Partial pressure
In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas as if it alone occupied the entire volume of the original mixture at the same temperature. The total pressure of an ideal gas mixture is the sum of the partial pressures of the gases in the mixture.
In respiratory physiology, the partial pressure of a dissolved gas in liquid is also defined as the partial pressure of that gas as it would be undissolved in gas phase yet in equilibrium with the liquid. This concept is also known as blood gas tension. In this sense, the diffusion of a gas liquid is said to be driven by differences in partial pressure. In chemistry and thermodynamics, this concept is generalized to non-ideal gases and instead called fugacity. The partial pressure of a gas is a measure of its thermodynamic activity. Gases dissolve, diffuse, and react according to their partial pressures and not according to their concentrations in a gas mixture or as a solute in solution. This general property of gases is also true in chemical reactions of gases in biology.
Symbol
The symbol for pressure is usually or 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.Examples:
- or = pressure at time 1
- or = partial pressure of hydrogen
- or or PaO2 = arterial partial pressure of oxygen
- or or PvO2 = venous partial pressure of oxygen
Dalton's law of partial pressures
where:
- = total pressure of the gas mixture
- = partial pressure of nitrogen
- = partial pressure of hydrogen
- = partial pressure of ammonia
Ideal gas mixtures
and the partial pressure of an individual gas component in an ideal gas can be obtained using this expression:
The mole fraction of a gas component in a gas mixture is equal to the volumetric fraction of that component in a gas mixture.
The ratio of partial pressures relies on the following isotherm relation:
- VX is the partial volume of any individual gas component
- Vtot is the total volume of the gas mixture
- pX is the partial pressure of gas X
- ptot is the total pressure of the gas mixture
- nX is the amount of substance of gas
- ntot is the total amount of substance in gas mixture
Partial volume (Amagat's law of additive volume)
It can be approximated both from partial pressure and molar fraction:
- VX is the partial volume of an individual gas component X in the mixture
- Vtot is the total volume of the gas mixture
- pX is the partial pressure of gas X
- ptot is the total pressure of the gas mixture
- nX is the amount of substance of gas X
- ntot is the total amount of substance in the gas mixture
Vapor pressure
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. 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, which is where the vapor pressure curve of methyl chloride intersects the horizontal pressure line of one atmosphere 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 of Mount Everest, the atmospheric pressure is approximately 0.333 atm, so by using the graph, the boiling point of diethyl ether would be approximately 7.5 °C versus 34.6 °C at sea level.
Equilibrium constants of reactions involving gas mixtures
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:the equilibrium constant of the reaction would be:
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 overriding factor to consider.
Henry's law and the solubility of gases
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. The equilibrium constant for that equilibrium is:where:
- = the equilibrium constant for the solvation process
- = partial pressure of gas in equilibrium with a solution containing some of the gas
- = the concentration of gas in the liquid solution
Henry's law is sometimes written as:
where is also referred to as the Henry's law constant. As can be seen by comparing equations and 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 not react chemically with the gas being dissolved.
In diving breathing gases
In underwater diving the physiological effects of individual component gases of breathing gases are a function of partial pressure.Using diving terms, partial pressure is calculated as:
For the component gas "i":
For example, at underwater, the total absolute pressure is and the partial pressures of the main components of air, oxygen 21% by volume and nitrogen approximately 79% by volume are:
The minimum safe lower limit for the partial pressures of oxygen in a breathing gas mixture for diving is absolute. Hypoxia and sudden unconsciousness can become 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 also determines the maximum operating depth of a gas mixture.
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 may be around 4.5 bar absolute, based on an equivalent narcotic depth of.
The effect of a toxic contaminant such as carbon 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 of carbon dioxide in the breathing loop of a diving rebreather may become intolerable within seconds during descent when the partial pressure rapidly increases, and could lead to panic or incapacitation of the diver.
In medicine
The partial pressures of particularly oxygen and carbon dioxide are important parameters in tests of arterial blood gases, but can also be measured in, for example, cerebrospinal fluid.| Unit | Arterial blood gas | Venous blood gas | Cerebrospinal fluid | Alveolar pulmonary gas pressures | |
| oxygen partial pressure| | kPa | 11–13 | 4.0–5.3 | 5.3–5.9 | 14.2 |
| oxygen partial pressure| | mmHg | 75–100 | 30–40 | 40–44 | 107 |
| carbon dioxide partial pressure| | kPa | 4.7–6.0 | 5.5–6.8 | 5.9–6.7 | 4.8 |
| carbon dioxide partial pressure| | mmHg | 35–45 | 41–51 | 44–50 | 36 |