Library / Foundations: Chemistry / FCH-28
Foundations: Chemistry
Partial pressure from mole fraction
Pressure contributed by one gas in a mixture: its mole fraction multiplied by the total pressure.
- Ref
- FCH-28
- Rev
- v1
- Field
- Foundations: Chemistry
- Result
- pi [bar]
Dalton’s law says each gas in a mixture exerts the pressure it would if it were alone, and these partial pressures add up to the total pressure. The partial pressure of component i is its mole fraction times the total pressure: pi = yi ptotal. For ideal gases the mole fraction equals the volume fraction.
Pressure contributed by one gas in a mixture: its mole fraction multiplied by the total pressure. The partial pressures add up to the total.
Calculator
- Partial pressure in kPa21.27 kPa
- Pressure of everything else, ptotal − pi0.8003 bar
- Share of the total pressure21 %
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Oxygen at a mole fraction of 0.21 in air at 1.013 bar has a partial pressure of 0.2127 bar (21.27 kPa), the pressure that governs how much a breather can absorb.
- A rise in the total pressure raises it in proportion: at 3.04 bar the same mixture would give 0.638 bar of oxygen. Divers keep the oxygen partial pressure below about 1.4 bar, which is why the mix is changed with depth.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (bar) | Local step | Change in result |
|---|---|---|---|---|---|---|
| ptotal Total pressure | 0.1 to 100 bar | 0.021 | 21 | 20.98 | +10% | +10 % |
| yi Mole fraction of the gas | 0.001 to 1 | 0.001013 | 1.013 | 1.012 | +10% | +10 % |
Sweep of Total pressure
| Total pressure (bar) | Partial pressure (bar) |
|---|---|
| 0.1 | 0.021 |
| 0.2371 | 0.0498 |
| 0.5623 | 0.1181 |
| 1.334 | 0.28 |
| 3.162 | 0.6641 |
| 7.499 | 1.575 |
| 17.78 | 3.734 |
| 42.17 | 8.856 |
| 100 | 21 |
Sweep one variable
Variables and how each one contributes
Partial pressure
What the equation gives you. Everything else feeds it.
Mole fraction of the gas
The mole fraction of the component, between 0 and 1 (for example 0.21 for oxygen in air). Raises the partial pressure in direct proportion. Raising it by 0.05 (to 0.26) moves the result by +23.8 %, from 0.2127 to 0.2634 bar.
Total pressure
The total pressure of the mixture, in bar. Raises the partial pressure in direct proportion, for the same composition. Raising it by 0.5 bar (to 1.513 bar) moves the result by +49.4 %, from 0.2127 to 0.3177 bar.
Worked example with the values above
- Mole fraction: y = 0.21. Total pressure: p = 1.013 bar.
- Multiply: 0.21 × 1.013.
- pi = 0.2127 bar.
Assumptions and limits
- An ideal gas mixture, in which mole fractions equal volume fractions.
- The total pressure is the sum of all the partial pressures.
Common mistakes
- Using the mass fraction instead of the mole fraction.
- Forgetting that the mole fraction is on a wet or dry basis: water vapour counts if present.
Statistics and uncertainty
The partial pressure carries the relative error of both inputs: a 2 % error in the composition and a 1 % error in the pressure give a result with about a 2.2 % error. Composition by volume from an analyser is usually the larger uncertainty.
Where it is used
- Input to equilibrium constants Kp and to combustion calculations.
- Oxygen and carbon dioxide levels in confined spaces, diving and altitude.
Maths you need
- Mole fraction: moles of one gas divided by total moles
- Dalton’s law: partial pressures add to the total