Partial Pressure Calculator

What a partial pressure is

A partial pressure is the pressure one gas contributes to a mixture. When air pushes on you with 101.325 kPa, that is not 101.325 kPa of nitrogen plus another 101.325 kPa of oxygen. Each gas pushes with its own share, and the shares add up to the total you feel. The nitrogen in that air carries about 79.12 kPa of it and the oxygen about 21.22 kPa.

There are two ways to work out a partial pressure, and good labs use whichever one the data supports. The first starts with the total pressure and the share of each gas: multiply the total by the fraction of the mixture the gas makes up. The second starts with the moles of the gas, the temperature and the volume, and works out the pressure that amount of gas reaches on its own. Both routes end at the same number, and both need the same assumption: the gas behaves ideally, meaning the particles are far apart and do not push on each other.

This page starts with the total pressure, since that is what most people can measure with a gauge or read off a weather report, and then adds the second route for anyone who has a cylinder, a bottle or a sealed container in front of them.

Dalton's law: total pressure times the share

The shortcut comes from Dalton's law of partial pressures, published in 1801. Each gas in a mixture expands to fill the whole space and pushes with a pressure that does not depend on the other gases. The share of the total pressure a gas holds is therefore its mole fraction, the fraction of all the particles in the mixture that belong to it.

The formula is short: Pi = yi x Ptotal, where Pi is the partial pressure of gas i, yi is its mole fraction, and Ptotal is the pressure of the whole mixture. The mole fraction comes from the mole count, so if the mixture holds 78.084 percent nitrogen by volume, its mole fraction is 0.78084, and 0.78084 x 101.325 = 79.12 kPa is the nitrogen part of that pressure.

The shares come from NOAA's JetStream description of the atmosphere, which lists nitrogen at 78.084 percent, oxygen at 20.946 percent, argon at 0.934 percent and carbon dioxide at 0.042 percent for a completely dry atmosphere. The pressure column adds to 101.33 kPa, and the four shares add to 100.006 percent rather than exactly 100 because each one is rounded; the trace gases NOAA lists in parts per million sit inside that gap.

One atmosphere is defined as exactly 101 325 Pa, which is 101.325 kPa, according to the NIST Guide to the SI, Appendix B. That is why 101.325 kPa shows up as the reference total on so many gauges and tables.

The second route: moles, temperature and volume

When you know how much gas there is and how much room it has, you can skip the mixture fractions and ask the gas directly. The ideal gas law gives the pressure of each component:

Pi = ni x R x T / V, where ni is the moles of that gas, T is the temperature in kelvin, V is the volume in liters, and R is the molar gas constant. CODATA at NIST lists R as 8.314 462 618 J per mol per kelvin, and because one joule equals one kilopascal times one liter, the constant works directly with liters and kilopascals.

Take 2 moles of gas in a 50 liter container at 25 degrees Celsius, which is 298.15 kelvin. First 8.314462618 x 298.15 = 2478.96 for each mole, so 2 x 2478.96 = 4957.92, and 4957.92 / 50 = 99.16 kPa. Change the amount and the picture changes fast: 1 mole in the same container gives 49.58 kPa and 3 moles give 148.74 kPa.

The same formula gives the total pressure of a mixture: add the partial pressures of every component. The reason both routes agree is that the mole fraction of a gas is the same as its share of the total particles, and the ideal gas law ties that share to the pressure it produces.

Mole fraction, mass fraction, volume fraction

Three different percentages get called the share of a gas, and picking the wrong one is the most common mistake in this kind of work. Mole fraction counts particles. Mass fraction counts weight. Volume fraction counts space, and for a gas mixture at one temperature and pressure, volume fraction and mole fraction are the same number, because equal amounts of any gas at the same conditions take up the same volume.

Weight is where the three part company. A mixture of 2 moles of nitrogen and 1 mole of oxygen has a mole fraction of 0.6667 for nitrogen, but nitrogen weighs 2 x 28.014 = 56.03 g against 32.00 g of oxygen, so the mass fraction is 56.03 / 88.03 = 0.6365. The nitrogen is two thirds of the particles but under two thirds of the weight, because an oxygen molecule is heavier.

For partial pressure work, the mole fraction is the one to use. A gas cylinder label that lists nitrogen at 80 percent and oxygen at 20 percent by volume gives you the mole fractions directly, so 0.80 x 3000 psi is the nitrogen part of 3000 psi.

Wet gas: taking the water vapor out

Air is never dry, and that changes the arithmetic. Water vapor takes up room in the mixture and pushes with its own pressure, so the pressure left for the other gases is the total minus the water part: Pdry = Ptotal - PH2O. NOAA puts the water vapor share of ordinary air at up to about 4 percent of the volume, and more on hot humid days, so the size of the correction depends on the weather.

How much the water pushes depends on the temperature. The National Weather Service gives the saturated vapor pressure as 6.11 x 10 to the power of (7.5 x T divided by 237.3 + T), in millibars, where T is the air temperature in Celsius. At 20 degrees that formula gives 2.34 kPa of water vapor in fully saturated air, at 25 degrees it gives 3.17 kPa, and at 10 degrees it gives 1.23 kPa.

So a 100.00 kPa sample of saturated air at 20 degrees Celsius is made of 97.66 kPa of dry gases and 2.34 kPa of water vapor, and the oxygen inside it holds 0.20946 x 97.66 = 20.46 kPa instead of the 21.22 kPa it would hold in bone dry air at the same total pressure. The wet air feels closer to the altitude numbers below than to the sea level numbers above.

Altitude changes the total, not the mix

The composition of the air does not shift with height, so the mole fraction of oxygen stays at 0.20946 whether you are at the beach or on a mountain. What changes is the total pressure, and with it every partial pressure. The 1976 U.S. Standard Atmosphere table, which is the reference used for most altitude charts, gives the pressure falling from 101.325 kPa at sea level to 54.02 kPa at 5,000 meters.

That last column is why people who climb get tired. The share of oxygen in every breath does not change, so the lungs cannot complain that the air is poorer. What changes is how hard the air pushes, and the body has to work harder to get the same oxygen. Scuba divers run into the same arithmetic from the other direction: at 30 meters of seawater the total pressure is about 4 atmospheres, so the partial pressure of the nitrogen in the cylinder air is four times what it would be at the surface, and that is what makes decompression stops necessary.

Where partial pressure shows up, and what it leaves out

Partial pressure is the number behind a surprising number of everyday checks. Tire and scuba gauges work this way. A pressure cooker works this way too: sealing the pot lets the water vapor build until the total pressure inside is well above the air outside, and the water boils hotter than 100 degrees Celsius as a result. A gas mask rated for a certain oxygen partial pressure is rated for a certain altitude, and the ratings assume a fraction of 0.20946 for air.

Three limits are worth naming. First, real gases bend away from ideal behavior at high pressure, because the particles get close enough to push on each other, and the error grows past a few hundred atmospheres. Second, dissolved gases do not follow the mixture rule, which is why a gas dissolved in a liquid brings off bubbles when the pressure drops. Third, nothing here says how much of a gas you should breathe or be around, since that depends on health factors this page cannot judge.

The neighbouring tools cover the pieces around this one. The ideal gas law calculator handles one gas with a volume and a temperature, the mole fraction calculator turns a set of components into shares and mass percents, and the mole calculator works out how many moles a given weight of a substance holds. When the gas comes out of a liquid, the tire pressure calculator covers the everyday version of the same idea, and the molar mass calculator gives you the per-gram figure needed to turn a weight into moles.