# Molar volume

Physical size
Surname Molar volume
Formula symbol ${\ displaystyle V _ {\ mathrm {m}}}$
Size and
unit system
unit dimension
SI m 3 · mol -1 L 3 N −1

The molar volume or molar volume ( symbol : V m ) of a substance indicates the volume of a mole of this substance . Its SI unit is m 3 / mol.

It results from the quotient of the volume V and the amount of substance n and can be calculated from the molar mass M and the density ρ of the corresponding substance.

${\ displaystyle V _ {\ mathrm {m}} = {\ frac {V} {n}} = {\ frac {M} {\ rho}}}$

It describes the volume that is filled by a total of 6.022 · 10 23 particles ( Avogadro's constant ) of a substance . The molar volume is an intensive quantity , while the volume itself is an extensive quantity .

For solids and liquids , the molar volume depends on the respective substance ( substance property ). The molar volume, like the (mass) specific volume, is a standardized volume.

## Molar volume of the ideal gas

The relationship between mass, amount of substance, volume and number of particles.

By rearranging the ideal gas equation one obtains for the molar volume of an ideal gas :

${\ displaystyle V _ {\ mathrm {m}} = {\ frac {RT} {p}}}$,

With

The molar volume of an ideal gas is, according to the current measurement accuracy ( regardless of which gas is present in detail ):

conditions pressure temperature Molar volume annotation
Physical standard conditions 101.325 kPa 0 ° C 22.413 969 54 ... 10 −3  m 3 / mol " Standard volume "
Standard chemical conditions (IUPAC 1982) 100,000 kPa 0 ° C 22.710 954 64 ... 10 −3  m 3 / mol
SATP terms 101,300 kPa 25 ° C 24.471 441 56 ... 10 −3  m 3 / mol.

In the German standard DIN 1343, January 1990 edition, the molar standard volume of the ideal gas is still given with the older value of (22.414 962 ± 0.000 013) l / mol. The older value completely covers the younger one due to its greater uncertainty.

For real gases , the numbers from the ideal gas law only apply at low pressure and not too low temperatures.

## Individual evidence

1. CODATA Recommended Values. National Institute of Standards and Technology, accessed July 30, 2019 . Value for the molar volume under standard conditions (273.15  Kelvin , 101.325  kPa ). The value is exact, but has an infinite number of decimal places in the decimal representation.
2. CODATA Recommended Values. National Institute of Standards and Technology, accessed July 30, 2019 . Value for the molar volume at 273.15  Kelvin and 100  kPa . The value is exact, but has an infinite number of decimal places in the decimal representation.