Molar volume

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search

In chemistry and related fields, the molar volume, symbol Vm,[1] or of a substance is the occupied volume divided by the amount of substance 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 of cubic metres per mole (m3/mol),[1] although it is typically more practical to use the units cubic decimetres per mole (dm3/mol) for gasses, and cubic centimetres per mole (cm3/mol) for liquids and solids.

Definition[edit]

Change in volume with increasing ethanol fraction.

The molar volume of a substance is defined as its molar mass divided by its density:

.

For an ideal mixture containing N components, the molar volume is the weighted sum of the molar volumes of its individual components. For a real mixture the molar volume cannot be calculated without knowing the density:

.

There are many liquid–liquid mixtures, for instance mixing pure ethanol and pure water, which may experience contraction or expansion upon mixing. This effect is called "excess volume".

Ideal gases[edit]

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 based on the gas constant: R = 8.31446261815324 m3⋅Pa⋅K−1⋅mol−1, or about 8.20573660809596×10−5 m3⋅atm⋅K−1⋅mol−1.

The molar volume of an ideal gas at 100 kPa (1 bar) is

0.022710954641485... m3/mol at 0 °C,
0.024789570296023... m3/mol at 25 °C.

The molar volume of an ideal gas at 1 atmosphere of pressure is

0.022413969545014... m3/mol at 0 °C,
0.024465403697038... m3/mol at 25 °C.

Crystalline solids[edit]

For crystalline solids, the molar volume can be measured by X-ray crystallography. 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".

Molar volume of silicon[edit]

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).[2] The interest stems from 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.[3]

The CODATA recommended value for the molar volume of silicon is 1.205883199(60)×10−5 m3⋅mol−1, with a relative standard uncertainty of 4.9×10−8.[4]

See also[edit]

References[edit]

  1. ^ 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.
  2. ^ 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.
  3. ^ Mohr, Peter J.; Taylor, Barry N. (1999). "CODATA recommended values of the fundamental physical constants: 1998" (PDF). Journal of Physical and Chemical Reference Data. 28 (6): 1713–1852. Bibcode:1999JPCRD..28.1713M. doi:10.1063/1.556049. Archived from the original (PDF) on 2017-10-01.
  4. ^ "2018 CODATA Value: molar volume of silicon". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-06-23. CS1 maint: discouraged parameter (link)

External links[edit]