# 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

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.