partial pressure is its fraction times the total.
- The ideal-gas route needs kelvin. If you compute a partial pressure from moles, volume and temperature using PV = nRT, temperature must be in kelvin. 25°C is 298 K, not 25 K.
Common questions
How do you calculate the partial pressure of a gas?
Multiply the gas's mole fraction by the total pressure of the mixture. For oxygen in air at 1 atm: 0.21 times 1 atm is 0.21 atm, which is about 160 mmHg.
What is the difference between mole fraction and partial pressure?
Mole fraction is just the share of molecules that are that gas, a number between 0 and 1 with no units. Partial pressure is what that gas alone would push against the container walls. They are linked by partial pressure equals mole fraction times total pressure.
Why does partial pressure of oxygen drop at altitude?
The fraction of oxygen in air stays at about 21% everywhere, but total pressure falls as you climb. Since partial pressure is the fraction times the total, less total pressure means less oxygen pressure. On Everest total pressure is about a third of sea level, so oxygen pressure drops with it.
