Molar volume
From Wikipedia, the free encyclopedia
The molar volume, symbol Vm,[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 (m3/mol),[1] although it is more practical to use the units cubic decimetres per mole (dm3/mol) for gases and cubic centimetres per mole (cm3/mol) for liquids and solids.
The molar volume of a substance can be found by measuring its mass density then applying the relation
-
.
If a sample is 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.
Contents |
[edit] 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 = 8.314 472(15) J mol–1 K–1, that is a relative standard uncertainty of 1.7×10–6, according to the 2006 CODATA recommended value.[2] The molar volume of an ideal gas at 100 kPa (1 bar) is
- 22.710 980(38) dm3/mol at 0 °C
- 24.789 598(42) dm3/mol at 25 °C
[edit] 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".
[edit] Molar volume of silicon
High quality single crystals of ultrapure silicon 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).[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 m3/mol, with a relative standard uncertainty of 9.1×10–8.[5]
[edit] References
- ^ a b 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. http://physics.nist.gov/cgi-bin/cuu/Value?r. Retrieved on 2007-10-14.
- ^ 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: 463–66. doi:.
- ^ a b Mohr, Peter J.; Taylor, Barry N. (1999). "CODATA recommended values of the fundamental physical constants: 1998". J. Phys. Chem. Ref. Data 28 (6): 1713–1852. doi:.
- ^ a b Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). "CODATA Recommended Values of the Fundamental Physical Constants: 2006". Rev. Mod. Phys. 80: 633–730. doi:. http://physics.nist.gov/cuu/Constants/codata.pdf.
[edit] See also
Interactive table of molar volumes at http://www.webelements.com/periodicity/molar_volume/
