Article — Partial Pressure Calculator
Partial pressure calculator: Dalton's law in practice
Partial pressure is the pressure a single gas in a mixture would exert if it occupied the whole volume alone. Dalton's law states P_total = P₁ + P₂ + … + Pₙ, and each component obeys Pᵢ = xᵢ · P_total, where xᵢ is its mole fraction. At sea level, oxygen partial pressure is about 0.21 atm or 160 mmHg.
John Dalton published the law of partial pressures in 1801. He noticed that water vapour could be added to dry air without changing the total pressure beyond what the water alone contributed — the gases behaved independently. That insight underpins everything from clinical blood-gas analysis to scuba diving safety to industrial gas separation.
What is partial pressure?
Partial pressure is a theoretical quantity that simplifies the physics of gas mixtures. Imagine removing every gas except nitrogen from a room — the pressure that nitrogen alone would exert in that same volume is its partial pressure. Dalton's insight was that this theoretical quantity adds up linearly: total pressure of a mixture equals the sum of the partial pressures of its components.
The cleanest way to compute partial pressure is by mole fraction. The mole fraction of gas i is xᵢ = nᵢ / n_total, and the partial pressure follows: Pᵢ = xᵢ · P_total. Mole fractions are dimensionless and always sum to 1 across all components.
Dalton was colourblind, which he discovered while teaching. He published the first known scientific paper on the condition in 1798, three years before formulating his law of partial pressures. Colourblindness was called "Daltonism" for over a century.
Dalton's law and the partial pressure formula
Two related formulas cover almost every partial-pressure question:
Dalton's law P_total = P₁ + P₂ + … + PₙComponent Pᵢ = xᵢ · P_totalMole fraction xᵢ = nᵢ ÷ n_totalIdeal gas Pᵢ = nᵢRT ÷ VConversion across pressure units gets used constantly: 1 atm = 760 mmHg = 101.325 kPa = 1.01325 bar = 14.696 psi. The calculator above outputs all five units simultaneously so you don't have to keep flipping between them.
Partial pressure in atmospheric air
Dry air at sea level has a remarkably stable composition. By mole fraction:
- Nitrogen N₂ — 78.09% (0.7809 atm or 593.7 mmHg).
- Oxygen O₂ — 20.95% (0.2095 atm or 159.2 mmHg).
- Argon Ar — 0.934% (0.00934 atm or 7.1 mmHg).
- Carbon dioxide CO₂ — 0.042% (about 0.32 mmHg, rising).
- Trace gases — Ne, He, CH₄, Kr together under 0.002%.
Mole fractions stay constant through the lower atmosphere because air mixes rapidly. What changes with altitude is the total pressure: about 1 atm at sea level, 0.7 atm at 2,500 m (Mexico City), 0.5 atm at 5,500 m, and 0.34 atm at the summit of Everest (8,848 m). Oxygen partial pressure on Everest is 0.21 × 0.34 ≈ 0.07 atm — well into the hypoxaemia zone for unacclimatised humans.
Partial pressure in medicine and breathing
Clinical medicine measures arterial blood gases in partial pressure units. Normal arterial oxygen partial pressure (PaO₂) is 95–100 mmHg; below 60 mmHg is clinically defined as hypoxaemia and requires intervention. Arterial CO₂ partial pressure (PaCO₂) normally sits at 35–45 mmHg; values above 45 mmHg indicate hypercapnia, often from inadequate ventilation.
The drop from inhaled to arterial oxygen is built into normal physiology. Atmospheric oxygen at 159 mmHg falls to roughly 150 mmHg in the upper airways (humidified) and to 100 mmHg in the alveoli (mixed with CO₂ and water vapour). Diffusion across the alveolar membrane brings arterial blood to 95–100 mmHg. The 60-mmHg drop is the basic budget of breathing.
The ideal gas law PV = nRT requires absolute temperature. 25°C is 298.15 K, not 25 K. Plugging Celsius directly into PV = nRT throws off the result by a factor of more than 10 and gives nonsense pressures.
Partial pressure and scuba diving
Underwater pressure rises by 1 atm every 10 m of depth. At 30 m the total pressure is 4 atm. Breathing air (21% O₂) at 30 m means PO₂ = 0.21 × 4 = 0.84 atm — still safe. Breathing pure oxygen would give PO₂ = 4 atm, well above the 1.4–1.6 atm safety limit, risking oxygen toxicity (seizures).
This is why divers use blended breathing gases. Common mixes:
- Air — 21% O₂, 79% N₂, max ~40 m for recreational diving.
- Nitrox 32 — 32% O₂, 68% N₂, longer bottom times up to about 33 m.
- Trimix — 18% O₂, 35% He, 47% N₂, technical diving past 60 m.
- Heliox — ~10% O₂, 90% He, deep saturation diving past 100 m.
Partial pressure from the ideal gas law
When you have moles, volume, and temperature instead of mole fraction, use Pᵢ = nᵢRT / V with R = 0.08206 L·atm·mol⁻¹·K⁻¹. Worked example: 0.5 mol of oxygen in a 10 L tank at 25°C (298.15 K). PO₂ = (0.5 × 0.08206 × 298.15) / 10 = 1.22 atm.
The result represents the contribution of that gas to the total pressure of whatever mixture occupies the tank. If 0.5 mol oxygen and 1.5 mol nitrogen share the 10 L tank at 25°C, P_total = (2.0 × 0.08206 × 298.15) / 10 = 4.89 atm, and PO₂ is 1.22 atm — exactly its share of the total.
Use ideal gas mode when you know how much of each gas you charged into a container. Use Dalton mode when you know percentages by mole and total pressure — for example, reading a gas blend specification or atmospheric composition.
Partial pressure pitfalls
Six errors that cause confusion in homework, lab work, and clinical settings:
- Mole fraction confused with mass fraction — 21% O₂ by mole is roughly 23% by mass in air because O₂ is heavier than N₂.
- Temperature in Celsius — always convert to Kelvin for PV = nRT.
- Ignoring water vapour — humid air contains H₂O, and its partial pressure subtracts from dry-gas partial pressures. At 25°C, 50% RH, water contributes about 11.9 mmHg.
- Treating partial pressure as concentration — concentration depends on volume; partial pressure depends on mole fraction and total pressure.
- Forgetting the safety limit for pO₂ — divers and HBO treatment must stay below 1.4–1.6 atm to avoid CNS oxygen toxicity.
- Assuming pressure units transfer — 1 atm ≠ 1 bar; always convert through a defined ratio (1 atm = 1.01325 bar).