Molar mass constant

The molar mass constant, symbol M_u, is a physical constant which relates relative atomic mass and molar mass. Its value is defined to be 1 g/mol in SI units.^[1]

The molar mass constant is important in writing dimensionally correct equations.^[2] It is common to see phrases such as

The molar mass of an element is the atomic weight in grams per mole.

However, atomic weight, i.e., relative atomic mass, is a dimensionless quantity, and cannot take the units of grams per mole. Formally, the operation is the multiplication by a constant which has the value 1 g/mol, that is the molar mass constant.

The molar mass constant is 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,^[3] the molar mass of carbon 12 is exactly 12 g/mol. From the definition of relative atomic mass,^[4] the relative atomic mass of carbon 12, that is the atomic weight of a sample of pure carbon 12, is exactly 12. The molar mass constant is given by

$M_{{{\rm {u}}}}={{M({}^{{12}}{{\rm {C}}})} \over {A_{{{\rm {r}}}}({}^{{12}}{{\rm {C}}})}}={1\ {{\rm {g/mol}}}}$

The speed of light, the electric constant and the magnetic constant are other examples of physical constants whose values are fixed by the definitions of the International System of Units (SI),^[1] in these cases by the definitions of the metre^[5] and the ampere.^[6]

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

$m({}^{{12}}{{\rm {C}}})={\frac {12M_{{{\rm {u}}}}}{N_{{{\rm {A}}}}}}$

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 is 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 is also a consequence of the way in which the International System of Units is defined. It is possible to quote the value of the molar mass constant in other units: for example, it is equal to (1/453.592 37) lb/mol ~ 2.204 623 262 × 10⁻³ lb/mol.^[7]

Future

According to the proposed new SI definitions, including a new definition of the mole through giving the Avogadro constant an exact numerical value, and assuming that the definition of an atomic mass unit (one twelfth of the rest mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state) does not change, the molar mass constant, while still with great accuracy remaining equal to 1 g/mol, will no longer be exactly equal to that.

See also

• Atomic mass constant

References

1. Mohr, Peter J.; Taylor, Barry N. (2005). "CODATA recommended values of the fundamental physical constants: 2002". Rev. Mod. Phys. 77: 1–107. Bibcode:2005RvMP...77....1M. doi:10.1103/RevModPhys.77.1.
2. de Bièvre, P.; Peiser, H. S. (1992). "'Atomic Weight' – The Name, Its History, Definition and Units" (PDF). Pure Appl. Chem. 64: 1536–43. doi:10.1351/pac199264101535.
3. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), pp. 114–15, ISBN 92-822-2213-6
4. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "relative atomic mass (atomic weight)".
5. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 112, ISBN 92-822-2213-6
6. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 113, ISBN 92-822-2213-6
7. 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.