Dalton's Law of Partial Pressures Calculator

Free Dalton's Law of Partial Pressures Calculator

This Dalton's Law Calculator adds up any number of partial pressures to find the total pressure of a gas mixture, and can also solve for a single gas's partial pressure, its mole fraction, or the mixture's total pressure using Pᵢ = xᵢ × P_total. Add or remove gases freely in the total-pressure mode, or switch to one of the mole-fraction modes for a two-value problem. Every answer comes with the full working and a labelled gas-mixture bar diagram.

It is built for chemistry and physics students, lab write-ups, and anyone working with real gas mixtures like air, scuba tank blends, or gas collected over water. Built-in presets for dry air, a nitrox scuba fill, and gas collected over water let you see realistic numbers instantly.

What Is Dalton's Law of Partial Pressures?

Dalton's law of partial pressures states that in a mixture of non-reacting gases, the total pressure exerted equals the sum of the pressures each individual gas would exert if it alone occupied the same volume at the same temperature. Each gas's own contribution is called its partial pressure. The law is named after English chemist John Dalton, who described it in 1801.

This works because each gas in a mixture behaves independently of the others in the ideal gas approximation — the molecules of one gas do not change how the molecules of another gas collide with the container walls.

Dalton's Law Formula

The core Dalton's law formula is P_total = P₁ + P₂ + P₃ + ... + Pₙ, the simple sum of every gas's partial pressure. A second, equally useful form connects partial pressure to mole fraction: Pᵢ = xᵢ × P_total, where xᵢ is the mole fraction of gas i (its moles divided by the total moles of gas in the mixture). Rearranging this second form gives xᵢ = Pᵢ/P_total and P_total = Pᵢ/xᵢ, both supported by this calculator.

Finding Total Pressure by Adding Partial Pressures

The most direct use of Dalton's law: list the partial pressure of every gas in the mixture, and add them together. This is exactly how the composition of dry air is built up — nitrogen contributes about 79.12 kPa, oxygen about 21.22 kPa, and argon, carbon dioxide, and trace gases together about 1 kPa, adding to a total pressure close to 101.3 kPa at sea level.

Finding a Partial Pressure from Mole Fraction

When the mole fraction of one gas in a mixture and the total pressure are both known, its partial pressure follows directly from Pᵢ = xᵢ × P_total. For example, dry air is about 20.95% oxygen by moles, so at a total pressure of 101.325 kPa, the partial pressure of oxygen is 0.2095 × 101.325 ≈ 21.23 kPa.

Finding Mole Fraction or Total Pressure

If a gas's partial pressure and the mixture's total pressure are known, its mole fraction is xᵢ = Pᵢ/P_total. Conversely, if a partial pressure and mole fraction are both known, the total pressure can be recovered with P_total = Pᵢ/xᵢ — useful for checking lab measurements or working backward from a single sensor reading in a multi-gas system.

Real-Life Examples of Dalton's Law

Dalton's law shows up anywhere gases mix without reacting, which makes it one of the most practically useful gas laws.

• Earth's atmosphere: total air pressure is the sum of the partial pressures of nitrogen, oxygen, argon, carbon dioxide, and trace gases.
• Scuba and technical diving gas blends, like Nitrox and Trimix, where the partial pressure of oxygen must be kept within a safe range at depth.
• Gas collected over water in a chemistry lab, where the measured pressure includes both the collected gas and water vapor, and Dalton's law is used to subtract out the vapor pressure of water.
• Anesthesia and respiratory gas mixtures in medicine, where the partial pressure of oxygen and other gases must be carefully controlled.
• Industrial gas cylinders filled with blended gases, where suppliers use partial pressures to certify the exact composition of the mix.

Dalton's Law and Gas Collected Over Water

A classic application: when a gas is collected by bubbling it through water into an inverted container, the trapped gas is never pure — it is mixed with water vapor that evaporated into the same space. The measured total pressure equals the pressure of the dry gas plus the vapor pressure of water at that temperature. Subtracting the known water vapor pressure from the total measured pressure, using Dalton's law, gives the true partial pressure of the collected gas.

Common Mistakes When Using Dalton's Law

A handful of errors come up repeatedly with Dalton's law problems.

• Forgetting to subtract water vapor pressure when a gas has been collected over water.
• Mixing pressure units between different gases in the same sum, such as adding kPa and mmHg without converting first.
• Confusing mole fraction (a ratio between 0 and 1) with a percentage — remember to divide a percent by 100 before using it as xᵢ.
• Applying Dalton's law to gases that actually react with each other, where the simple additive rule no longer holds.

How to Use This Calculator

For the total-pressure mode, add a row for each gas in the mixture, name it, and enter its partial pressure — the calculator sums them automatically and shows the mole fraction each gas contributes. For the other three modes, pick which single quantity you need — partial pressure, mole fraction, or total pressure — and fill in the two values you already know. The gas-mixture diagram and full step-by-step working update immediately as you type.