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.

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

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, the molar mass of carbon 12 is exactly 12 g/mol. From the definition of relative atomic mass, 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

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), in these cases by the definitions of the metre and the ampere.

The molar mass constant is 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 is 1.992 646 54(10)×10⁻²⁶ kg (u_r = 5×10⁻⁸).

...
Wikipedia