Calculate Partial Pressure of Gases
Dalton's Law of Partial Pressures states that the total pressure exerted by a mixture of non-reacting gases equals the sum of the partial pressures of each individual gas. The partial pressure of any single gas is calculated as P_i = x_i × P_total, where x_i is the mole fraction of that gas and P_total is the total pressure of the mixture. This law is essential in chemistry, respiratory physiology, scuba diving safety, industrial gas engineering, and atmospheric science — any scenario where gas mixtures are analyzed at the component level.
When to use this calculator
- Calculating the partial pressure of oxygen (PO₂) in a diver's breathing mix at depth — e.g., at 40 m (5 atm), air gives PO₂ = 0.21 × 5 = 1.05 atm, approaching oxygen toxicity threshold.
- Determining alveolar oxygen pressure in respiratory physiology using the alveolar gas equation, where PO₂ at sea level ≈ 0.21 × 760 mmHg = 159.6 mmHg before correction for water vapor.
- Analyzing natural gas pipeline mixtures to ensure methane partial pressure stays within safe combustion and transport limits per industrial process specifications.
- Checking nitrogen partial pressure in spacecraft cabin atmospheres — NASA uses ~0.79 atm N₂ and ~0.21 atm O₂ at 1 atm total to mimic sea-level breathing conditions safely.
Calculation example
- Oxygen in air: x=0.21, P=1 atm
- P_O2 = 0.21 × 1 = 0.21 atm
How it works
3 min readHow It's Calculated
Dalton's Law defines the partial pressure of gas component i in a mixture:
P_i = x_i × P_total
Where:
P_i = Partial pressure of gas i (atm, mmHg, kPa, or bar)
x_i = Mole fraction of gas i (dimensionless, 0 to 1)
P_total = Total pressure of the gas mixture (same units as P_i)
Mole fraction: x_i = n_i / n_total
n_i = moles of gas i
n_total = total moles of all gases
Verification: ΣP_i = P_total (sum of all partial pressures = total pressure)The mole fraction x_i is always between 0 and 1, and the sum of all mole fractions in a mixture must equal exactly 1.00.
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Reference Table
Standard atmospheric composition and partial pressures at sea level (P_total = 1 atm = 760 mmHg = 101.325 kPa):
| Gas | Mole Fraction (x_i) | Partial Pressure (atm) | Partial Pressure (mmHg) | Partial Pressure (kPa) |
|---|---|---|---|---|
| Nitrogen (N₂) | 0.7808 | 0.7808 | 593.4 | 79.12 |
| Oxygen (O₂) | 0.2095 | 0.2095 | 159.2 | 21.22 |
| Argon (Ar) | 0.0093 | 0.0093 | 7.1 | 0.94 |
| Carbon Dioxide (CO₂) | 0.0004 | 0.0004 | 0.3 | 0.04 |
| Total | 1.0000 | 1.0000 | 760.0 | 101.325 |
Source: NOAA / U.S. Standard Atmosphere
Scuba diving — O₂ partial pressures at depth (air mix, x_O₂ = 0.21):
| Depth (m) | Depth (ft) | Absolute Pressure (atm) | PO₂ (atm) | Safety Note |
|---|---|---|---|---|
| 0 | 0 | 1.0 | 0.21 | Normal breathing |
| 10 | 33 | 2.0 | 0.42 | Safe |
| 30 | 99 | 4.0 | 0.84 | Safe |
| 40 | 132 | 5.0 | 1.05 | Near toxicity threshold |
| 57 | 187 | 6.7 | 1.40 | NOAA recreational limit |
| 66 | 218 | 7.6 | 1.60 | Absolute maximum |
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Typical Examples
Example 1 — Oxygen in air at sea level
Example 2 — Nitrox 32 diving mix at 30 m
Example 3 — Carbon dioxide in a sealed lab vessel
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Common Errors
1. Confusing volume percent with mole fraction for ideal gases — For ideal gases, volume % equals mole % exactly (Avogadro's Law), so "21% O₂ by volume" correctly gives x_O₂ = 0.21. However, for real gases at high pressure or low temperature this equivalence breaks down.
2. Forgetting water vapor pressure — In physiological calculations, the alveolar gas equation subtracts water vapor pressure (P_H₂O ≈ 47 mmHg at 37 °C body temperature). Ignoring this overestimates alveolar PO₂ by ~10 mmHg.
3. Using gauge pressure instead of absolute pressure — Dalton's Law requires absolute pressure. A scuba tank at 200 psi gauge = 214.7 psi absolute. Using gauge pressure directly understates partial pressures, which is dangerous in diving contexts.
4. Assuming the law applies to reactive gas mixtures — Dalton's Law holds only for non-reacting ideal gas mixtures. Mixtures involving reactions (e.g., NO + O₂ → NO₂) cannot be analyzed this way without accounting for equilibrium shifts.
5. Mixing unit systems mid-calculation — Partial pressure must be expressed in the same units as total pressure. Converting atm to mmHg (× 760) or to kPa (× 101.325) must happen before or after the multiplication, never during.
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Frequently asked questions
What is Dalton's Law of Partial Pressures?
Dalton's Law states that the total pressure of a gas mixture equals the sum of the partial pressures of its individual components: P_total = P₁ + P₂ + … + Pₙ. Equivalently, each gas exerts a pressure proportional to its mole fraction — as if it alone occupied the entire container. John Dalton published this observation in 1801.
What is the partial pressure of oxygen in normal air at sea level?
At sea level, total atmospheric pressure is 1 atm (760 mmHg). Since oxygen makes up approximately 20.95% of dry air by moles, its partial pressure is P_O₂ = 0.2095 × 760 = 159.2 mmHg (≈ 0.209 atm or 21.2 kPa). This value is the benchmark used in altitude medicine and respiratory physiology worldwide.
Why does PO₂ matter for scuba divers?
Breathing oxygen at partial pressures above 1.4 atm (NOAA recreational limit) causes central nervous system oxygen toxicity, which can lead to seizures underwater — a potentially fatal event. On standard air (21% O₂), this limit is reached at approximately 57 m (187 ft) depth. Divers using enriched air nitrox must recalculate their maximum operating depth (MOD) using this exact formula: MOD = (P_O₂_max / x_O₂ − 1) × 10 meters.
How is mole fraction different from mass fraction?
Mole fraction (x_i = n_i / n_total) is based on the number of moles of each gas; mass fraction (w_i = m_i / m_total) is based on mass. For air, oxygen's mole fraction is 0.2095 but its mass fraction is ≈0.232 because O₂ (MW = 32 g/mol) is heavier than the average air molecule (MW ≈ 29 g/mol). Dalton's Law requires mole fraction, not mass fraction.
Does Dalton's Law work for real gases or only ideal gases?
Dalton's Law is strictly exact only for ideal gases, where intermolecular forces are negligible. For real gases at moderate pressures (below ~10 atm) and temperatures well above their boiling points, the law is an excellent approximation. At high pressures or low temperatures, equations of state like van der Waals or Peng-Robinson must be used instead to account for molecular interactions.
What is the partial pressure of CO₂ in a room with 1,000 ppm CO₂?
1,000 ppm = 0.001 mole fraction (x_CO₂ = 0.001). At sea level (1 atm), P_CO₂ = 0.001 × 1 atm = 0.001 atm = 0.76 mmHg = 0.101 kPa. OSHA's permissible exposure limit (PEL) for CO₂ is 5,000 ppm (8-hour TWA), corresponding to P_CO₂ = 0.005 atm (3.8 mmHg). Indoor air quality guidelines generally target below 1,000 ppm.
How does altitude affect partial pressure of oxygen?
At higher altitudes, total atmospheric pressure decreases, so even though the mole fraction of O₂ stays constant at ~0.2095, the partial pressure drops. At Denver (1,609 m / 5,280 ft), P_total ≈ 0.840 atm, giving P_O₂ ≈ 0.176 atm (134 mmHg). At the summit of Mt. Everest (8,849 m), P_total ≈ 0.337 atm, giving P_O₂ ≈ 0.071 atm (54 mmHg) — roughly one-third of sea-level oxygen, which is why supplemental oxygen is typically required above 7,000 m.
Why is water vapor pressure subtracted in the alveolar gas equation?
Air in the lungs is fully saturated with water vapor at body temperature (37 °C), where P_H₂O = 47 mmHg. This water vapor 'dilutes' the inspired gases, so the effective total pressure for dry gases is only 760 − 47 = 713 mmHg. The alveolar gas equation accounts for this: P_A_O₂ = F_I_O₂ × (P_atm − P_H₂O) − P_a_CO₂ / RQ. Skipping this correction overestimates alveolar PO₂ by about 10 mmHg.