Molar volume

Definition

The molar volume of a substance i is defined as its molar mass divided by its density ρ**i0: V_{\rm m,i} = {M_i\over\rho_i^0} For an ideal mixture containing N components, the molar volume of the mixture 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: 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 represented by the quantity excess volume of the mixture, an example of excess property.

Relation to specific volume

Molar volume is related to specific volume by the product with molar mass. This follows from above where the specific volume is the reciprocal of the density of a substance: V_{\rm m,i} = {M_i \over \rho_i^0} = M_i v_i

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: 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 V_{\rm m} = \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

Ultra-pure 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 in 1974.{{cite journal | last=Deslattes | first=R. D. |author2=Henins, A. |author3=Bowman, H. A. |author4=Schoonover, R. M. |author5=Carroll, C. L. |author6=Barnes, I. L. |author7=Machlan, L. A. |author8=Moore, L. J. |author9= Shields, W. R. | year=1974 | journal=Phys. Rev. Lett. | volume=33 | issue=8 | pages=463–66 | doi = 10.1103/PhysRevLett.33.463

The CODATA recommended value for the molar volume of silicon is , with a relative standard uncertainty of

References

References

1. {{GreenBookRef2nd
2. (1999). "CODATA recommended values of the fundamental physical constants: 1998". [[Journal of Physical and Chemical Reference Data]].