The molar volume, symbol V_m,^[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 1 Ideal gases 2 Crystalline solids 3 Molar volume of silicon 4 References 5 See also

[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

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

22.414 L/mol at 0 °C

24.465 L/mol at 25 °C

mols are measured n=m/M n=mols m=mass M=mass of compound

[edit] Crystalline solids

The unit cell volume (V_cell) 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 N_A 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

[edit] See also

Interactive table of molar volumes at http://www.webelements.com/periodicity/molar_volume/