Molar volume
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The '''molar volume''', symbol ''V''<sub>m</sub>,<ref name="GreenBook">{{GreenBookRef|page=41}}</ref> is the [[volume]] occupied by one [[mole (unit)|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 metre]]s per mole (m³/mol),<ref name="GreenBook"/> although it is more practical to use the units [[cubic decimetre]]s per mole (dm³/mol) for [[gas]]es and [[cubic centimetre]]s per mole (cm³/mol) for [[liquid]]s and [[solid]]s.
The molar volume of a substance can be found by measuring its mass density then applying the relation
::<math>V_{\rm m} = {M\over\rho}</math>.
If a sample is [[mixture]] containing ''N'' components, the molar volume is calculated using:
::<math>V_{m} = \frac{\displaystyle\sum_{i=1}^{N}x_{i}M_{i}}{\rho_{mixture}}</math>.
For [[ideal gas]]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]]. For [[Crystal|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:
::<math>V_{\rm m} = {V\over{n}} = {{RT}\over{P}}</math>.
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<sup>–1</sup> K<sup>–1</sup>, that is a [[Standard uncertainty|relative standard uncertainty]] of 1.7×10<sup>–6</sup>, according to the 2006 [[CODATA]] recommended value.<ref>{{cite web | title = CODATA value: molar gas constant | url = http://physics.nist.gov/cgi-bin/cuu/Value?r | publisher = [[NIST]] | accessdate = 2007-10-14}}</ref> The molar volume of an ideal gas at 100 [[Pascal (unit)|kPa]] (1 [[bar (unit)|bar]]) is
:22.710 980(38) dm³/mol at 0 °C
:24.789 598(42) dm³/mol at 25 °C
== Crystalline solids ==
The [[unit cell]] volume (''V''<sub>cell</sub>) may be calculated from the [[unit cell parameter]]s, 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
::<math>V_{\rm m} = {{N_{\rm A}V_{\rm cell}}\over{Z}}</math>
where ''N''<sub>A</sub> 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 ==
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).<ref>{{cite journal | last = Deslattes | first = R. D. | coauthors = Henins, A.; Bowman, H. A.; Schoonover, R. M.; Carroll, C. L.; Barnes, I. L.; Machlan, L. A.; Moore, L. J.; Shields, W. R. | year = 1974 | journal = [[Physical Review Letters|Phys. Rev. Lett.]] | volume = 33 | pages = 463–66
| doi = 10.1103/PhysRevLett.33.463
| title = Determination of the Avogadro Constant}}</ref> 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]].<ref name="CODATA98">{{cite journal | last = Mohr | first = Peter J. | coauthors = Taylor, Barry N. | title = CODATA Recommended Values of the Fundamental Physical Constants: 1998 | journal = [[Journal of Physical and Chemical Reference Data|J. Phys. Chem. Ref. Data]] | year = 1999 | volume = 28 | pages = 1713–1852 | doi = 0047-2689/99/28(6)/1713/140 | doi_brokendate = 2008-06-26}}</ref> At present (2006 [[CODATA]] recommended value),<ref>{{cite web | title = CODATA value: Avogadro constant | url = http://physics.nist.gov/cgi-bin/cu<!-- Ballin -->u/Value?na | publisher = [[NIST]] | accessdate = 2007-10-14}}</ref> the precision of the value of the Avogadro constant is limited by the [[Standard uncertainty|uncertainty]] in the value of the [[Planck constant]] (relative standard uncertainty of 5×10<sup>–8</sup>).<ref name="CODATA98"/><ref>{{cite web | title = CODATA value: Planck constant | url = http://physics.nist.gov/cgi-bin/cuu/Value?h | publisher = [[NIST]] | accessdate = 2007-10-14}}</ref>
The 2006 CODATA recommended value for the molar volume of silicon is 12.058 8349(11)×10<sup>–6</sup> m³/mol, with a relative standard uncertainty of 9.1×10<sup>–8</sup>.<ref>{{cite web | title = CODATA value: molar volume of silicon | url = http://physics.nist.gov/cgi-bin/cuu/Value?mvolsil | publisher = [[NIST]] | accessdate = 2007-10-14}}</ref>
== References ==
<references />
[[Category:Chemical properties]]
[[Category:Physical quantity]]
[[Category:Volume]]
[[ast:Volume molar]]
[[bs:Molarni volumen]]
[[bg:Моларен обем]]
[[ca:Volum molar]]
[[cs:Molární objem]]
[[de:Molares Volumen]]
[[et:Molaarruumala]]
[[es:Volumen molar]]
[[fr:Volume molaire]]
[[it:Volume molare]]
[[lt:Molinis tūris]]
[[mk:Моларен волумен]]
[[nl:Molair volume]]
[[ja:モル体積]]
[[no:Molar]]
[[nn:Molart volum]]
[[uz:Molyar hajm]]
[[pl:Objętość molowa]]
[[pt:Volume molar]]
[[ro:Volum molar]]
[[ru:Молярный объём]]
[[sk:Mólový objem]]
[[sl:Molarna prostornina]]
[[sr:Молска запремина]]
[[fi:Moolitilavuus]]
[[sv:Molvolym]]
[[uk:Молярний об'єм]]
[[zh:摩尔体积]]