How this instrument works
Dalton's law of partial pressures says that in a mixture of gases that don't react with each other, each gas contributes to the total pressure in direct proportion to its share of the mixture by moles — its mole fraction. The partial pressure of any one gas, P_gas, equals its mole fraction, x_gas, multiplied by the total pressure of the mixture, P_total. Add up the partial pressures of every gas present and the sum equals the total pressure exactly, which is really just restating that the mole fractions of all components in a mixture must add up to 1.
The law holds because, in an ideal gas mixture, each type of molecule behaves as though the others weren't there — collisions with container walls from oxygen molecules don't care whether nitrogen molecules are also present, they just add their own share of impacts to the total. John Dalton proposed the law in 1801, working from his study of atmospheric gases, well before anyone had a molecular theory to explain why it should be true; the kinetic theory of gases later supplied that explanation, showing the law follows directly from treating gas pressure as the sum of independent molecular collisions.
Partial pressure matters wherever a specific gas's behavior, not the mixture's overall total, is what actually drives a physical or biological process. The rate oxygen diffuses into blood in the lungs depends on oxygen's own share of that total, not on the reading of the whole atmosphere — which is exactly why altitude sickness sets in at high elevation even though the air is still about 21% oxygen by mole fraction: the total has dropped, so oxygen's contribution has dropped right along with it, even though its proportion of the mixture hasn't changed at all.
- Enter the gas's share of the mixture into Mole fraction of gas — a number between 0 and 1, such as 0.21 for oxygen in dry air.
- Enter the mixture's total pressure into Total pressure (atm).
- Read Partial pressure (atm) — that single gas's contribution to the total pressure.
- To find a different gas's partial pressure in the same mixture, change only Mole fraction of gas to that gas's share and re-read the result.
- Mole fraction of gas must stay between 0 and 1: 0 means the gas is absent, 1 means it's the only gas present.
Worked example — oxygen's partial pressure in dry air at sea level
Enter 0.21 into Mole fraction of gas and 1.0 into Total pressure (atm) — oxygen's approximate share of dry air by mole fraction, at typical sea-level atmospheric pressure. Partial pressure (atm) reads 0.2100: the instrument multiplies 0.21 x 1.0 = 0.21 directly.
That figure matches the commonly cited partial pressure of atmospheric oxygen at sea level, close to a fifth of an atmosphere. Change Mole fraction of gas to 0.78 for nitrogen, leaving Total pressure (atm) at 1.0, and Partial pressure (atm) becomes 0.7800 — together, oxygen and nitrogen alone already account for about 99% of dry air's total pressure at sea level.
Questions
Why does each gas act as if the others aren't there?
Because in an ideal gas mixture, pressure comes from the frequency and force of molecular collisions with the container walls, and each type of molecule contributes its own collisions independent of what else is present. Oxygen molecules don't need to 'know' nitrogen molecules are also in the room to keep colliding with the walls at their own characteristic rate — the two contributions simply add together, which is the physical basis for Dalton's law.
Do all the partial pressures in a mixture add up to the total pressure?
Yes, always — that's essentially a restatement of the same law. Since every gas's mole fraction is its share of the total moles present, and all the mole fractions in a mixture must sum to exactly 1, multiplying through by total pressure shows the partial pressures must also sum to the total pressure. If you know every partial pressure but one, you can find the missing one by subtracting the rest from the total.
Why does oxygen's partial pressure drop at high altitude even though air is still 21% oxygen?
Because partial pressure depends on both the mole fraction and the total, and altitude changes that total, not the mixture's composition. Dry air stays close to 21% oxygen by mole fraction from sea level up through the troposphere, but total atmospheric pressure falls steadily with altitude, so oxygen's own share (0.21 x a shrinking total) falls right along with it — which is the real physiological cause of altitude sickness and the need for supplemental oxygen at high elevation.
How is partial pressure different from concentration?
They're related but not identical: partial pressure is measured in force per area, while concentration is typically an amount per volume, like moles per litre. For an ideal gas, the two are proportional to each other at a fixed temperature via the ideal gas law (P = nRT/V), so a higher value here does correspond to a higher concentration of that gas — but this figure specifically isolates the force contribution from one component, which is what matters for processes like gas diffusion across a membrane.
Does Dalton's law apply to gases that react with each other?
Not reliably. Dalton's law assumes the gases in the mixture don't chemically react, so their individual mole counts (and therefore mole fractions) stay fixed. If two gases in a mixture react — nitrogen dioxide and dinitrogen tetroxide interconverting, for example — the mole fractions themselves shift as the reaction proceeds, and a separate chemical equilibrium calculation is needed to find each species' true partial pressure at equilibrium.
What happens to the partial pressure if I enter a mole fraction of exactly 1?
Partial pressure (atm) becomes equal to Total pressure (atm) exactly — a mole fraction of 1 describes a pure gas with no other gases present in the mixture, so by definition that single gas accounts for the entire total pressure. It's a useful degenerate case for checking that the calculation is behaving correctly.