Molar 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: $${\displaystyle V_{\mathrm{m}}=\frac{V}{n}=\frac{RT}{P}}$$ 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 (V_cell) 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 $${\displaystyle V_{\mathrm{m}}=\frac{N_{\mathrm{A}}{V}_{\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{l}}}{Z}}$$ where N_A 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. 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.

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.