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Dalton's Law of Partial Pressures

Also known as total pressure of a gas mixture · sum of partial pressures · gas collected over water · law of partial pressures

Ptotal=P1+P2+P3P_{\text{total}} = P_1 + P_2 + P_3

Worked example: 80.0 + 21.0 + 3.17 kPa → 104.17 kPa total — press Try an example to run it live, then adjust anything.

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See also
Partial Pressure from Mole Fraction — The other face of the same law: each partial pressure as its share of the total.Ideal Gas Law — Why the law holds at all — each gas fills the whole volume as though the others were not there.

Learning zone

John Dalton's 1801 observation is that gases in a mixture ignore each other. Each one fills the whole container and pushes on the walls exactly as hard as it would if the others were not there, so the total pressure is simply the sum. It follows directly from the ideal-gas picture — molecules that do not interact cannot know they have company — and it fails only where that picture fails, at high pressure or near condensation.

The everyday use is the wet-gas correction. Collect hydrogen by displacing water in an inverted cylinder and what you have collected is not hydrogen: it is hydrogen plus water vapour, and the water contributes its full saturation pressure at the collection temperature no matter how little of it there is. At 25 °C that is 3.17 kPa; at 20 °C, 2.34 kPa. Level the cylinder so the inside and outside water surfaces match, read the barometer, and the hydrogen's own pressure is the barometric reading minus the vapour pressure. Skip that subtraction and you overstate the dry gas by about 3% at room temperature — small enough to look like ordinary experimental scatter, which is exactly why it survives so long uncorrected.

Worked: barometer reads 101.325 kPa, water vapour at 25 °C contributes 3.17 kPa, and a trace of dissolved air accounts for 0.50 kPa. The hydrogen partial pressure is 101.325 − 3.17 − 0.50 = 97.66 kPa, and that is the number that goes into PV = nRT.

The law's other face is the mole-fraction form, P_i = x_i·P_total, which follows by dividing the sum through by itself. Both say the same thing; this one is the version you reach for when you know the components and want the total, or when one component's pressure has to come back out of a reading.

Two cautions. Volume percent equals mole percent for ideal gases and only for ideal gases, so a specification written in volume percent can be used here directly at ordinary pressures and not in a high-pressure cylinder. And a component's partial pressure never exceeds the total: if the arithmetic asks for a negative one, the reading you called the total is not the total.

Dalton's Law of Partial Pressures
Ptotal=P1+P2+P3P_{\text{total}} = P_1 + P_2 + P_3
Where
  • PtotalP_{\text{total}}= Total pressure (kPa)
  • P1P_1= Partial pressure of gas 1 (kPa)
  • P2P_2= Partial pressure of gas 2 (kPa)
  • P3P_3= Partial pressure of gas 3 (kPa)
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