chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...

and related fields, the molar volume, symbol ''V''_m, or

\tilde V

of a substance is the ratio of the volume 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, ions, ...

, usually given at a given temperature and pressure. It is equal to the molar mass (''M'') divided by the mass density (''ρ''):

V_ = \frac .

The molar volume has the SI unit 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 (m³/mol), although it is more typical to use the units cubic decimetres per mole (dm³/mol) for gases, and cubic centimetres per mole (cm³/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, a ...

s and solids.

Definition

Excess Volume Mixture of Ethanol and Water-int

The molar volume of a substance ''i'' is defined as its molar mass divided by its density ''ρ''_''i''⁰:

V_ = .

For an

ideal mixture In chemistry, an ideal solution or ideal mixture is a solution that exhibits thermodynamic properties analogous to those of a mixture of ideal gases. The enthalpy of mixing is zero as is the volume change on mixing by definition; the closer to zer ...

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:

V_ = \frac.

There are many liquid–liquid mixtures, for instance mixing pure ethanol and pure water, 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 by the product with molar mass. This follows from above where the specific volume is the

reciproc In mathematics, a multiplicative inverse or reciprocal for a number ''x'', denoted by 1/''x'' or ''x''−1, is a number which when multiplied by ''x'' yields the multiplicative identity, 1. The multiplicative inverse of a fraction ''a''/''b ...

al of the density of a substance:

V_ =  = M_i v_i.

Ideal gases

For ideal gases, 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 o ...

. The ideal gas equation can be rearranged to give an expression for the molar volume of an ideal gas:

V_ = \frac = \frac.

Hence, for a given temperature and pressure, the molar volume is the same for all ideal gases and is based on the gas constant: ''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 (u ...

) 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, macrosc ...

, the molar volume can be measured by X-ray crystallography. The unit cell volume (''V''_cell) 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

V_ =

where ''N''_A 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

Ultra-pure silicon 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 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

References

External links

Interactive table of molar volumes
{{Authority control Volume