# Partial pressure

Partial pressure describes the partial pressure of an individual component or fraction in an ( ideal ) gas mixture .

The literal translation is partial pressure because the total pressure additive is composed of several parts, namely the partial pressures of the individual gas components. The sum of all partial pressures is equal to the total pressure. The partial pressure corresponds to the pressure that the individual gas component would exert if it were only present in the relevant volume .

## Distinction

In meteorology , the term vapor pressure is used as a synonym for the partial pressure of water in the air. In a gas mixture such as air, the boiling or condensation temperature of a gas component (e.g. water vapor) is that which is assigned to the partial pressure of the component, not the total pressure. It is also known as the dew point in meteorology .

## application

In biology and medicine , the oxygen and carbon dioxide partial pressures are particularly important. Here the term is also applied to the concentrations of these gases in solution , for example in blood or in water. The partial pressure given is that pressure of the gas which is in diffusion equilibrium with the relevant concentration in solution (at an imaginary or real interface between gas and liquid) . The Henry's law macroscopically describes the ratio of the partial pressures occurring in the gas phase, depending on the respective concentrations in the liquid phase. The partial pressure is always used instead of the mass concentration when the diffusion behavior of the dissolved gas is considered. Typical topics for this are the respiratory exchange processes in the lungs, the risk of gas embolism in diving ( decompression sickness and deep intoxication ) and aviation medicine and the development of gas bubble disease in fish. Because of this, the calculation of gas partial pressures in technical scuba diving or nitrox diving is the basis of the associated training courses.

In fire protection , the so-called active fire prevention lowers the oxygen content in the air so that people can still work in it for a certain time, but the flammability of certain materials is practically reduced to zero.

## Dalton's law

Dalton's law (Dalton's law, law of partial pressures), formulated by John Dalton in 1805 , states that the sum of all partial pressures in ideal gases is equal to the total pressure of the mixture . ${\ displaystyle p_ {i}}$${\ displaystyle p _ {\ text {total}}}$

For components results ${\ displaystyle k}$

${\ displaystyle p _ {\ text {total}} = \ sum _ {i = 1} ^ {k} p_ {i}}$

and from the equation of state of the ideal gases follows:

${\ displaystyle n _ {\ text {Total}} = \ sum _ {i = 1} ^ {k} n_ {i}}$

If a gas does not dissolve or practically does not dissolve from a mixture, the gas space created above is filled according to the two formulas. The partial pressure of a component is the boiling pressure of the pure component at this temperature.

From this it can be deduced that the partial pressure of the -th gas is equal to the product of the mole fraction of the gas times the total pressure of the mixture (for example air pressure ). This is an idealized representation for the case that the particles of the gas phase have no mutual interactions apart from mechanical ones (ideal gases), but these can normally be neglected. ${\ displaystyle i}$ ${\ displaystyle \ chi _ {i}}$

${\ displaystyle p_ {i} = \ chi _ {i} \ cdot p _ {\ text {total}}}$

The ratio of the number of particles ( amount of substance ) of a component to the total number of particles of the mixture corresponds to the amount of substance and thus also the partial pressure of the component to the total pressure of the mixture. Hence: ${\ displaystyle n_ {i}}$${\ displaystyle i}$${\ displaystyle n _ {\ mathrm {total}}}$${\ displaystyle \ chi _ {i}}$${\ displaystyle p_ {i}}$${\ displaystyle i}$${\ displaystyle p _ {\ mathrm {total}}}$

${\ displaystyle {\ frac {n_ {i}} {n _ {\ mathrm {Total}}}} = {\ frac {p_ {i}} {p _ {\ mathrm {Total}}}}}$

Example : dry air at sea ​​level

The following table shows the composition of completely dry air at sea level ( normal condition ), i.e. at an air pressure of 1013.25  hPa .

The volume fraction can be equated with the particle fraction ( molar fraction ), since these are approximately ideal gases . Other components of the air can be neglected due to their low proportion.

Overview: partial pressures of dry air at sea level
(using all common units)
component Volume fraction% Partial pressure in
hPa (mbar) kPa mmHg (Torr) bar atm
air 100.00 1013.25 101.325 759.96 1.01325 1.00000
nitrogen 78.090 791.25 79.13 593.45 0.79125 0.78090
oxygen 20,950 212.28 21.23 159.21 0.21228 0.20950
argon 0.927 9.39 0.939 7.04 0.00939 0.00927
carbon dioxide 0.039 0.39 0.039 0.293 0.00039 0.00039
Overview: Selected partial pressures of air / compressed air in the water depth
Water depth Ambient pressure Oxygen partial pressure Nitrogen partial pressure
0 m 1 bar 0.21 bar 0.78 bar
10 m 2 bar 0.42 bar 1.56 bar
20 m 3 bar 0.63 bar 2.34 bar
30 m 4 bar 0.84 bar 3.12 bar
40 m 5 bar 1.05 bar 3.90 bar

## Individual evidence

1. partial pressure. (PDF; 322 kB) Archived from the original on December 3, 2012 ; Retrieved May 19, 2011 .
2. John Dalton. Retrieved May 19, 2011 .
3. ^ Dalton's law or partial pressure law. Retrieved May 19, 2011 .
4. a b Mixtures (PDF). (PDF; 591 kB) Archived from the original on November 15, 2016 ; Retrieved May 19, 2011 .
5. For moist air you have to subtract the water vapor pressure from the air pressure and divide the residual pressure among the gases in proportion to their proportions in the dry air.