User:Milton Beychok/Sandbox

The molar volume (symbol V_m) 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 molecular mass (M) divided by the density (ρ) at the given temperature and pressure:

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

It has an SI unit of cubic metres per mole (m³/mol). However, molar volumes are often expressed as cubic metres per 1,000 moles (m³/kmol) or cubic decimetres per mol (dm³/mol) for gases and as centimetres per mole (cm³/mol) for liquids and solids.

If a substance is a mixture containing N components, the molar volume is calculated using:

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

where x _i is the mole fraction of the ith component, M _i is the molecular mass of the ith component and ρ_mixture is the mixture density at the given temperature and pressure.

Ideal gases

The ideal gas law equation can be rearranged to give this expression for the molar volume of an ideal gas:

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

where (in SI metric units):

P	= the gas absolute pressure, in Pa
n	= number of moles, in mol
Vm	= the gas molar volume, in m3/mol
T	= the gas absolute temperature, in K
R	= the universal gas law constant of 8.314472 m3·Pa·mol-1·K-1

or where (in U.S. customary units):

P	= the gas absolute pressure, in psia
n	= number of moles, in lb-mol
Vm	= the gas molar volume, in ft3/lb-mol
T	= the gas absolute temperature, in degrees Rankine (°R)
R	= the universal gas law constant of 10.7316 ft3·psia·lb-mol-l·°R-1

The molar volume of any ideal gas may be calculated at various standard reference conditions as shown below:

• In SI metric units:

V_m = 8.314472 × 273.15 / 101,325 = 0.022414 m³/mol at 0 °C and 101,325 Pa absolute pressure = 22.414 kmol at 0 °C and 101.325 kPa absolute pressure

V_m = 8.314472 × 273.15 / 100,000 = 0.022711 m³/kmol at 0 °C and 100,000 Pa absolute pressure = 22.711 kmol at 0 °C and 100 kPa absolute pressure

• In customary USA units:

V_m = 10.7316 × 519.67 / 14.696 = 379.48 ft³/lb-mol at 60 °F and 14.696 psia

The technical literature can be confusing because some authors fail to explain whether they are using the universal gas law constant R, which applies to any ideal gas, or whether they are using the specific gas law constant R_s, which only applies to a specific individual gas. The relationship between the two constants is R_s = R / M, where M is the molecular mass of the gas.

Notes:

• lb-mol is an abbreviation for pound-mol
• °R is degrees Rankine (an absolute temperature scale) and °F is degrees Fahrenheit (a temperature scale).
• °R = °F + 459.67