Key takeaways

  • Dalton's Law states that the total pressure of a gas mixture equals the sum of the partial pressures of each gas in it.
  • A gas's partial pressure depends on its share of the total number of molecules (its mole fraction), not on what other gases are present.
  • It's the basis for how scuba divers, hospitals, and aircraft cabins manage gas mixtures safely as pressure changes with depth or altitude.
  • The law is an idealization that works well at ordinary pressures but becomes less accurate at very high pressures, where gas molecules interact more with each other.
  • It's closely related to atmospheric pressure, which is itself the sum of the partial pressures of nitrogen, oxygen, and the other gases in air.

Table of Contents

What Is Dalton's Law?

Dalton's Law of Partial Pressures, named after the chemist John Dalton, says that for a mixture of gases that don't react with each other, the total pressure is simply the sum of the pressures each individual gas would exert if it occupied the container alone, at the same temperature.

The "partial pressure" of a gas is the pressure it would have on its own. In a sealed room full of air, the nitrogen molecules are colliding with the walls and contributing pressure, completely independent of what the oxygen and argon molecules are doing - add up all those independent contributions, and you get the total pressure in the room.

The Formula

Ptotal = P1 + P2 + P3 + ... + Pn

To find the partial pressure of one gas in the mixture, multiply the total pressure by that gas's mole fraction - its share of the total number of gas molecules:

Px = Ptotal × (nx / ntotal)
  • Px = partial pressure of gas x
  • Ptotal = total pressure of the mixture
  • nx = number of moles of gas x
  • ntotal = total number of moles of all gases

For example, dry air at 1 atm is roughly 78% nitrogen and 21% oxygen by mole fraction, so the partial pressure of oxygen is about 0.21 atm - this is the figure that matters for how efficiently your lungs can take up oxygen.

Real-Life Examples

  1. Scuba diving: as a diver descends, the total pressure of the breathing gas increases, so the partial pressure of each gas in their tank rises too. Too much partial pressure of nitrogen can cause nitrogen narcosis, and too much oxygen can become toxic - which is why divers use specially blended gas mixtures for deep dives, an approach described in dive-training references such as the NOAA Diving Manual.
  2. Medical oxygen therapy: ventilators and oxygen masks are set to deliver a specific fraction of inspired oxygen (FiO2), which directly controls the partial pressure of oxygen reaching a patient's lungs.
  3. Aircraft cabin pressurization: at cruising altitude, outside air pressure is too low to supply enough oxygen, so cabins are pressurized to maintain a partial pressure of oxygen that keeps passengers comfortable without fully repressurizing to sea-level pressure.
  4. Industrial gas storage: tanks holding mixed gases are rated based on the partial pressures of their components, since each gas contributes independently to the stress on the container.
  5. Carbonated drinks: the fizz in a soda comes from carbon dioxide dissolved under pressure - when the partial pressure of CO2 above the liquid drops after opening the can, dissolved gas escapes as bubbles.
  6. Weather balloons: as a balloon rises, the total atmospheric pressure drops, changing the partial pressures of the gases inside the instrument package and the surrounding air that sensors measure.

Where the Law Breaks Down

Dalton's Law is an idealization based on the assumption that gas molecules don't interact with each other except through collisions. At ordinary pressures, this holds well enough for most calculations. But at very high pressures - like those found deep underwater or in industrial gas cylinders - real gas molecules take up a meaningful amount of space and start to attract or repel each other, so the simple additive formula becomes less accurate. Corrections for these effects are part of what real-gas equations of state, such as the van der Waals equation, are designed to handle.

Frequently asked questions

What is Dalton's Law of Partial Pressures in simple terms?

It says the total pressure of a mixture of gases equals the sum of the pressures each gas would have if it were alone in the same container.

How do you calculate the partial pressure of a gas?

Multiply the total pressure of the mixture by the gas's mole fraction: P_x = P_total times (n_x divided by n_total).

Why does Dalton's Law matter for scuba divers?

As pressure increases with depth, the partial pressures of nitrogen and oxygen in a diver's breathing gas rise as well, which can lead to nitrogen narcosis or oxygen toxicity if not managed with appropriate gas mixtures.

What is the partial pressure of oxygen in normal air?

At sea level, where total atmospheric pressure is about 1 atm and oxygen makes up roughly 21% of air by mole fraction, the partial pressure of oxygen is approximately 0.21 atm.

Does Dalton's Law apply to gases that react with each other?

No. Dalton's Law assumes the gases in the mixture do not chemically react with one another. If a reaction occurs, the amounts and identities of the gases change over time, so the simple additive relationship no longer applies directly.