| Molar volume | |
|---|---|
Common symbols | Vm, |
| SI unit | m3/mol |
Other units | dm3/mol, cm3/mol |
| Dimension | L3N−1 |
Inchemistry and related fields, themolar volume, symbolVm,[1] or of a substance is the ratio of thevolume (V) occupied by a substance to theamount of substance (n), usually at a giventemperature andpressure. It is also equal to themolar mass (M) divided by themass density (ρ):
The molar volume has theSI unit ofcubic metres per mole (m3/mol),[1] although it is more typical to use the unitscubic decimetres per mole (dm3/mol) forgases, andcubic centimetres per mole (cm3/mol) forliquids andsolids.
The molar volume of a substancei is defined as itsmolar mass divided by its densityρi0:For anideal mixture containingN components, the molar volume of the mixture is theweighted 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 pureethanol and purewater, which may experience contraction or expansion upon mixing. This effect is represented by the quantityexcess volume of the mixture, an example ofexcess property.
Molar volume is related tospecific volume by the product withmolar mass. This follows from above where the specific volume is thereciprocal of the density of a substance:
Forideal gases, the molar volume is given by theideal gas equation; this is a good approximation for many common gases atstandard 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 thegas constant:R =8.31446261815324 m3⋅Pa⋅K−1⋅mol−1, or about8.20573660809596×10−5 m3⋅atm⋅K−1⋅mol−1.
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
Forcrystalline solids, the molar volume can be measured byX-ray crystallography.Theunit cell volume (Vcell) may be calculated from theunit 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 bywhereNA is theAvogadro constant andZ is the number of formula units in the unit cell. The result is normally reported as the "crystallographic density".
Ultra-puresilicon is routinely made for theelectronics 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 atNIST in 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 is1.205883199(60)×10−5 m3⋅mol−1, with a relative standard uncertainty of4.9×10−8.[4]
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