Molar volume 70989 221834967 2008-06-26T09:03:49Z DOI bot 6652755 Citation maintenance. Added: doi_brokendate. You can [[WP:DOI|use this bot]] yourself! Please [[User:DOI_bot/bugs|report any bugs]]. 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]] (&rho;). 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''&nbsp;= 8.314&nbsp;472(15)&nbsp;J&nbsp;mol<sup>–1</sup>&nbsp;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&nbsp;[[Pascal (unit)|kPa]] (1&nbsp;[[bar (unit)|bar]]) is :22.710&nbsp;980(38)&nbsp;dm³/mol at 0&nbsp;°C :24.789&nbsp;598(42)&nbsp;dm³/mol at 25&nbsp;°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&nbsp;8349(11)×10<sup>–6</sup>&nbsp;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]]