Molar Volume
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Molar Volume

In chemistry and related fields, the molar volume, symbol Vm,[1] or ${\displaystyle {\tilde {V}}}$ 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 (?):

${\displaystyle V_{m}={\frac {M}{\rho }}}$

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

Change in volume with increasing ethanol fraction.

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

${\displaystyle V_{\rm {m}}={M \over \rho }}$.

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:

${\displaystyle V_{\rm {m}}={\frac {\displaystyle \sum _{i=1}^{N}x_{i}M_{i}}{\rho _{\mathrm {mixture} }}}}$.

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

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:

${\displaystyle V_{\rm {m}}={\frac {V}{n}}={\frac {RT}{P}}.}$

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 = , or about .

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

at 0 °C,
at 25 °C.

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

at 0 °C,
at 25 °C.

## Crystalline solids

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

${\displaystyle V_{\rm {m}}={{N_{\rm {A}}V_{\rm {cell}}} \over {Z}}}$

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

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 , with a relative standard uncertainty of .[4]