Dalton's Law of Partial Pressures Explained with Air
By Tools Star Hub Editorial Team · Published
Quick answer: Dalton's law of partial pressures says the total pressure of a mixture of non-reacting gases equals the sum of the pressures each gas would exert on its own, P(total) = P₁ + P₂ + …. Each gas's share is its mole fraction times the total, Pᵢ = Xᵢ × P(total). Dry air is about 21% oxygen, so at 1 atm the oxygen partial pressure is 0.21 × 1 = 0.21 atm. The Partial Pressure Calculator gives that result with a mole fraction of 0.21 and a total of 1 atm.
Dalton's law connects what you can measure, the total pressure, with what often matters, the pressure of one gas. It is used in chemistry problems about collecting gases, in breathing and diving gas calculations and in any mixture where you need the contribution of one component. Our step-by-step calculator guide covers each mode; this article explains the law itself and how to reason with it.
What does Dalton's law actually say?
OpenStax Chemistry 2e states that the total pressure of a mixture of ideal gases equals the sum of the partial pressures of the component gases. A partial pressure is the pressure one gas would exert if it alone filled the same container at the same temperature.
In an ideal gas, molecules are treated as far apart with no attraction between them, so each gas behaves independently. Doubling the number of molecules of one gas doubles its contribution to the pressure, regardless of what else is in the container.
Why does mole fraction give the partial pressure?
At a fixed volume and temperature, pressure is proportional to the number of moles of gas. If oxygen makes up 21 of every 100 moles of gas, it supplies 21% of the collisions with the walls and so 21% of the pressure. That is why Pᵢ = Xᵢ × P(total), where Xᵢ is moles of gas i divided by total moles.
A mole fraction is a number between 0 and 1. The calculator rejects values above 1 and tells you to divide a percentage by 100 first, so 21% must be entered as 0.21.
How does Dalton's law work for air?
Treat dry air as about 78% nitrogen, 21% oxygen and 1% argon by moles, a common textbook simplification. At standard atmospheric pressure, 101.325 kPa, the calculator's gas mixture mode with those amounts gives nitrogen 79.0335 kPa, oxygen 21.27825 kPa and argon 1.01325 kPa.
Add the three and you get 101.325 kPa back, exactly as the law predicts. In the total-from-partials mode, entering 0.78, 0.21 and 0.01 atm likewise returns a total of 1 atm.
| Gas | Mole fraction | Partial pressure (kPa) |
|---|---|---|
| Nitrogen | 0.78 | 79.0335 |
| Oxygen | 0.21 | 21.27825 |
| Argon | 0.01 | 1.01325 |
| Total | 1.00 | 101.325 |
What happens when the total pressure changes?
The fractions stay the same but every partial pressure scales with the total. If the same air mixture is compressed to 2 atm, oxygen's partial pressure doubles to 0.42 atm. If the total falls to 0.5 atm, oxygen drops to 0.105 atm, even though air is still 21% oxygen.
This is why the share of a gas and its partial pressure are different ideas. The percentage tells you the mixture; the partial pressure tells you how strongly that gas acts, which is what matters for breathing, reactions and dissolving gases.
How is Dalton's law used when collecting gas over water?
OpenStax describes a common laboratory method: a gas is collected by bubbling it into an inverted container of water. The collected gas is mixed with water vapour, so the measured total pressure is the gas plus the vapour pressure of water at that temperature.
To find the pressure of the dry gas, subtract water's vapour pressure from the total. Use the vapour pressure value from your textbook table for the measured temperature, then use the calculator's total-from-partials or mole fraction modes to check the arithmetic.
When does Dalton's law not hold well?
The law assumes ideal behaviour and gases that do not react with each other. At high pressures or low temperatures, real gas molecules attract each other and take up space, so the sum of partial pressures can differ from the measured total.
If gases react, the number of moles changes, so use the amounts after the reaction. For ordinary classroom conditions near atmospheric pressure, Dalton's law is accurate enough for most problems.
Which units should I use?
Any pressure unit works, as long as every value uses the same one. The calculator supports atm, kPa, Pa, bar and mmHg, and in most modes it shows the result in all of them. 1 atm is 101.325 kPa or 760 mmHg, so the oxygen partial pressure in air at 1 atm is about 159.6 mmHg.
Mixing units is a common error: adding 0.78 atm to 21 kPa gives nonsense. Convert first, or let the calculator handle units for you.
What mistakes do students make with Dalton's law?
The most common is using a percentage instead of a fraction, for example 21 instead of 0.21, which makes a partial pressure larger than the total. Another is using mass fractions instead of mole fractions; you must convert grams to moles before working out fractions.
A third is forgetting that the law applies to the gas phase only. Liquids and solids in the container do not contribute, apart from the vapour they produce.
Where does Dalton's law come from?
The law is named after John Dalton, the English chemist best known for his atomic theory. It follows naturally from the idea that gas particles are tiny and far apart, so the pressure from one kind of particle does not depend on the others.
Today it is taught alongside the ideal gas law, PV = nRT. Because each gas obeys that law separately, adding their pressures in the same volume and temperature gives the total, which is Dalton's law in one line.
How does the ideal gas mode relate to Dalton's law?
The calculator's ideal gas mode finds the pressure of one gas from its amount, temperature and volume, P = nRT/V. If you run it once for each gas in the same container at the same temperature and volume, the results are the partial pressures, and their sum is the total.
This gives a second way to check homework answers. Find each partial pressure from moles with the ideal gas mode, then add them in the total-from-partials mode and compare with the total you expected.
What is a quick way to check my answer?
Two checks catch most errors. First, every partial pressure must be smaller than the total. Second, the partial pressures must add up to the total, within rounding. If either check fails, look for a percentage typed as a whole number, a unit mismatch or a missing gas.
The calculator's Steps panel shows the working for each result, so you can compare it line by line with your own method.
How do I apply Dalton's law step by step?
- List the gases. Write each gas and its amount in moles, or its mole fraction.
- Find mole fractions. Divide each amount by the total moles; fractions must add to 1.
- Multiply by the total. Pᵢ = Xᵢ × P(total) for each gas.
- Check the sum. The partial pressures should add up to the total.
- Verify in the calculator. Use the gas mixture or mole fraction mode to confirm your numbers.
Example
Oxygen in air at 1 atm
X = 0.21, P(total) = 1 atm, so P(O₂) = 0.21 atm.
Air at 101.325 kPa
Nitrogen 79.0335, oxygen 21.27825 and argon 1.01325 kPa, summing to 101.325 kPa.
Compressed air
At 2 atm total, oxygen's partial pressure is 0.42 atm.
What should I keep in mind?
Ideal gases
The law is exact only for ideal, non-reacting gases.
Dry versus humid air
Water vapour takes part of the total pressure in humid air.
Fractions
Enter 0.21, not 21, for 21%.
FAQ
- What is Dalton's law of partial pressures?
- The total pressure of a gas mixture equals the sum of the partial pressures of its gases.
- What is the formula?
- P(total) = P₁ + P₂ + …, and each Pᵢ = Xᵢ × P(total).
- What is the partial pressure of oxygen at 1 atm?
- About 0.21 atm, or roughly 159.6 mmHg, for dry air.
- Why do I get a partial pressure bigger than the total?
- You probably entered a percentage instead of a fraction.
- Is Dalton's law exact for real gases?
- Approximately; it is most accurate at low pressures and moderate temperatures.
- Can I use mass fractions?
- No. Convert masses to moles first.
- What if the gases react?
- Use the amounts after the reaction, since moles change.
- How do I handle gas collected over water?
- Subtract the vapour pressure of water at that temperature from the total.
- Which units does the calculator support?
- atm, kPa, Pa, bar and mmHg.
- How is this guide different from the calculator guide?
- This one explains the law; How to Calculate Partial Pressure walks through each calculator mode.
- How does Dalton's law relate to mole fraction?
- For ideal mixtures, each partial pressure equals the mole fraction times the total pressure.
- Can I apply Dalton's law inside a scuba tank?
- Divers use it for planning, but real-gas and temperature effects still matter at high pressure.
- Why subtract water vapor for gases collected over water?
- The vapor contributes its own partial pressure, so dry-gas pressure is total minus vapor pressure.
- Does altitude change oxygen's mole fraction in air?
- Dry air’s mole fraction stays near 21%; partial pressure falls as total atmospheric pressure falls.
- How should lab reports show unit consistency?
- Keep every pressure in the same unit before adding or multiplying by mole fractions.
- What breaks Dalton's law in ammonia absorption?
- When a gas dissolves or reacts strongly, composition and pressure no longer follow a simple ideal sum.
- Is volume percent equal to mole percent here?
- For ideal gases at the same T and P, yes; real gases can deviate.
- Can I find total pressure from known partials?
- Add the partial pressures of all components when Dalton’s assumptions hold.
- How do temperature changes enter the story?
- They can change vapor pressures and real-gas behavior even if mole fractions stay fixed.
- Should students memorize 760 mmHg as 1 atm?
- It is a common conversion; still prefer the unit your problem states explicitly.
Check any gas mixture with the free Partial Pressure Calculator.
Follow each calculator mode in How to Calculate Partial Pressure.
Convert pressures with the Unit Converter.
Turn percentages into fractions with the Percentage Calculator.