Gas Mixture Partial Pressure Calculator

Calculate partial pressures, mole fractions, and total pressure for gas mixtures.

Moles of gas 1 n1 (mol)

Moles of gas 2 n2 (mol)

Moles of gas 3 n3 (mol)

Total pressure P_total (atm) (atm)

Temperature T (K) for volumes (K)

Please check your inputs and try again.

Why Gases Behave Independently

Dalton’s law states that each gas in a mixture exerts the pressure it would exert alone in the same container. The reason is the same assumption behind the ideal gas law: gas molecules do not interact, so a nitrogen molecule is unaffected by the presence of oxygen.

p_i = x_iP_total P_total = Σp_i

A useful consequence: for ideal gases mole fraction equals volume fraction. Equal numbers of molecules occupy equal volumes regardless of identity, so a gas that is 21% by volume is also 21% by moles. This does not hold for mass fraction, since molar masses differ.

Component of dry air	Volume / mole fraction	Partial pressure at 1 atm
Nitrogen	0.780	0.780 atm
Oxygen	0.209	0.209 atm
Argon	0.0093	0.0093 atm
Carbon dioxide	0.00042	0.00042 atm

Why Partial Pressure Matters Physiologically

Gas exchange in the body is driven by partial pressure, not concentration. This explains several things at once:

Situation	Total pressure	p(O₂)	Consequence
Sea level	1.0 atm	0.21 atm	Normal
5,500 m altitude	0.5 atm	0.105 atm	Hypoxia despite unchanged 21% O₂
Diving at 30 m on air	4.0 atm	0.84 atm	Nitrogen narcosis risk
Diving at 60 m on air	7.0 atm	1.46 atm	Approaching oxygen toxicity limit

At altitude the fraction of oxygen is unchanged at 21% — what falls is total pressure, and therefore partial pressure. Conversely, divers face the opposite problem: oxygen becomes toxic above roughly 1.6 atm partial pressure, which on air is reached around 67 m. This is why deep diving uses trimix with reduced oxygen fraction.

Worked Examples

Example 1: Air: N2=0.78mol, O2=0.21mol, Ar=0.01mol, P=1atm

p_N2=0.78, p_O2=0.21, p_Ar=0.01

Result: Partial pressures of air

Standard composition of dry air

Example 2: Scuba at 3atm: 0.21mol O2, 0.79mol N2

p_O2=0.21x3=0.63atm

Result: O2 toxicity risk above 1.6 atm pO2

Divers use trimix to avoid O2 toxicity

Example 3: Oxygen at altitude

Everest summit, atmospheric pressure about 0.33 atm

Result: p(O₂) = 0.209 × 0.33 = 0.069 atm

One third of the sea-level value despite the same 21% composition. This is why supplemental oxygen is needed at extreme altitude.

Example 4: Alveolar oxygen

Sea level, minus 47 mmHg water vapour: (760 − 47) × 0.209

Result: p(O₂) = 149 mmHg in the trachea

Saturation with water vapour reduces the effective pressure available. Alveolar p(O₂) is lower still, around 100 mmHg, after CO₂ exchange.

Example 5: Oxygen toxicity depth limit

Air (21% O₂), limit p(O₂) = 1.6 atm

Result: P_total = 1.6/0.209 = 7.66 atm ≈ 67 m

Beyond this depth, breathing air risks central nervous system oxygen toxicity, which is why technical divers reduce the oxygen fraction.

Common Mistakes

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Confusing mole fraction with mass fraction

Mole fraction equals volume fraction for ideal gases, but not mass fraction. Oxygen is 21% of air by moles and volume but about 23% by mass, since O₂ is heavier than N₂.

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Thinking oxygen percentage falls at altitude

It stays at about 21% all the way up. What decreases is total pressure, so partial pressure falls proportionally — which is what causes hypoxia.

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Forgetting water vapour in the lungs

Inspired air is saturated with water vapour at body temperature, contributing 47 mmHg. This must be subtracted from total pressure before applying the oxygen fraction.

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Applying Dalton’s law to reacting or condensable gases

The law assumes independence. If components react, or one condenses, the total is no longer the simple sum of independent contributions.

Frequently Asked Questions

Dalton's law applications?

Humid air: P_total = P_dry_air + P_H2O. Body gas corrections (blood gas measurements correct for water vapor at 37C: 47 mmHg). Scuba diving gas planning. Industrial gas blending for welding, medical use.

Mole fraction vs volume fraction?

For ideal gases at same T and P: mole fraction = volume fraction. 21% O2 by volume = 21 mol% = mole fraction 0.21. This makes gas concentration calculations straightforward.

What is Dalton’s law of partial pressures?

Each gas in a mixture exerts the pressure it would exert alone in the same volume, and the total is the sum of those partial pressures.

Is mole fraction the same as volume fraction?

For ideal gases, yes — equal molecule numbers occupy equal volumes. It is not the same as mass fraction, because molar masses differ.

Why does altitude cause hypoxia if oxygen is still 21%?

Because total pressure falls, so the partial pressure of oxygen falls with it. Gas exchange is driven by partial pressure, not by percentage composition.

Why do divers worry about oxygen toxicity?

Partial pressure rises with depth. Above about 1.6 atm p(O₂), central nervous system toxicity becomes a risk — reached at roughly 67 m on air.

Why subtract water vapour pressure in respiratory calculations?

Inspired air becomes saturated at body temperature, contributing 47 mmHg. That fraction of total pressure is unavailable to the other gases.

Formula Explorer connections

Interpretation: This relationship connects pressure, volume, temperature, amount or phase composition for gases and volatile mixtures. Assumption: Use absolute temperature and compatible pressure-volume units. Ideal behavior weakens at high pressure, low temperature, strong intermolecular attraction or near phase change.

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