Dalton's Law of Partial Pressures Calculator

Dalton’s Law of Partial Pressures says that in a mixture of non-reacting gases, the total pressure is just the sum of the pressures each gas would exert if it were alone in the same volume at the same temperature.

The formula:

P_total = P₁ + P₂ + P₃ + … + Pₙ

Mole fraction of each gas:

xᵢ = Pᵢ / P_total

This is the fraction of total moles contributed by gas i. Equivalently, Pᵢ = xᵢ × P_total.

John Dalton published this in 1801, working from the same atomic theory that he was building at the time. It works because ideal-gas molecules do not interact with each other — each gas behaves as though the others were not there.

Why this matters in everyday life:

Scuba diving and gas blending. Compressed-air tanks are about 21% O₂ and 79% N₂ at the surface. At 30 m depth the total pressure is roughly 4 atm, so the partial pressure of O₂ is 4 × 0.21 = 0.84 atm. Above about 1.4 atm partial-pressure O₂, oxygen toxicity becomes a real hazard, which is why tech divers use trimix (helium replaces some N₂) and watch their gas blend carefully.

Altitude and the lungs. At sea level, total atmospheric pressure is about 101.3 kPa, so the partial pressure of O₂ in air is 0.21 × 101.3 ≈ 21.3 kPa. On Everest’s summit, total pressure is around 33 kPa, dropping O₂ partial pressure to about 7 kPa. Hemoglobin has trouble loading oxygen below about 8 kPa partial pressure, which is why supplemental oxygen is needed above ~7,500 m.

Lab gas collection over water. When you collect a gas over water, the bubble contains both your target gas and water vapor. The total pressure equals the atmospheric pressure (because the water level inside the inverted tube equals the level outside). To find the dry-gas pressure you subtract the water-vapor pressure at that temperature, which you can look up in a table.

Worked example: A tank contains nitrogen at 250 kPa and oxygen at 150 kPa.

P_total = 250 + 150 = 400 kPa x(N₂) = 250 / 400 = 0.625 = 62.5% x(O₂) = 150 / 400 = 0.375 = 37.5%

Worked example, lab gas collection: You collect hydrogen over water at 25°C. The barometer reads 101.3 kPa. The vapor pressure of water at 25°C is 3.17 kPa. What is the partial pressure of the dry hydrogen?

P(H₂) = P_total − P(H₂O) = 101.3 − 3.17 = 98.13 kPa

Where it breaks down: Dalton’s Law assumes ideal-gas behavior — no intermolecular forces, no reactions between components. At high pressure (hundreds of atm) or near a gas’s critical temperature, real-gas corrections matter and you would use the van der Waals equation or a real-gas mixture model instead. For ordinary lab and atmospheric conditions, Dalton’s Law is accurate to better than 1%.

Pressure unit reference:

• 1 atm = 101.325 kPa = 760 mmHg = 14.696 psi = 101,325 Pa
• 1 bar = 100 kPa = 0.987 atm (close enough to atm for casual conversions)
• Standard atmospheric pressure (sea level): 101.325 kPa
• Standard scuba tank: 200 bar (= 200 × 100 kPa = 20,000 kPa = ~2,940 psi)