The **molar mass constant**, usually denoted by *M*_{u}, is a physical constant which connects the relative atomic mass of an element (the average mass of one atom of an element, relative to the mass of some reference particle) and its molar mass (the mass of one mole of atoms the element). The constant also connects the relative molecular mass of a compound and its molar mass (the mass of one mole of molecules).

The mole and the relative atomic mass were originally defined in the International System of Units (SI) in such a way that the constant was exactly 1 g/mol. That is, the numerical value of the molar mass of an element, in grams per mole of atoms, was equal to its atomic mass relative to the SI unit of atomic mass (dalton). Thus, for example the average atomic mass of chlorine is approximately 35.446 daltons, and the mass of one mole of chlorine atoms is approximately 35.446 grams.

On May 20, 2019, the SI definition of mole changed in such a way that the molar mass constant is not exactly 1 g/mol anymore. However, the difference is insignificant for all practical purposes. According to the SI, the value of *M*_{u} now depends on the mass of one atom of carbon-12, which must be determined experimentally. As of that date, the CODATA recommended value of *M*_{u} is 0.99999999965(30)×10^{−3} kg⋅mol^{−1}.^{[1]}^{[2]}

The molar mass constant is important in writing dimensionally correct equations.^{[3]} While one may informally say "the molar mass of an element *M* is the same as it atomic weight *A*", the atomic weight (relative atomic mass) *A* is a dimensionless quantity, whereas the molar mass *M* has the units of mass per mole. Formally, *M* is *A* times the molar mass constant *M*_{u}.

## Prior to 2019 redefinition

The molar mass constant was unusual (but not unique) among physical constants by having an exactly defined value rather than being measured experimentally. It is fixed by the definitions of the mole and of relative atomic mass. From the definition of the mole,^{[4]} the molar mass of carbon 12 is exactly 12 g/mol. From the definition of relative atomic mass,^{[5]} the relative atomic mass of carbon 12, that is the atomic weight of a sample of pure carbon 12, was exactly 12. The molar mass constant was thus given by

The speed of light is another example of a physical constant whose value is fixed by the definitions of the International System of Units (SI).^{[citation needed]}

The molar mass constant was also related to the mass of a carbon-12 atom in grams:

Hence the uncertainty in the value of the mass of a carbon-12 atom in SI units is governed by the uncertainty in the Avogadro constant: the CODATA 2006 recommended value was 1.992 646 54(10)×10^{−26} kg (*u*_{r} = 5×10^{−8}).

The relatively simple value of the molar mass constant in SI units was also a consequence of the way in which the International System of Units is defined. It was also possible to quote the value of the molar mass constant in other units: for example, it was equal to (1/453.592 37) lb/mol ~ 2.204 623 262 × 10^{−3} lb/mol.^{[6]}

## Post-2019 redefinition

Because the 2019 redefinition of SI base units includes a new definition of the mole through giving the Avogadro constant an exact numerical value. As a consequence, the value of the molar mass constant no longer has an exactly defined value, since the atomic mass constant is still defined as one twelfth of the rest mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state. Therefore, while still with having great accuracy a value of 1 g/mol, the molar mass constant is no longer defined at that value.

## See also

## References

**^**"2018 CODATA Value: molar mass constant".*The NIST Reference on Constants, Units, and Uncertainty*. NIST. 20 May 2019. Retrieved 2019-05-20.**^**Mohr, Peter J.; Taylor, Barry N. (2005). "CODATA recommended values of the fundamental physical constants: 2002".*Rev. Mod. Phys.***77**: 1.–107. arXiv:1507.07956. Bibcode:2005RvMP...77....1M. doi:10.1103/RevModPhys.77.1.**^**de Bièvre, Paul; Peiser, H. Steffen (1992). "'Atomic Weight' — The Name, Its History, Definition, and Units" (PDF).*Pure and Applied Chemistry*.**64**(10): 1535–43. doi:10.1351/pac199264101535.**^**International Bureau of Weights and Measures (2006),*The International System of Units (SI)*(PDF) (8th ed.), pp. 114–15, ISBN 92-822-2213-6, archived (PDF) from the original on 2017-08-14**^**IUPAC,*Compendium of Chemical Terminology*, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "relative atomic mass (atomic weight)". doi:10.1351/goldbook.R05258**^**International Union of Pure and Applied Chemistry (1993).*Quantities, Units and Symbols in Physical Chemistry*, 2nd edition, Oxford: Blackwell Science. ISBN 0-632-03583-8. p. 111. Electronic version.