# Molar volume

The **molar volume**, symbol *V*_{m},^{[1]} is the volume occupied by one mole of a substance (chemical element or chemical compound) at a given temperature and pressure. It is equal to the molar mass (*M*) divided by the mass density (ρ). It has the SI unit cubic metres per mole (m^{3}/mol),^{[1]} although it is more practical to use the units cubic decimetres per mole (dm^{3}/mol) for gases and cubic centimetres per mole (cm^{3}/mol) for liquids and solids.

The molar volume of a substance can be found by measuring its molar mass and density then applying the relation

If the sample is a mixture containing *N* components, the molar volume is calculated using:

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. For crystalline solids, the molar volume can be measured by X-ray crystallography.

## 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: *R* = 8.314 4621(75) J mol^{−1} K^{−1}, that is a relative standard uncertainty of 9.1×10^{−7}, according to the 2010 CODATA recommended value.^{[2]} The molar volume of an ideal gas at 100 kPa (1 bar) is

- 22.710 980(38) dm
^{3}/mol at 0 °C - 24.789 598(42) dm
^{3}/mol at 25 °C

The molar volume of an ideal gas at 1 atmosphere of pressure is

- 22.414 dm
^{3}/mol at 0 °C - 24.465 dm
^{3}/mol at 25 °C

## Crystalline solids

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

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

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 by Deslattes *et al.* (1974).^{[3]} The interest stems from the fact 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.^{[4]} 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 (relative standard uncertainty of 5×10^{−8}).^{[4]}^{[5]}

The 2006 CODATA recommended value for the molar volume of silicon is 12.058 8349(11)×10^{−6} m^{3}/mol, with a relative standard uncertainty of 9.1×10^{−8}.^{[5]}

## References

- ↑
^{1.0}^{1.1}Template:GreenBookRef2nd - ↑ Template:Cite web
- ↑ {{#invoke:Citation/CS1|citation |CitationClass=journal }}
- ↑
^{4.0}^{4.1}Template:CODATA1998 - ↑
^{5.0}^{5.1}Template:CODATA2006

## See also

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