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| The '''molar volume''', symbol ''V''<sub>m</sub>,<ref name="GreenBook">{{GreenBookRef2nd|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 (m<sup>3</sup>/mol),<ref name="GreenBook"/> although it is more practical to use the units [[cubic decimetre]]s per mole (dm<sup>3</sup>/mol) for [[gas]]es and [[cubic centimetre]]s per mole (cm<sup>3</sup>/mol) for [[liquid]]s and [[solid]]s.
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| The molar volume of a substance can be found by measuring its molar mass and density then applying the relation
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| ::<math>V_{\rm m} = {M\over\rho}</math>.
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| If the sample is a [[mixture]] containing ''N'' components, the molar volume is calculated using:
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| ::<math>V_{\rm m} = \frac{\displaystyle\sum_{i=1}^{N}x_{i}M_{i}}{\rho_{\mathrm{mixture}}}</math>.
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| 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]].
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| == Ideal gases ==
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| The ideal gas equation can be rearranged to give an expression for the molar volume of an ideal gas:
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| ::<math>V_{\rm m} = {V\over{n}} = {{RT}\over{P}}</math>.
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| 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<sup>−1</sup> K<sup>−1</sup>, that is a [[Standard uncertainty|relative standard uncertainty]] of 9.1×10<sup>−7</sup>, according to the 2010 [[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 = 2011-10-26}}</ref> The molar volume of an ideal gas at 100 [[Pascal (unit)|kPa]] (1 [[bar (unit)|bar]]) is
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| :22.710 980(38) dm<sup>3</sup>/mol at 0 °C
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| :24.789 598(42) dm<sup>3</sup>/mol at 25 °C
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| The molar volume of an ideal gas at 1 atmosphere of pressure is
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| :22.414 L/mol at 0 °C
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| :24.465 L/mol at 25 °C
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| == Crystalline solids ==
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| 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
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| ::<math>V_{\rm m} = {{N_{\rm A}V_{\rm cell}}\over{Z}}</math>
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| 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".
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| === Molar volume of silicon ===
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| [[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 | issue = 8 | pages = 463–66
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| | doi = 10.1103/PhysRevLett.33.463
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| | title = Determination of the Avogadro Constant | bibcode=1974PhRvL..33..463D}}</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">{{CODATA1998}}</ref> 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<sup>−8</sup>).<ref name="CODATA98"/><ref name="CODATA2006">{{CODATA2006}}</ref>
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| The 2006 CODATA recommended value for the molar volume of silicon is 12.058 8349(11)×10<sup>−6</sup> m<sup>3</sup>/mol, with a relative standard uncertainty of 9.1×10<sup>−8</sup>.<ref name="CODATA2006" />
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| == References ==
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| {{reflist}}
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| ==See also==
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| Interactive table of molar volumes at http://www.webelements.com/periodicity/molar_volume/
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| *[[specific volume]]
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| [[Category:Molar quantities]]
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| [[Category:Physical quantities]]
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| [[Category:Volume]]
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