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Molar volume
 
 
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The molar volume, symbol Vm, is the volume
Volume

The volume of any solid, liquid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies, often quantified numerically....
 occupied by one mole
Mole (unit)

The mole is a Units of measurement of amount of substance: it is an SI base unit, and one of the few units used to measure this physical quantity....
 of a substance (chemical element
Chemical element

A chemical element is a type of atom that is distinguished by its atomic number; that is, by the number of protons in its atomic nucleus. The term is also used to refer to a pure chemical Chemical substance composed of atoms with the same number of protons....
 or chemical compound
Chemical compound

A chemical compound is a Chemical substance consisting of two or more different chemical element Chemical bond together in a fixed mass ratio that can be split into simpler substances....
) at a given temperature
Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
 and pressure
Pressure

Pressure is the force per unit area applied to an object in a direction surface normal to the surface. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure....
. It is equal to the molar mass
Molar mass

Molar mass, symbol M, is the mass of one mole of a substance . It is a physical property which is characteristic of each pure substance. The base SI unit for mass is the kilogram but, for both practical and historical reasons, molar masses are almost always quoted in grams per mole , especially in chemistry....
 (M) divided by the mass density. It has the SI unit cubic metre
Cubic metre

The cubic metre is the SI derived unit of volume. It is the volume of a cube with edges one metre in length. An alternative name, which allowed a different usage with SI prefix, was the st?re....
s per mole (m³/mol), although it is more practical to use the units cubic decimetres per mole (dm³/mol) for gas
Gas

In physics, a gas is a state of matter, consisting of a collection of particles without a definite shape or volume that are in more or less random motion....
es and cubic centimetre
Cubic centimetre

A cubic centimetre or cubic centimeter is a commonly used unit of volume extending the derived International System of Units-unit cubic metre and corresponds to the volume of a cube measuring 1?1?1 cm....
s per mole (cm³/mol) for liquid
Liquid

Liquid is one of the principal states of matter. A liquid is a fluid that has the particles loose and can freely form a distinct surface at the boundaries of its bulk material....
s and solid
Solid

A solid object is in the states of matter characterized by resistance to deformation and changes of volume. In other words, it has high values both of Young's modulus and of shear modulus; this contrasts e.g....
s.

The molar volume of a substance can be found by measuring its mass density then applying the relation
.
If a sample is mixture
Mixture

In chemistry, a mixture is a substance made by combining two or more different materials without a chemical reaction occurring .While there are no physical changes in a mixture, the chemical properties of a mixture, such as its melting point, may differ from those of its components....
 containing N components, the molar volume is calculated using:
.
For ideal gas
Ideal gas

The ideal gas model is a model of matter in which the molecules are treated as non-interacting point particles which are engaged in a random motion that obeys conservation of energy....
es, the molar volume is given by the ideal gas equation: this is a good approximation for many common gases at standard temperature and pressure.






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The molar volume, symbol Vm, is the volume
Volume

The volume of any solid, liquid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies, often quantified numerically....
 occupied by one mole
Mole (unit)

The mole is a Units of measurement of amount of substance: it is an SI base unit, and one of the few units used to measure this physical quantity....
 of a substance (chemical element
Chemical element

A chemical element is a type of atom that is distinguished by its atomic number; that is, by the number of protons in its atomic nucleus. The term is also used to refer to a pure chemical Chemical substance composed of atoms with the same number of protons....
 or chemical compound
Chemical compound

A chemical compound is a Chemical substance consisting of two or more different chemical element Chemical bond together in a fixed mass ratio that can be split into simpler substances....
) at a given temperature
Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
 and pressure
Pressure

Pressure is the force per unit area applied to an object in a direction surface normal to the surface. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure....
. It is equal to the molar mass
Molar mass

Molar mass, symbol M, is the mass of one mole of a substance . It is a physical property which is characteristic of each pure substance. The base SI unit for mass is the kilogram but, for both practical and historical reasons, molar masses are almost always quoted in grams per mole , especially in chemistry....
 (M) divided by the mass density. It has the SI unit cubic metre
Cubic metre

The cubic metre is the SI derived unit of volume. It is the volume of a cube with edges one metre in length. An alternative name, which allowed a different usage with SI prefix, was the st?re....
s per mole (m³/mol), although it is more practical to use the units cubic decimetres per mole (dm³/mol) for gas
Gas

In physics, a gas is a state of matter, consisting of a collection of particles without a definite shape or volume that are in more or less random motion....
es and cubic centimetre
Cubic centimetre

A cubic centimetre or cubic centimeter is a commonly used unit of volume extending the derived International System of Units-unit cubic metre and corresponds to the volume of a cube measuring 1?1?1 cm....
s per mole (cm³/mol) for liquid
Liquid

Liquid is one of the principal states of matter. A liquid is a fluid that has the particles loose and can freely form a distinct surface at the boundaries of its bulk material....
s and solid
Solid

A solid object is in the states of matter characterized by resistance to deformation and changes of volume. In other words, it has high values both of Young's modulus and of shear modulus; this contrasts e.g....
s.

The molar volume of a substance can be found by measuring its mass density then applying the relation
.
If a sample is mixture
Mixture

In chemistry, a mixture is a substance made by combining two or more different materials without a chemical reaction occurring .While there are no physical changes in a mixture, the chemical properties of a mixture, such as its melting point, may differ from those of its components....
 containing N components, the molar volume is calculated using:
.
For ideal gas
Ideal gas

The ideal gas model is a model of matter in which the molecules are treated as non-interacting point particles which are engaged in a random motion that obeys conservation of energy....
es, the molar volume is given by the ideal gas equation: this is a good approximation for many common gases at standard temperature and pressure. For crystalline solids
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 molar volume can be measured by X-ray crystallography
X-ray crystallography

X-ray crystallography is a method of determining the arrangement of atoms within a crystal, in which a beam of X-rays strikes a crystal and scatters into many different directions....
.

Ideal gases

The ideal gas equation can be rearranged to give an expression for the molar volume of an ideal gas:
.
Hence, for a given temperature and pressure, the molar volume is the same for all ideal gases and is known to the same precision as the gas constant
Gas constant

The gas constant is a physical constant which is featured in a large number of fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation....
: R = 8.314 472(15) J mol–1 K–1, that is a relative standard uncertainty of 1.7×10–6, according to the 2006 CODATA recommended value. The molar volume of an ideal gas at 100 kPa
Pascal (unit)

The pascal is the SI derived unit of pressure, stress , Young's modulus and tensile strength. It is a measure of force per unit area i.e. equivalent to one newton per square meter or one joule per cubic meter....
 (1 bar
Bar (unit)

The bar , decibar and the millibar are units of pressure. They are not SI units, nor are they cgs units, but they are accepted for use with the SI....
) is
22.710 980(38) dm³/mol at 0 °C
24.789 598(42) dm³/mol at 25 °C


Crystalline solids

The unit cell volume (Vcell) may be calculated from the unit cell parameters, whose determination is the first step in an X-ray crystallography experiment (the calculation is performed automatically by the structure determination software). This is related to the molar volume by
where NA is the Avogadro constant and Z is the number of formula units in the unit cell. The result is normally reported as the "crystallographic density".

Molar volume of silicon

High quality single crystals of ultrapure silicon
Silicon

Silicon is the most common metalloid. It is a chemical element, which has the symbol Si and atomic number 14. The atomic mass is 28.0855....
 are routinely made for the electronics industry, and the measurement of the molar volume of silicon, both by X-ray crystallography and by the ratio of molar mass to mass density, has attracted much attention since the pioneering work at NIST by Deslattes et al. (1974). The interest stems from the fact that accurate measurements of the unit cell volume, atomic weight
Atomic weight

Atomic weight is a Dimensionless quantity physical quantity, the ratio of the average mass of atoms of an chemical element to 1/12 of the mass of an atom of carbon-12....
 and mass density of a pure crystalline solid provide a direct determination of the Avogadro constant. At present (2006 CODATA recommended value), the precision of the value of the Avogadro constant is limited by the uncertainty in the value of the Planck constant
Planck constant

The Planck constant , also called Planck's constant, is a physical constant used to describe the sizes of quantum in quantum mechanics. It is named after Max Planck, one of the founders of quantum theory....
 (relative standard uncertainty of 5×10–8).

The 2006 CODATA recommended value for the molar volume of silicon is 12.058 8349(11)×10–6 m³/mol, with a relative standard uncertainty of 9.1×10–8.

See Also

Interactive table of molar volumes at http://www.webelements.com/periodicity/molar_volume/