In
chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, proper ...
and related fields, the molar volume, symbol ''V''
m,
or
of a substance is the ratio of the
volume
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...
occupied by a substance to the
amount of substance
In chemistry, the amount of substance ''n'' in a given sample of matter is defined as the quantity or number of discrete atomic-scale particles in it divided by the Avogadro constant ''N''A. The particles or entities may be molecules, atoms, io ...
, usually given at a given
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
and
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
. It is equal to the
molar mass
In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecular, ...
(''M'') divided by the
mass density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
(''ρ''):
The molar volume has the
SI unit
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...
of
cubic metre
The cubic metre (in Commonwealth English and international spelling as used by the International Bureau of Weights and Measures) or cubic meter (in American English) is the unit of volume in the International System of Units (SI). Its symbol is m ...
s per mole (m
3/mol),
although it is more typical to use the units
cubic decimetres per mole (dm
3/mol) for
gases, and
cubic centimetre
A cubic centimetre (or cubic centimeter in US English) (SI unit symbol: cm3; non-SI abbreviations: cc and ccm) is a commonly used unit of volume that corresponds to the volume of a cube that measures 1 cm × 1 cm × 1 cm. One cu ...
s per mole (cm
3/mol) for
liquid
A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, ...
s and
solid
Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic energy. A solid is characterized by structur ...
s.
Definition
The molar volume of a substance ''i'' is defined as its
molar mass
In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecular, ...
divided by its density ''ρ''
''i''0:
For an
ideal mixture containing ''N'' components, the molar volume of the mixture is the
weighted sum of the molar volumes of its individual components. For a real mixture the molar volume cannot be calculated without knowing the density:
There are many liquid–liquid mixtures, for instance mixing pure
ethanol
Ethanol (abbr. EtOH; also called ethyl alcohol, grain alcohol, drinking alcohol, or simply alcohol) is an organic compound. It is an alcohol with the chemical formula . Its formula can be also written as or (an ethyl group linked to a ...
and pure
water
Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...
, which may experience contraction or expansion upon mixing. This effect is represented by the quantity excess volume of the mixture, an example of
excess property
In chemical thermodynamics, excess properties are properties of mixtures which quantify the non- ideal behavior of real mixtures. They are defined as the difference between the value of the property in a real mixture and the value that would exist ...
.
Relation to specific volume
Molar volume is related to
specific volume
In thermodynamics, the specific volume of a substance (symbol: , nu) is an intrinsic property of the substance, defined as the ratio of the substance's volume () to its mass (). It is the reciprocal of density (rho) and it is related to the m ...
by the product with
molar mass
In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecular, ...
. This follows from above where the specific volume is the
reciprocal of the density of a substance:
Ideal gases
For
ideal gas
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is a ...
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
Standard temperature and pressure (STP) are standard sets of conditions for experimental measurements to be established to allow comparisons to be made between different sets of data. The most used standards are those of the International Union ...
.
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 based on the
gas constant
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...
: ''R'' = , or about .
The molar volume of an ideal gas at 100
kPa (1
bar
Bar or BAR may refer to:
Food and drink
* Bar (establishment), selling alcoholic beverages
* Candy bar
* Chocolate bar
Science and technology
* Bar (river morphology), a deposit of sediment
* Bar (tropical cyclone), a layer of cloud
* Bar ( ...
) is
: at 0 °C,
: at 25 °C.
The molar volume of an ideal gas at 1 atmosphere of pressure is
: at 0 °C,
: at 25 °C.
Crystalline solids
For
crystalline solids
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...
, the molar volume can be measured by
X-ray crystallography
X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles ...
.
The
unit cell
In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector, for example) does not necessaril ...
volume (''V''
cell) may be calculated from the
unit cell
In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector, for example) does not necessaril ...
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 ''N''
A is the
Avogadro constant
The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining ...
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
Ultra-pure
silicon
Silicon is a chemical element with the symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic luster, and is a tetravalent metalloid and semiconductor. It is a member of group 14 in the periodic ...
is 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
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...
in 1974.
The interest stems from that accurate measurements of the unit cell volume,
atomic weight
Relative atomic mass (symbol: ''A''; sometimes abbreviated RAM or r.a.m.), also known by the deprecated synonym atomic weight, is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a giv ...
and mass density of a pure crystalline solid provide a direct determination of the Avogadro constant.
The CODATA recommended value for the molar volume of silicon is , with a relative standard uncertainty of
See also
*
Specific volume
In thermodynamics, the specific volume of a substance (symbol: , nu) is an intrinsic property of the substance, defined as the ratio of the substance's volume () to its mass (). It is the reciprocal of density (rho) and it is related to the m ...
References
External links
Interactive table of molar volumes
{{Authority control
Volume