Partial Pressure Calculator (Dalton’s law)

Understanding the partial pressure calculator — concept and principle

Dalton's law of partial pressures says that in a mixture of gases each component pushes on the walls as if it were alone, and the total pressure is the sum of these contributions. Enter the total pressure and the mole fraction of each gas as a comma-separated list of percentages, and the calculator returns each gas's partial pressure. It is used in respiratory physiology, diving and chemical equilibrium problems.

How it is calculated

pᵢ = xᵢ × P_total

• P_total: total absolute pressure of the mixture, in kPa.
• xᵢ: mole fraction of component i, entered in percent and divided by 100.
• pᵢ: partial pressure of component i, in the same unit as P_total.

The sum of the fractions should be 100; otherwise the list is incomplete or has a typo.

The principle

For ideal gases the pressure depends only on the number of molecules per unit volume and on temperature, not on what kind of molecules they are. In a mixture, each gas therefore exerts pᵢ = nᵢRT/V, and adding them gives P_total = (Σnᵢ)RT/V. Dividing one by the other gives pᵢ / P_total = nᵢ / n_total = xᵢ. John Dalton described this behaviour in the early 1800s. For ideal gases mole fraction equals volume fraction, so air composition by volume can be used directly.

Worked example

1. Inputs: P_total = 101.325 kPa (sea-level standard atmosphere); dry air composition 78.08% N₂, 20.95% O₂, 0.93% Ar, 0.04% CO₂.
2. Nitrogen: 101.325 × 0.7808 = 79.1146 kPa.
3. Oxygen: 101.325 × 0.2095 = 21.2276 kPa.
4. Argon: 101.325 × 0.0093 = 0.942323 kPa.
5. Carbon dioxide: 101.325 × 0.0004 = 0.04053 kPa.
6. Sum of fractions: 78.08 + 20.95 + 0.93 + 0.04 = 100.

How to read the result

The partial pressure, not the percentage, is what governs how much of a gas dissolves in liquids and how fast it diffuses into blood. At altitude the oxygen fraction stays near 20.95%, but the total pressure falls, so the oxygen partial pressure falls with it; that is why breathing is harder in the mountains. At 10 m underwater the total pressure roughly doubles, and so does every partial pressure. Divers keep oxygen partial pressure below a set limit to avoid oxygen toxicity.

Common mistakes

• Using gauge pressure (such as a cylinder gauge reading) instead of absolute pressure.
• Entering fractions as decimals (0.21) when the input expects percent (21).
• Forgetting water vapour: humid or exhaled air contains H₂O, which takes up part of the total pressure.

Frequently asked questions

What is the oxygen partial pressure at the top of a high mountain?

Multiply the local total pressure by 0.2095. If the pressure is half of sea level, the oxygen partial pressure is also about half.

Is mole fraction the same as mass fraction?

No. Mass fractions must first be converted to moles by dividing by each molar mass before using Dalton's law.

Sources: P. Atkins and J. de Paula, Atkins' Physical Chemistry, Oxford University Press · ISO 2533:1975, Standard Atmosphere · OpenStax, Chemistry 2e, Section 9.3 "Stoichiometry of Gaseous Substances, Mixtures, and Reactions"