This Dalton’s law calculator handles partial pressures in gas mixtures both ways: from mole fractions and total pressure to each gas’s partial pressure — and by adding partial pressures back to the total.
The Law of Shared Containers
P_total = P₁ + P₂ + P₃ + …, and each partial pressure is the gas’s mole fraction of the total: Pᵢ = xᵢ × P_total. The deep reason is the Ideal Gas Law: at fixed V and T, pressure counts molecules regardless of species, so each population contributes its own count’s worth. Partial pressure — not concentration, not percentage — is what drives gases into liquids and lungs (Henry’s law, alveolar exchange), which is why divers and anesthesiologists think in partial pressures natively. Part of our Chemistry Calculators collection.
Worked Example (Verified)
A 5.00 atm mixture holding 2 mol N₂, 1 mol O₂, 1 mol Ar (4 mol total):
- Mole fractions: N₂ 0.500, O₂ 0.250, Ar 0.250
- Partial pressures: N₂ 2.50 atm, O₂ 1.25 atm, Ar 1.25 atm — summing back to 5.00 atm exactly
- Air at sea level is the same math at 1 atm: N₂ ≈ 0.78 atm, O₂ ≈ 0.21 atm (the physiologically operative number), water vapor and argon sharing the rest
- Collected over water: the classic lab correction — gas gathered in a wet bottle includes water vapor’s partial pressure (~0.031 atm at 25 °C), which you subtract before claiming the gas’s own pressure
Where Dalton Meets the Real World
- Diving: at 40 m depth (≈5 atm total), air’s oxygen partial pressure is ~1.05 atm — nearing toxicity thresholds, which is why deep divers dilute oxygen with helium (trimix) calculated in partial pressures.
- Altitude: total pressure falls, and with it P_O₂ — at 5,500 m it’s half the sea-level value; acclimatization is physiology negotiating with Dalton.
- Anesthesia and respirators dose gases by partial pressure because that’s what equilibrates with blood.
Related Tools
- Ideal Gas Law Calculator — the single-gas foundation
- Combined Gas Law Calculator — P, V, T changes
- Chemistry Calculators — the full collection
Frequently Asked Questions
What is Dalton’s law in simple terms?
In a mixture, the total pressure equals the sum of each gas’s partial pressure, and each gas’s share equals its mole fraction of the whole: Pᵢ = (nᵢ/n_total) × P_total.
How do you calculate mole fraction?
Moles of the one gas ÷ total moles of all gases. 2 mol in a 4 mol mixture is x = 0.500 — unitless, and the three mole fractions always sum to exactly 1.
Why does partial pressure matter more than percentage?
Because physical and biological exchanges — dissolving, diffusing, binding hemoglobin — respond to the partial pressure gradient, and the same 21% oxygen is generous at sea level (0.21 atm) and inadequate on Everest (about 0.07 atm). Percentages describe the mix; partial pressures describe the effect.
How do you correct for water vapor when collecting gas?
Subtract water’s vapor pressure at the collection temperature from the total: P_gas = P_total − P_H₂O (0.0313 atm at 25 °C; look up the table value for your temperature). The collected “gas” is always a Dalton mixture.
Does Dalton’s law hold for real gases?
Well at ordinary pressures — it’s exact for ideal gases and a good approximation until high pressures or near-condensation conditions make intermolecular forces matter, where fugacity corrections take over in serious engineering.
Is this Dalton’s law calculator free?
Yes — free, instant, no sign-up.