In a mixture ofgases, each constituent gas has apartial pressure which is the notionalpressure of that constituent gas as if it alone occupied the entirevolume of the original mixture at the sametemperature.[1] Thetotal pressure of anideal gas mixture is the sum of the partial pressures of the gases in the mixture (Dalton's Law).
Inrespiratory physiology, the partial pressure of a dissolved gas in liquid (such as oxygen in arterial blood) is also defined as the partial pressure of that gas as it would be undissolved in gas phase yet in equilibrium with the liquid.[2][3] This concept is also known asblood gas tension. In this sense, the diffusion of a gas liquid is said to be driven by differences in partial pressure (not concentration). Inchemistry andthermodynamics, this concept is generalized to non-ideal gases and instead calledfugacity. The partial pressure of a gas is a measure of itsthermodynamic activity. Gases dissolve, diffuse, and react according to their partial pressures and not according to theirconcentrations in a gas mixture or as a solute in solution.[4] This general property of gases is also true in chemical reactions of gases in biology.
The symbol for pressure is usuallyp orpp which may use a subscript to identify the pressure, and gas species are also referred to by subscript. When combined, these subscripts are applied recursively.[5][6]
Examples:
Dalton's law expresses the fact 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.[7] This equality arises from the fact that in an ideal gas, the molecules are so far apart that they do not interact with each other. Most actual real-world gases come very close to this ideal. For example, given an ideal gas mixture ofnitrogen (N2),hydrogen (H2) andammonia (NH3):
where:
Ideally the ratio of partial pressures equals the ratio of the number of molecules. That is, themole fraction of an individual gas component in anideal gasmixture can be expressed in terms of the component's partial pressure or themoles of the component:
and the partial pressure of an individual gas component in an ideal gas can be obtained using this expression:
| where: | |
| = mole fraction of any individual gas component in a gas mixture | |
| = partial pressure of any individual gas component in a gas mixture | |
| = moles of any individual gas component in a gas mixture | |
| = total moles of the gas mixture | |
| = total pressure of the gas mixture |
The mole fraction of a gas component in a gas mixture is equal to the volumetric fraction of that component in a gas mixture.[8]
The ratio of partial pressures relies on the following isotherm relation:
The partial volume of a particular gas in a mixture is the volume of one component of the gas mixture. It 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:[9]
Vapor pressure is the pressure of avapor in equilibrium with its non-vapor phases (i.e., liquid or solid). Most often the term is used to describe aliquid's tendency toevaporate. It is a measure of the tendency ofmolecules andatoms to escape from a liquid or asolid. 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 thenormal 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 displayed has graphs of the vapor pressures versus temperatures for a variety of liquids.[10] 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. At higher altitudes, the atmospheric pressure is less than that at sea level, so boiling points of liquids are reduced. At the top ofMount Everest, the atmospheric pressure is approximately 0.333 atm, so by using the graph, the boiling point ofdiethyl ether would be approximately 7.5 °C versus 34.6 °C at sea level (1 atm).
It is possible to work out theequilibrium 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:
the equilibrium constant of the reaction would be:
| where: | |
| = the equilibrium constant of the reaction | |
| = coefficient of reactant | |
| = coefficient of reactant | |
| = coefficient of product | |
| = coefficient of product | |
| = the partial pressure of raised to the power of | |
| = the partial pressure of raised to the power of | |
| = the partial pressure of raised to the power of | |
| = the partial pressure of raised to the power of |
For reversible reactions, changes in the total pressure, temperature or reactant concentrations will shift theequilibrium so as to favor either the right or left side of the reaction in accordance withLe Chatelier's Principle. However, thereaction kinetics may either oppose or enhance the equilibrium shift. In some cases, the reaction kinetics may be the overriding factor to consider.
Gases willdissolve inliquids to an extent that is determined by the equilibrium between the undissolved gas and the gas that has dissolved in the liquid (called thesolvent).[11] The equilibrium constant for that equilibrium is:
| 1 |
where:
The form of the equilibrium constant shows thatthe concentration of asolute gas in a solution is directly proportional to the partial pressure of that gas above the solution. This statement is known asHenry's law and the equilibrium constant is quite often referred to as the Henry's law constant.[11][12][13]
Henry's law is sometimes written as:[14]
| 2 |
where is also referred to as the Henry's law constant.[14] As can be seen by comparing equations (1) and (2) above, is the reciprocal of. 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 notreact chemically with the gas being dissolved.
Inunderwater diving the physiological effects of individual component gases ofbreathing gases are a function of partial pressure.[15]
Using diving terms, partial pressure is calculated as:
For the component gas "i":
For example, at 50 metres (164 ft) underwater, the total absolute pressure is 6 bar (600 kPa) (i.e., 1 bar ofatmospheric pressure + 5 bar of water pressure) and the partial pressures of the main components ofair,oxygen 21% by volume andnitrogen approximately 79% by volume are:
| where: | |
| pi | = partial pressure of gas component i = in the terms used in this article |
|---|---|
| P | = total pressure = in the terms used in this article |
| Fi | = volume fraction of gas component i = mole fraction,, in the terms used in this article |
| pN2 | = partial pressure of nitrogen = in the terms used in this article |
| pO2 | = partial pressure of oxygen = in the terms used in this article |
The minimum safe lower limit for the partial pressures of oxygen in a breathing gas mixture for diving is 0.16 bars (16 kPa) absolute.Hypoxia and sudden unconsciousness can become a problem with an oxygen partial pressure of less than 0.16 bar absolute.[16]Oxygen toxicity, involving convulsions, becomes a problem when oxygen partial pressure is too high. TheNOAA 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 also determines themaximum operating depth of a gas mixture.[15]
Narcosis is a problem when breathing gases at high pressure. Typically, the maximum total partial pressure of narcotic gases used when planning fortechnical diving may be around 4.5 bar absolute, based on anequivalent narcotic depth of 35 metres (115 ft).
The effect of a toxic contaminant such ascarbon monoxide in breathing gas is also related to the partial pressure when breathed. A mixture which may be relatively safe at the surface could be dangerously toxic at the maximum depth of a dive, or a tolerable level ofcarbon dioxide in the breathing loop of adiving rebreather may become intolerable within seconds during descent when the partial pressure rapidly increases, and could lead to panic or incapacitation of the diver.[15]
The partial pressures of particularly oxygen () and carbon dioxide () are important parameters in tests ofarterial blood gases, but can also be measured in, for example,cerebrospinal fluid.[why?]
| Unit | Arterial blood gas | Venous blood gas | Cerebrospinal fluid | Alveolarpulmonary gas pressures | |
|---|---|---|---|---|---|
| kPa | 11–13[17] | 4.0–5.3[17] | 5.3–5.9[17] | 14.2 | |
| mmHg | 75–100[18] | 30–40[19] | 40–44[20] | 107 | |
| kPa | 4.7–6.0[17] | 5.5–6.8[17] | 5.9–6.7[17] | 4.8 | |
| mmHg | 35–45[18] | 41–51[19] | 44–50[20] | 36 |
All symbols referring to gas species are in subscript,
