# Molar volume

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.

## Definition

Change in volume with increasing ethanol.

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

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

If the sample is a mixture containing N components, the molar volume may be approximated as the sum of the molar volume of its individual components, using the density of the mixture.

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

However, many liquid–liquid mixtures, for instance mixing pure ethanol and pure water, 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 = 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

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 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.[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]