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 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.^[4][5]

Examples:

• ${\displaystyle P_1}$  or${\displaystyle p_1}$  = pressure at time 1
• ${\displaystyle P_{{\text{H}}_2^{}}}$  or${\displaystyle p_{{\text{H}}_2^{}}}$  = partial pressure of hydrogen
• ${\displaystyle P_{a_{{\text{O}}_2^{}}}}$  or${\displaystyle p_{a_{{\text{O}}_2^{}}}}$  orP_aO₂ = arterial partial pressure of oxygen
• ${\displaystyle P_{v_{{\text{O}}_2^{}}}}$  or${\displaystyle p_{v_{{\text{O}}_2^{}}}}$  orP_vO₂ = venous partial pressure of oxygen

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.^[6] 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):

$${\displaystyle p=p_{{\text{N}}_2^{}}+p_{{\text{H}}_2^{}}+p_{{\text{NH}}_3^{}}}$$ where:

• ${\displaystyle p}$  = total pressure of the gas mixture
• ${\displaystyle p_{{\text{N}}_2^{}}}$  = partial pressure of nitrogen (N₂)
• ${\displaystyle p_{{\text{H}}_2^{}}}$  = partial pressure of hydrogen (H₂)
• ${\displaystyle p_{{\text{NH}}_3^{}}}$  = partial pressure of ammonia (NH₃)

Ideally the ratio of partial pressures equals the ratio of the number of molecules. That is, themole fraction${\displaystyle x_{\mathrm{i}}}$  of an individual gas component in anideal gasmixture can be expressed in terms of the component's partial pressure or themoles of the component:$${\displaystyle x_{\mathrm{i}}=\frac{p_{\mathrm{i}}}{p}=\frac{n_{\mathrm{i}}}{n}}$$ 

and the partial pressure of an individual gas component in an ideal gas can be obtained using this expression:$${\displaystyle p_{\mathrm{i}}=x_{\mathrm{i}}\cdot p}$$ 

The mole fraction of a gas component in a gas mixture is equal to the volumetric fraction of that component in a gas mixture.^[7]

The ratio of partial pressures relies on the following isotherm relation:$${\displaystyle \frac{V_{\mathrm{X}}}{V_{\mathrm{t}\mathrm{o}\mathrm{t}}}=\frac{p_{\mathrm{X}}}{p_{\mathrm{t}\mathrm{o}\mathrm{t}}}=\frac{n_{\mathrm{X}}}{n_{\mathrm{t}\mathrm{o}\mathrm{t}}}}$$ 

• V_X is the partial volume of any individual gas component (X)
• V_tot is the total volume of the gas mixture
• p_X is thepartial pressure of gas X
• p_tot is the total pressure of the gas mixture
• n_X is theamount of substance of gas (X)
• n_tot is the total amount of substance in gas mixture

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:^[8]$${\displaystyle V_{\mathrm{X}}=V_{\mathrm{t}\mathrm{o}\mathrm{t}}\times \frac{p_{\mathrm{X}}}{p_{\mathrm{t}\mathrm{o}\mathrm{t}}}=V_{\mathrm{t}\mathrm{o}\mathrm{t}}\times \frac{n_{\mathrm{X}}}{n_{\mathrm{t}\mathrm{o}\mathrm{t}}}}$$ 

• V_X is the partial volume of an individual gas component X in the mixture
• V_tot is the total volume of the gas mixture
• p_X is the partial pressure of gas X
• p_tot is the total pressure of the gas mixture
• n_X is theamount of substance of gas X
• n_tot is the total amount of substance in the gas mixture

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.^[9] 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:$${\displaystyle K_{\mathrm{p}}=\frac{p_C^c{p}_D^d}{p_A^a{p}_B^b}}$$ 

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).^[10] The equilibrium constant for that equilibrium is:

where:

• ${\displaystyle k}$  =  the equilibrium constant for thesolvation process
• ${\displaystyle p_x}$  =  partial pressure of gas${\displaystyle x}$  in equilibrium with asolution containing some of the gas
• ${\displaystyle C_x}$  =  the concentration of gas${\displaystyle x}$  in the liquid solution

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${\displaystyle k}$  is quite often referred to as the Henry's law constant.^[10][11][12]

Henry's law is sometimes written as:^[13]

where${\displaystyle k^{\prime }}$  is also referred to as the Henry's law constant.^[13] As can be seen by comparing equations (1) and (2) above,${\displaystyle k^{\prime }}$  is the reciprocal of${\displaystyle k}$ . 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 notreact chemically with the gas being dissolved.

Inunderwater diving the physiological effects of individual component gases ofbreathing gases are a function of partial pressure.^[14]

Using diving terms, partial pressure is calculated as:

partial pressure = (total absolute pressure) × (volume fraction of gas component)^[14]

For the component gas "i":

p_i = P × F_i^[14]

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:

pN₂ = 6 bar × 0.79 = 4.7 bar absolute

pO₂ = 6 bar × 0.21 = 1.3 bar absolute

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.^[15]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.^[14]

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.^[14]

The partial pressures of particularly oxygen (${\displaystyle p_{{\mathrm{O}}_2}}$ ) and carbon dioxide (${\displaystyle p_{\mathrm{C}{\mathrm{O}}_2}}$ ) are important parameters in tests ofarterial blood gases, but can also be measured in, for example,cerebrospinal fluid.^[why?]

• Blood gas tension – Partial pressure of blood gases
• Breathing gas – Gas used for human respiration
• Henry's law – Gas law regarding proportionality of dissolved gas
• Ideal gas – Mathematical model which approximates the behavior of real gases
  • Ideal gas law – Equation of the state of a hypothetical ideal gas
• Mole fraction – Proportion of a constituent in a mixture
  • Mole (unit) – SI unit of amount of substance
• Vapor – Substances in the gas phase at a temperature lower than its critical point