# 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.

## Calculation

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 complex. It can be simply the sum of the components individualcal components, and calculated using:

- .

But this is violated by many liquid-liquid mixtures. For instance mixing pure ethanol into pure water causes a *decrease* in the volume calculated by this formula. This effect is called "excess volume".

## 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 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* = 0.08206 L atm K^{−1} mol^{−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

For crystalline solids, 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

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]}

## See also

## References

- 1 2 International Union of Pure and Applied Chemistry (1993).
*Quantities, Units and Symbols in Physical Chemistry*, 2nd edition, Oxford: Blackwell Science. ISBN 0-632-03583-8. p. 41. Electronic version. - ↑ "CODATA value: molar gas constant". NIST. Retrieved 2011-10-26.
- ↑ Deslattes, R. D.; Henins, A.; Bowman, H. A.; Schoonover, R. M.; Carroll, C. L.; Barnes, I. L.; Machlan, L. A.; Moore, L. J.; Shields, W. R. (1974). "Determination of the Avogadro Constant".
*Phys. Rev. Lett.***33**(8): 463–66. Bibcode:1974PhRvL..33..463D. doi:10.1103/PhysRevLett.33.463. - 1 2 Mohr, Peter J.; Taylor, Barry N. (1999). "CODATA recommended values of the fundamental physical constants: 1998".
*Journal of Physical and Chemical Reference Data*.**28**(6): 1713–1852. doi:10.1103/RevModPhys.72.351. - 1 2 Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). "CODATA Recommended Values of the Fundamental Physical Constants: 2006".
*Reviews of Modern Physics*.**80**(2): 633–730. arXiv:0801.0028. Bibcode:2008RvMP...80..633M. doi:10.1103/RevModPhys.80.633.

## External links

Wikidata has the property: (see uses)molar volume (P2807) |