ciencia

Dalton's Law Partial Pressure Calculator

Calculator Free · Private

Reviewed by: Martín Rodríguez (editorial policy ) · Last reviewed: Jun 4, 2026

Was this calculator helpful?

Dalton's Law of Partial Pressures states that in a mixture of non-reacting ideal gases, each gas exerts a pressure proportional to its mole fraction — as if it alone occupied the container. The formula is P_i = x_i × P_total, where x_i is the mole fraction (0 to 1) and P_total is the total pressure. This law underpins scuba diving safety (PO₂ limits), respiratory physiology (alveolar gas equation), industrial gas engineering, and atmospheric science.

Last reviewed: June 3, 2026 Verified by Martín Rodríguez Source: NOAA – U.S. Standard Atmosphere, Atmospheric Composition, NIH / NCBI – Oxygen Toxicity in Diving (Undersea and Hyperbaric Medicine), OSHA – Carbon Dioxide: Chemical Sampling Information, NIST Chemistry WebBook – Gas Phase Thermochemistry Data, Wikipedia – Dalton's Law of Partial Pressures 100% private

Dalton's Law: partial pressure P_i = x_i × P_total, where x_i is the mole fraction (0–1) and P_total is the total pressure of the mixture. Example: oxygen in air at sea level — P_O₂ = 0.2095 × 1 atm = **0.210 atm** (159.2 mmHg). The sum of all partial pressures equals the total pressure.

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 the 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 water vapor correction.
Analyzing natural gas pipeline mixtures to ensure methane partial pressure stays within safe combustion and transport limits.
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.

Worked example: oxygen in air at sea level

Mole fraction of O₂ in dry air: x = 0.2095
Total pressure at sea level: P_total = 1.000 atm
P_O₂ = 0.2095 × 1.000 = 0.2095 atm
Converting: 0.2095 atm × 760 mmHg/atm = 159.2 mmHg

Result: P_O₂ = 0.210 atm (159.2 mmHg) — the reference value in pulmonary physiology and altitude medicine

How it works

3 min read

Dalton's Law Formula

The partial pressure of gas component i in a mixture is:

P_i = x_i × P_total

Where:
  P_i      = Partial pressure of gas i (atm, mmHg, kPa — same units as P_total)
  x_i      = Mole fraction of gas i  (dimensionless, 0 to 1)
  P_total  = Total pressure of the gas mixture

Mole fraction:   x_i = n_i / n_total
                 n_i     = moles of gas i
                 n_total = total moles of all gases in the mixture

Verification:    Σ P_i = P_total   (all partial pressures sum to total pressure)

The mole fraction x_i always lies between 0 and 1, and the sum of all mole fractions in a mixture equals exactly 1.00.

---

Reference Table: Atmospheric Composition and Partial Pressures

Standard dry atmosphere 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 Pressure vs. Depth (air, x_O₂ = 0.21)

Absolute pressure increases by 1 atm every 10 m of seawater. The NOAA recreational PO₂ limit is 1.40 atm.

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	Caution — near threshold
57	187	6.7	1.40	NOAA recreational limit
66	218	7.6	1.60	Absolute maximum

---

Unit Conversion Quick Reference

| 1 atm = | 760 mmHg | 101.325 kPa | 14.696 psi | 1.01325 bar |
|---------|----------|-------------|------------|-------------|

To convert partial pressure:

atm → mmHg: × 760

atm → kPa: × 101.325

mmHg → atm: ÷ 760

---

Worked Examples

Example 1 — Oxygen in air at sea level

x_O₂ = 0.2095, P_total = 1.000 atm

P_O₂ = 0.2095 × 1.000 = 0.2095 atm (≈159.2 mmHg)

Reference value in pulmonary physiology and altitude medicine.

Example 2 — Nitrox 32 diving mix at 30 m

Nitrox 32: 32% O₂ by moles, so x_O₂ = 0.32

Absolute pressure at 30 m: P_total = 4.0 atm

P_O₂ = 0.32 × 4.0 = 1.28 atm — within the NOAA limit of 1.40 atm.

Example 3 — CO₂ in a sealed lab vessel

A 10 L vessel: 0.5 mol CO₂ + 4.5 mol N₂ at 2.0 atm total.

x_CO₂ = 0.5 / (0.5 + 4.5) = 0.10

P_CO₂ = 0.10 × 2.0 = 0.20 atm (≈152 mmHg) — above OSHA's 8-h TWA of 0.005 atm (5,000 ppm).

---

Common Errors

1. Confusing volume % with mole fraction — For ideal gases, volume % = mole % (Avogadro's Law), so "21% O₂ by volume" gives x_O₂ = 0.21 correctly. For real gases at high pressure this equivalence breaks down.

2. Forgetting water vapor — In physiological calculations, subtract P_H₂O ≈ 47 mmHg at 37 °C body temperature. Ignoring it overestimates alveolar PO₂ by ~10 mmHg.

3. Gauge vs. absolute pressure — Dalton's Law requires absolute pressure. A tank at 200 psi gauge = 214.7 psi absolute. Using gauge pressure in diving calculations underestimates partial pressures — potentially dangerous.

4. Reactive gas mixtures — Dalton's Law applies only to non-reacting ideal gas mixtures. Equilibrium reactions shift concentrations and invalidate the simple calculation.

5. Mixing unit systems — Partial pressure must be expressed in the same units as total pressure throughout the calculation.

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 equal to its mole fraction times the total pressure: P_i = x_i × P_total. John Dalton published this observation in 1801.

What is the partial pressure of oxygen in air at sea level?

At sea level, total atmospheric pressure is 1 atm (760 mmHg). Oxygen makes up 20.95% of dry air by moles (x_O₂ = 0.2095), so P_O₂ = 0.2095 × 760 = 159.2 mmHg (≈0.209 atm or 21.2 kPa). This is the benchmark reference in altitude medicine, respiratory physiology, and anesthesiology worldwide.

How do I calculate partial pressure from mole fraction?

Multiply the mole fraction by the total pressure: P_i = x_i × P_total. Example: nitrogen in air (x = 0.7808) at 1 atm gives P_N₂ = 0.7808 × 1 = 0.781 atm. If total pressure is in mmHg, the result is also in mmHg — units carry through automatically.

Why does PO₂ matter for scuba divers?

Breathing oxygen above 1.4 atm (NOAA recreational limit) causes CNS oxygen toxicity, potentially causing seizures underwater. On standard air (21% O₂), this limit is reached at ~57 m depth (6.7 atm absolute). Divers on enriched-air nitrox must calculate their maximum operating depth (MOD) using: MOD (m) = (P_O₂_max / x_O₂ − 1) × 10.

How is mole fraction different from mass fraction?

Mole fraction (x_i = n_i / n_total) is based on moles; mass fraction (w_i = m_i / m_total) is based on mass. Oxygen in air: mole fraction ≈ 0.2095 but mass fraction ≈ 0.232 because O₂ (MW=32) is heavier than the average air molecule (MW≈29). Dalton's Law requires mole fraction, not mass fraction.

Does Dalton's Law work for real gases?

It is exact only for ideal gases. At moderate pressures (below ~10 atm) and temperatures well above boiling, it is an excellent approximation. At very high pressures or low temperatures, equations of state like van der Waals or Peng-Robinson must replace it.

What is the partial pressure of CO₂ at 1,000 ppm (typical indoor air)?

1,000 ppm = mole fraction 0.001. At sea level (1 atm): P_CO₂ = 0.001 atm = 0.76 mmHg = 0.101 kPa. OSHA's 8-hour TWA PEL is 5,000 ppm (P_CO₂ = 0.005 atm). Indoor air quality guidelines target below 1,000 ppm for cognitive performance.

How does altitude reduce the partial pressure of oxygen?

The mole fraction of O₂ stays constant at ~0.2095 at all altitudes, but total atmospheric pressure decreases with altitude, so PO₂ falls. At Denver (1,609 m): P_total ≈ 0.840 atm → P_O₂ ≈ 0.176 atm (134 mmHg). At Mt. Everest summit (8,849 m): P_total ≈ 0.337 atm → P_O₂ ≈ 0.071 atm (54 mmHg) — one-third of sea-level oxygen.

Why is water vapor subtracted in the alveolar gas equation?

Air in the lungs is fully saturated at body temperature (37 °C), where P_H₂O = 47 mmHg. This dilutes the inspired gases, so the effective dry-gas pressure is 760 − 47 = 713 mmHg. The alveolar gas equation corrects for this: P_A_O₂ = F_I_O₂ × (P_atm − 47) − P_a_CO₂ / RQ. Skipping the correction overestimates alveolar PO₂ by ~10 mmHg.