Vapor pressure

# Vapor pressure

Overview
Vapor pressure or equilibrium vapor pressure is the pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

of a vapor
Vapor
A vapor or vapour is a substance in the gas phase at a temperature lower than its critical point....

in thermodynamic equilibrium
Thermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...

with its condensed phase
Phase (matter)
In the physical sciences, a phase is a region of space , throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, and chemical composition...

s in a closed system. All liquid
Liquid
Liquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...

s have a tendency to evaporate, and some solid
Solid
Solid is one of the three classical states of matter . It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a...

s can sublimate into a gaseous form. Vice versa, all gas
Gas
Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...

es have a tendency to condense
Condensation
Condensation is the change of the physical state of matter from gaseous phase into liquid phase, and is the reverse of vaporization. When the transition happens from the gaseous phase into the solid phase directly, the change is called deposition....

back to their liquid form, or deposit back to solid form, as long as the temperature is below their critical temperature or decomposition temperature. In plain terms, a liquid evaporates at all pressures below its vapor pressure, while remaining stable at pressure above the vapor pressure.
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Encyclopedia
Vapor pressure or equilibrium vapor pressure is the pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

of a vapor
Vapor
A vapor or vapour is a substance in the gas phase at a temperature lower than its critical point....

in thermodynamic equilibrium
Thermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...

with its condensed phase
Phase (matter)
In the physical sciences, a phase is a region of space , throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, and chemical composition...

s in a closed system. All liquid
Liquid
Liquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...

s have a tendency to evaporate, and some solid
Solid
Solid is one of the three classical states of matter . It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a...

s can sublimate into a gaseous form. Vice versa, all gas
Gas
Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...

es have a tendency to condense
Condensation
Condensation is the change of the physical state of matter from gaseous phase into liquid phase, and is the reverse of vaporization. When the transition happens from the gaseous phase into the solid phase directly, the change is called deposition....

back to their liquid form, or deposit back to solid form, as long as the temperature is below their critical temperature or decomposition temperature. In plain terms, a liquid evaporates at all pressures below its vapor pressure, while remaining stable at pressure above the vapor pressure.

The equilibrium vapor pressure is an indication of a liquid's evaporation rate. It relates to the tendency of particles to escape from the liquid (or a solid). A substance with a high vapor pressure at normal temperatures is often referred to as volatile
Volatility (chemistry)
In chemistry and physics, volatility is the tendency of a substance to vaporize. Volatility is directly related to a substance's vapor pressure. At a given temperature, a substance with higher vapor pressure vaporizes more readily than a substance with a lower vapor pressure.The term is primarily...

.

The vapor pressure of any substance increases non-linearly with temperature according to the Clausius–Clapeyron relation. The atmospheric pressure
Atmospheric pressure
Atmospheric pressure is the force per unit area exerted into a surface by the weight of air above that surface in the atmosphere of Earth . In most circumstances atmospheric pressure is closely approximated by the hydrostatic pressure caused by the weight of air above the measurement point...

boiling point
Boiling point
The boiling point of an element or a substance is the temperature at which the vapor pressure of the liquid equals the environmental pressure surrounding the liquid....

of a liquid (also known as the normal boiling point) is the temperature at which the vapor pressure equals the ambient atmospheric pressure. With any incremental increase in that temperature, the vapor pressure becomes sufficient to overcome atmospheric pressure
Atmospheric pressure
Atmospheric pressure is the force per unit area exerted into a surface by the weight of air above that surface in the atmosphere of Earth . In most circumstances atmospheric pressure is closely approximated by the hydrostatic pressure caused by the weight of air above the measurement point...

and lift the liquid to form vapor bubbles inside the bulk of the substance. Bubble
Liquid bubble
A bubble is a globule of one substance in another, usually gas in a liquid.Due to the Marangoni effect, bubbles may remain intact when they reach the surface of the immersive substance.-Common examples:...

formation deeper in the liquid requires a higher pressure, and therefore higher temperature, because the fluid pressure increases above the atmospheric pressure as the depth increases.

The vapor pressure that a single component in a mixture contributes to the total pressure in the system is called partial pressure
Partial pressure
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. The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture....

. For example, air at sea level, saturated with water vapor at 20 °C has a partial pressures of 23 mbar of water
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

, and about 780 mbar of nitrogen
Nitrogen
Nitrogen is a chemical element that has the symbol N, atomic number of 7 and atomic mass 14.00674 u. Elemental nitrogen is a colorless, odorless, tasteless, and mostly inert diatomic gas at standard conditions, constituting 78.08% by volume of Earth's atmosphere...

, 210 mbar of oxygen
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...

and 9 mbar of argon
Argon
Argon is a chemical element represented by the symbol Ar. Argon has atomic number 18 and is the third element in group 18 of the periodic table . Argon is the third most common gas in the Earth's atmosphere, at 0.93%, making it more common than carbon dioxide...

.

## Measurement and units

Vapor pressure is measured in the standard units of pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

. The International System of Units
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

(SI) recognizes pressure as a derived unit
SI derived unit
The International System of Units specifies a set of seven base units from which all other units of measurement are formed, by products of the powers of base units. These other units are called SI derived units, for example, the SI derived unit of area is square metre , and of density is...

with the dimension of force per area and designates the pascal
Pascal (unit)
The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...

(Pa) as its standard unit. One pascal is one newton per square meter (N·m−2 or kg·m−1·s−2).

Experimental measurement of vapor pressure is a simple procedure for common pressures between 1 and 200 kPa. Most accurate results are obtained near the boiling point of substances and large errors result for measurements smaller than . Procedures often consist of purifying the test substance, isolating it in a container, evacuating any foreign gas, then measuring the equilibrium pressure of the gaseous phase of the substance in the container at different temperatures. Better accuracy is achieved when care is taken to ensure that the entire substance and its vapor are at the prescribed temperature. This is often done, as with the use of an isoteniscope
Isoteniscope
An Isoteniscope is a device used to measure the vapor pressure of liquids. It consists of a submerged manometer and container holding the substance whose vapor pressure is being measured. The open end of the manometer is then connected to a pressure measuring devise...

, by submerging the containment area in a liquid bath.

## Relation to boiling point of liquids

As a general trend, vapor pressures of liquids at ambient temperatures increase with decreasing boiling points.
This is illustrated in the vapor pressure chart (see right) that shows graphs of the vapor pressures versus temperatures for a variety of liquids.

For example, at any given temperature, propane
Propane
Propane is a three-carbon alkane with the molecular formula , normally a gas, but compressible to a transportable liquid. A by-product of natural gas processing and petroleum refining, it is commonly used as a fuel for engines, oxy-gas torches, barbecues, portable stoves, and residential central...

has the highest vapor pressure of any of the liquids in the chart. It also has the lowest normal boiling point (−42.1 °C), which is where the vapor pressure curve of propane (the purple line) intersects the horizontal pressure line of one atmosphere
Atmosphere (unit)
The standard atmosphere is an international reference pressure defined as 101325 Pa and formerly used as unit of pressure. For practical purposes it has been replaced by the bar which is 105 Pa...

(atm) of absolute vapor pressure.

Although the relation between vapor pressure and temperature is non-linear, the chart uses a logarithmic vertical axis to produce slightly curved lines, so one chart can graph many liquids. The vapor pressure of a liquid at its boiling point equals the pressure of its containing environment.

## Liquid mixtures

Raoult's law gives an approximation to the vapor pressure of mixtures of liquids. It states that the activity (pressure or fugacity
Fugacity
In chemical thermodynamics, the fugacity of a real gas is an effective pressure which replaces the true mechanical pressure in accurate chemical equilibrium calculations. It is equal to the pressure of an ideal gas which has the same chemical potential as the real gas. For example, nitrogen gas ...

) of a single-phase mixture is equal to the mole-fraction-weighted sum of the components' vapor pressures:

where p is vapor pressure, i is a component index
Index (mathematics)
The word index is used in variety of senses in mathematics.- General :* In perhaps the most frequent sense, an index is a number or other symbol that indicates the location of a variable in a list or array of numbers or other mathematical objects. This type of index is usually written as a...

, and χ is a mole fraction of that component in liquid mixture. The term is the partial pressure of component i in the mixture. Raoult's Law is applicable only to non-electrolytes (uncharged species); it is most appropriate for non-polar molecules with only weak intermolecular attractions (such as London forces).

Systems that have vapor pressures higher than indicated by the above formula are said to have positive deviations. Such a deviation suggests weaker intermolecular attraction than in the pure components, so that the molecules can be thought of as being "held in" the liquid phase less strongly than in the pure liquid. An example is the azeotrope
Azeotrope
An azeotrope is a mixture of two or more liquids in such a ratio that its composition cannot be changed by simple distillation. This occurs because, when an azeotrope is boiled, the resulting vapor has the same ratio of constituents as the original mixture....

of approximately 95% ethanol and water. Because the azeotrope's vapor pressure is higher than predicted by Raoult's law, it boils at a temperature below that of either pure component.

There are also systems with negative deviations that have vapor pressures that are lower than expected. Such a deviation is evidence for stronger intermolecular attraction between the constituents of the mixture than exists in the pure components. Thus, the molecules are "held in" the liquid more strongly when a second molecule is present. An example is a mixture of trichloromethane (chloroform) and 2-propanone (acetone), which boils above the boiling point of either pure component.

## Solids

Equilibrium vapor pressure can be defined as the pressure reached when a condensed phase is in equilibrium with its own vapor. In the case of an equilibrium solid, such as a crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...

, this can be defined as the pressure when the rate of sublimation
Sublimation (physics)
Sublimation is the process of transition of a substance from the solid phase to the gas phase without passing through an intermediate liquid phase...

of a solid matches the rate of deposition of its vapor phase. For most solids this pressure is very low, but some notable exceptions are naphthalene
Naphthalene
Naphthalene is an organic compound with formula . It is a white crystalline solid with a characteristic odor that is detectable at concentrations as low as 0.08 ppm by mass. As an aromatic hydrocarbon, naphthalene's structure consists of a fused pair of benzene rings...

, dry ice
Dry ice
Dry ice, sometimes referred to as "Cardice" or as "card ice" , is the solid form of carbon dioxide. It is used primarily as a cooling agent. Its advantages include lower temperature than that of water ice and not leaving any residue...

(the vapor pressure of dry ice is 5.73 MPa (831 psi, 56.5 atm) at 20 degrees Celsius, meaning it causes most sealed containers to explode), and ice. All solid materials have a vapor pressure. However, due to their often extremely low values, measurement can be rather difficult. Typical techniques include the use of thermogravimetry
Thermogravimetry
Thermogravimetry is a branch of physical chemistry, materials research, and thermal analysis...

and gas transpiration.

The sublimation pressure can be calculated from extrapolated liquid vapor pressures (of the supercooled liquid) if the heat of fusion
Enthalpy of fusion
The enthalpy of fusion is the change in enthalpy resulting from heating one mole of a substance to change its state from a solid to a liquid. The temperature at which this occurs is the melting point....

is known. The heat of fusion must be added, in addition to the heat of vaporization to vaporize a solid. Assuming that the heat of fusion is temperature-independent and ignoring additional transition temperatures between different solid phases the equation

with:
 = Sublimation pressure of the solid component at the temperature = Extrapolated vapor pressure of the liquid component at the temperature = Heat of fusion = Gas constantGas constantThe gas constant is a physical constant which is featured in many fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation. It is equivalent to the Boltzmann constant, but expressed in units of energy The gas constant (also known as the molar, universal,... = Sublimation temperature = Melting point temperature

gives a fair estimation for temperatures not too far from the melting point. This equation also shows that the sublimation pressure is lower than the extrapolated liquid vapor pressure (ΔH m is positive) and the difference grows with increased distance from the melting point.

## Boiling point of water in nature

Like all liquids, water boils when its vapor pressure reaches its surrounding pressure. In nature, the atmospheric pressure is lower at higher elevations and water boils at a lower temperature. The boiling temperature of water
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

for atmospheric pressures can be approximated by Antoine equation:

or transformed into this temperature-explicit form:

where the temperature is the boiling point in degrees Celsius
Celsius
Celsius is a scale and unit of measurement for temperature. It is named after the Swedish astronomer Anders Celsius , who developed a similar temperature scale two years before his death...

and the pressure is in Torr
Torr
The torr is a non-SI unit of pressure with the ratio of 760 to 1 standard atmosphere, chosen to be roughly equal to the fluid pressure exerted by a millimetre of mercury, i.e., a pressure of 1 torr is approximately equal to 1 mmHg...

.

## Dühring's rule

Dühring's rule states that a linear relationship exists between the temperatures at which two solutions exert the same vapor pressure.

## Examples

The following table is a list of a variety of substances ordered by increasing vapor pressure.
Substance Vapor Pressure
(SI units)
Vapor Pressure
(Bar);
Vapor Pressure
(mmHg);
Temperature
Tungsten
Tungsten
Tungsten , also known as wolfram , is a chemical element with the chemical symbol W and atomic number 74.A hard, rare metal under standard conditions when uncombined, tungsten is found naturally on Earth only in chemical compounds. It was identified as a new element in 1781, and first isolated as...

100 Pa 0.001 0.75 3203 °C
Ethylene glycol
Ethylene glycol
Ethylene glycol is an organic compound widely used as an automotive antifreeze and a precursor to polymers. In its pure form, it is an odorless, colorless, syrupy, sweet-tasting liquid...

500 Pa 0.005 3.75 20 °C
Xenon difluoride
Xenon difluoride
Xenon difluoride is a powerful fluorinating agent with the chemical formula , and one of the most stable xenon compounds. Like most covalent inorganic fluorides it is moisture sensitive. It decomposes on contact with light or water vapour. Xenon difluoride is a dense, white crystalline solid. It...

600 Pa 0.006 4.50 25 °C
Water
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

(H2O)
2.3 kPa 0.023 17.5 20 °C
Propanol
Propanol
Propanol may refer to:*Propan-1-ol, or n-propanol: CH3CH2CH2OH, the most common meaning*Propan-2-ol, or isopropyl alcohol, or isopropanol: 2CHOH...

2.4 kPa 0.024 18.0 20 °C
Ethanol
Ethanol
Ethanol, also called ethyl alcohol, pure alcohol, grain alcohol, or drinking alcohol, is a volatile, flammable, colorless liquid. It is a psychoactive drug and one of the oldest recreational drugs. Best known as the type of alcohol found in alcoholic beverages, it is also used in thermometers, as a...

5.83 kPa 0.0583 43.7 20 °C
Methyl isobutyl ketone
Methyl isobutyl ketone
Methyl isobutyl ketone is the organic compound with the formula 2CHCH2CCH3. This colourless liquid, a ketone, is widely used as a solvent.-Production:...

26.48 kPa 0.2648 198.62 25 °C
Freon 113 37.9 kPa 0.379 284 20 °C
Acetaldehyde
Acetaldehyde
Acetaldehyde is an organic chemical compound with the formula CH3CHO or MeCHO. It is one of the most important aldehydes, occurring widely in nature and being produced on a large scale industrially. Acetaldehyde occurs naturally in coffee, bread, and ripe fruit, and is produced by plants as part...

98.7 kPa 0.987 740 20 °C
Butane
Butane
Butane is a gas with the formula C4H10 that is an alkane with four carbon atoms. The term may refer to any of two structural isomers, or to a mixture of them: in the IUPAC nomenclature, however, butane refers only to the unbranched n-butane isomer; the other one being called "methylpropane" or...

220 kPa 2.2 1650 20 °C
Formaldehyde
Formaldehyde
Formaldehyde is an organic compound with the formula CH2O. It is the simplest aldehyde, hence its systematic name methanal.Formaldehyde is a colorless gas with a characteristic pungent odor. It is an important precursor to many other chemical compounds, especially for polymers...

435.7 kPa 4.357 3268 20 °C
Propane
Propane
Propane is a three-carbon alkane with the molecular formula , normally a gas, but compressible to a transportable liquid. A by-product of natural gas processing and petroleum refining, it is commonly used as a fuel for engines, oxy-gas torches, barbecues, portable stoves, and residential central...

7600 25.6 °C
Carbonyl sulfide
Carbonyl sulfide
Carbonyl sulfide is the chemical compound with the formula OCS. Commonly written as COS, it is a colourless flammable gas with an unpleasant odor. It is a linear molecule consisting of a carbonyl group double bonded to a sulfur atom...

1.255 MPa 12.55 9412 25 °C
Carbon dioxide
Carbon dioxide
Carbon dioxide is a naturally occurring chemical compound composed of two oxygen atoms covalently bonded to a single carbon atom...

5.7 MPa 57 20 °C

## Meaning in meteorology

In meteorology
Meteorology
Meteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw breakthroughs occur after observing networks developed across several countries...

, the term vapor pressure is used to mean the partial pressure
Partial pressure
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. The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture....

of water vapor
Water vapor
Water vapor or water vapour , also aqueous vapor, is the gas phase of water. It is one state of water within the hydrosphere. Water vapor can be produced from the evaporation or boiling of liquid water or from the sublimation of ice. Under typical atmospheric conditions, water vapor is continuously...

in the atmosphere, even if it is not in equilibrium, and the equilibrium vapor pressure is specified otherwise. Meteorologists also use the term saturation vapor pressure to refer to the equilibrium vapor pressure of water or brine
Brine
Brine is water, saturated or nearly saturated with salt .Brine is used to preserve vegetables, fruit, fish, and meat, in a process known as brining . Brine is also commonly used to age Halloumi and Feta cheeses, or for pickling foodstuffs, as a means of preserving them...

above a flat surface, to distinguish it from equilibrium vapor pressure, which takes into account the shape and size of water droplets and particulates in the atmosphere.

• Absolute humidity
• Clausius-Clapeyron relation
Clausius-Clapeyron relation
The Clausius–Clapeyron relation, named after Rudolf Clausius and Benoît Paul Émile Clapeyron, who defined it sometime after 1834, is a way of characterizing a discontinuous phase transition between two phases of matter. On a pressure–temperature diagram, the line separating the two phases is known...

• Partial pressure
Partial pressure
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. The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture....

• Relative humidity
Relative humidity
Relative humidity is a term used to describe the amount of water vapor in a mixture of air and water vapor. It is defined as the partial pressure of water vapor in the air-water mixture, given as a percentage of the saturated vapor pressure under those conditions...

• Relative volatility
Relative volatility
Relative volatility is a measure comparing the vapor pressures of the components in a liquid mixture of chemicals. This quantity is widely used in designing large industrial distillation processes. In effect, it indicates the ease or difficulty of using distillation to separate the more volatile...

• Saturation vapor density
Saturation vapor density
Saturation vapor density is a concept closely tied with saturation vapor pressure. It is useful for getting an exact quantity of water vapor in the air from a relative humidity . Given an RH percentage, the density of water in the air is given by RH * SVD = Actual Vapor Density. Alternatively, RH...

• Triple point
Triple point
In thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases of that substance coexist in thermodynamic equilibrium...

• Vapor-liquid equilibrium
Vapor-liquid equilibrium
Vapor–liquid equilibrium is a condition where a liquid and its vapor are in equilibrium with each other, a condition or state where the rate of evaporation equals the rate of condensation on a molecular level such that there is no net vapor-liquid interconversion...

• Vapour pressure of water
Vapour pressure of water
The vapour pressure of water is the pressure at which steam is saturated. At higher pressures water would condense. Vapour pressure is a function of temperature...

• Volatility
Volatility (chemistry)
In chemistry and physics, volatility is the tendency of a substance to vaporize. Volatility is directly related to a substance's vapor pressure. At a given temperature, a substance with higher vapor pressure vaporizes more readily than a substance with a lower vapor pressure.The term is primarily...

• Reid Vapor Pressure
Reid Vapor Pressure
Reid vapor pressure is a common measure of the volatility of gasoline. It is defined as theabsolute vapor pressure exerted by a liquid at 100 °F as determined by the test method ASTM-D-323...

• True vapor pressure
True vapor pressure
True vapor pressure is a common measure of the volatility of petroleum distillate fuels. It is defined as theequilibrium partial pressure exerted by a volatile organic liquid as a function of temperature as determined by the test method ASTM D 2879....

• Vapor pressures of the elements (data page)
Vapor pressures of the elements (data page)
- Vapor pressure :- Notes :*Values are given in terms of temperature necessary to reach the specified pressure.*Valid results within the quoted ranges from most equations are included in the table for comparison....