Molar volume

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The molar volume, symbol Vm,[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 and density then applying the relation

If the sample is a 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

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

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

mols are measured n=m/M n=mols m=mass M=molar mass

Crystalline solids

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

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