In a mixture of ideal gases, each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume.^[1] The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture.

In chemistry, the partial pressure of a gas in a mixture of gases is defined as above. The partial pressure of a gas dissolved in a liquid is the partial pressure of that gas which would be generated in a gas phase in equilibrium with the liquid at the same temperature. The partial pressure of a gas is a measure of thermodynamic activity of the gas's molecules. Gases will always flow from a region of higher partial pressure to one of lower pressure; the larger this difference, the faster the flow. Gases dissolve, diffuse, and react according to their partial pressures, and not according to their concentrations in gas mixtures or liquids.

This general property of gases is also true of chemical reactions of gases in biology. For example, the necessary amount of oxygen for human respiration, and the amount that is toxic, is set by the partial pressure of oxygen alone. This is true across a very wide range of different concentrations of oxygen present in various inhaled breathing gases, or dissolved in blood.

Dalton's law of partial pressures[link]

The partial pressure of an ideal gas in a mixture is equal to the pressure it would exert if it occupied the same volume alone at the same temperature. This is because ideal gas molecules are so far apart that they don't interfere with each other at all. Actual real-world gases come very close to this ideal.

A consequence of this is that the total pressure of a mixture of ideal gases is equal to the sum of the partial pressures of the individual gases in the mixture as stated by Dalton's law.^[2] For example, given an ideal gas mixture of nitrogen (N₂), hydrogen (H₂) and ammonia (NH₃):

Failed to parse (Missing texvc executable; please see math/README to configure.): p = p_{{\mathrm{N}}_2} + p_{{\mathrm{H}}_2} + p_{{\mathrm{NH}}_3}

Ideal gas mixtures[link]

Ideally the ratio of partial pressures is the same as the ratio of molecules. That is, the mole fraction of an individual gas component in an ideal gas mixture can be expressed in terms of the component's partial pressure or the moles of the component:

Failed to parse (Missing texvc executable; please see math/README to configure.): x_{\mathrm{i}} = \frac{p_{\mathrm{i}}}{p} = \frac{n_{\mathrm{i}}}{n}

and the partial pressure of an individual gas component in an ideal gas can be obtained using this expression:

Failed to parse (Missing texvc executable; please see math/README to configure.): p_{\mathrm{i}} = x_{\mathrm{i}} \cdot p

The mole fraction of a gas component in a gas mixture is equal to the volumetric fraction of that component in a gas mixture.^[3]

Partial volume (Amagat's law of additive volume)[link]

The partial volume of a particular gas is the volume which the gas would have if it alone occupied the volume, with unchanged pressure and temperature, and is useful in gas mixtures, e.g. air, to focus on one particular gas component, e.g. oxygen.

It can be approximated both from partial pressure and molar fraction:^[4]

Failed to parse (Missing texvc executable; please see math/README to configure.): V_x = V_{tot} \times \frac{p_x}{p_{tot}} = V_{tot} \times \frac{n_x}{n_{tot}}

• V_x is the partial volume of any individual gas component (X)
• V_tot is the total volume in gas mixture
• p_x is the partial pressure of gas X
• p_tot is the total pressure of gas mixture
• n_x is the amount of substance of a gas (X)
• n_tot is the total amount of substance in gas mixture

Vapor pressure[link]

A typical vapor pressure chart for various liquids

Vapor pressure is the pressure of a vapor in equilibrium with its non-vapor phases (i.e., liquid or solid). Most often the term is used to describe a liquid's tendency to evaporate. It is a measure of the tendency of molecules and atoms to escape from a liquid or a solid. A liquid's atmospheric pressure boiling point corresponds to the temperature at which its vapor pressure is equal to the surrounding atmospheric pressure and it is often called the normal boiling point.

The higher the vapor pressure of a liquid at a given temperature, the lower the normal boiling point of the liquid.

The vapor pressure chart to the right has graphs of the vapor pressures versus temperatures for a variety of liquids.^[5] As can be seen in the chart, the liquids with the highest vapor pressures have the lowest normal boiling points.

For example, at any given temperature, methyl chloride has the highest vapor pressure of any of the liquids in the chart. It also has the lowest normal boiling point (-24.2 °C), which is where the vapor pressure curve of methyl chloride (the blue line) intersects the horizontal pressure line of one atmosphere (atm) of absolute vapor pressure.

Equilibrium constants of reactions involving gas mixtures[link]

It is possible to work out the equilibrium constant for a chemical reaction involving a mixture of gases given the partial pressure of each gas and the overall reaction formula. For a reversible reaction involving gas reactants and gas products, such as:

Failed to parse (Missing texvc executable; please see math/README to configure.): a\,A + b\,B \leftrightarrow c\,C + d\,D

the equilibrium constant of the reaction would be:

Failed to parse (Missing texvc executable; please see math/README to configure.): K_p = \frac{p_C^c\, p_D^d} {p_A^a\, p_B^b}

raised to the power of Failed to parse (Missing texvc executable; please see math/README to configure.): c

raised to the power of Failed to parse (Missing texvc executable; please see math/README to configure.): d

raised to the power of Failed to parse (Missing texvc executable; please see math/README to configure.): a

raised to the power of Failed to parse (Missing texvc executable; please see math/README to configure.): b

For reversible reactions, changes in the total pressure, temperature or reactant concentrations will shift the equilibrium so as to favor either the right or left side of the reaction in accordance with Le Chatelier's Principle. However, the reaction kinetics may either oppose or enhance the equilibrium shift. In some cases, the reaction kinetics may be the over-riding factor to consider.

Henry's Law and the solubility of gases[link]

Gases will dissolve in liquids to an extent that is determined by the equilibrium between the undissolved gas and the gas that has dissolved in the liquid (called the solvent).^[6] The equilibrium constant for that equilibrium is:

(1)     Failed to parse (Missing texvc executable; please see math/README to configure.): k = \frac {p_x}{C_x}

where:
Failed to parse (Missing texvc executable; please see math/README to configure.): k	=  the equilibrium constant for the solvation process
Failed to parse (Missing texvc executable; please see math/README to configure.): p_x	=  partial pressure of gas Failed to parse (Missing texvc executable; please see math/README to configure.): x in equilibrium with a solution containing some of the gas
Failed to parse (Missing texvc executable; please see math/README to configure.): C_x	=  the concentration of gas Failed to parse (Missing texvc executable; please see math/README to configure.): x in the liquid solution

The form of the equilibrium constant shows that the concentration of a solute gas in a solution is directly proportional to the partial pressure of that gas above the solution. This statement is known as Henry's Law and the equilibrium constant Failed to parse (Missing texvc executable; please see math/README to configure.): k

is quite often referred to as the Henry's Law constant.[6][7][8]

Henry's Law is sometimes written as:^[9]

(2)     Failed to parse (Missing texvc executable; please see math/README to configure.): k' = \frac {C_x}{p_x}

where Failed to parse (Missing texvc executable; please see math/README to configure.): k'

is also referred to as the Henry's Law constant.[9] As can be seen by comparing equations (1) and (2) above,  Failed to parse (Missing texvc executable; please see math/README to configure.): k'
is the reciprocal of Failed to parse (Missing texvc executable; please see math/README to configure.): k

. Since both may be referred to as the Henry's Law constant, readers of the technical literature must be quite careful to note which version of the Henry's Law equation is being used.

Henry's Law is an approximation that only applies for dilute, ideal solutions and for solutions where the liquid solvent does not react chemically with the gas being dissolved.

Partial pressure in diving breathing gases[link]

In recreational diving and professional diving the richness of individual component gases of breathing gases is expressed by partial pressure.

Using diving terms, partial pressure is calculated as:

partial pressure = (total absolute pressure) × (volume fraction of gas component)

For the component gas "i":

ppi = P × Fi

For example, at 50 metres (165 feet), the total absolute pressure is 6 bar (600 kPa) (i.e., 1 bar of atmospheric pressure + 5 bar of water pressure) and the partial pressures of the main components of air, oxygen 21% by volume and nitrogen 79% by volume are:

ppN2 = 6 bar × 0.79 = 4.7 bar absolute

ppO2 = 6 bar × 0.21 = 1.3 bar absolute

in the terms used in this article

in the terms used in this article

in the terms used in this article

in the terms used in this article

The minimum safe lower limit for the partial pressures of oxygen in a gas mixture is 0.16 bar (16 kPa) absolute. Hypoxia and sudden unconsciousness becomes a problem with an oxygen partial pressure of less than 0.16 bar absolute. Oxygen toxicity, involving convulsions, becomes a problem when oxygen partial pressure is too high. The NOAA Diving Manual recommends a maximum single exposure of 45 minutes at 1.6 bar absolute, of 120 minutes at 1.5 bar absolute, of 150 minutes at 1.4 bar absolute, of 180 minutes at 1.3 bar absolute and of 210 minutes at 1.2 bar absolute. Oxygen toxicity becomes a risk when these oxygen partial pressures and exposures are exceeded. The partial pressure of oxygen determines the maximum operating depth of a gas mixture.

Nitrogen narcosis is a problem when breathing gases at high pressure. Typically, the maximum total partial pressure of narcotic gases used when planning for technical diving is 4.5 bar absolute, based on an equivalent narcotic depth of 35 metres (115 ft).

In medicine[link]

The partial pressures of particularly oxygen (Failed to parse (Missing texvc executable; please see math/README to configure.): p_{{\mathrm{O}}_2} ) and carbon dioxide (Failed to parse (Missing texvc executable; please see math/README to configure.): p_{{\mathrm{CO}}_2} ) are important parameters in tests of arterial blood gases, but can also be measured in, for example, cerebrospinal fluid.

See also[link]

Underwater diving portal

• Breathing gas
• Henry's law
• Ideal gas and Ideal gas law
• Mole fraction and Mole (unit)
• Vapor

References[link]