Molar mass

Molar mass
A diagram comparing moles and molar masses of iron and gold samples that have equal masses
Common symbols	M
SI unit	kg/mol
Other units	g/mol
Dimension	M N−1

In chemistry, the molar mass (M) (sometimes called molecular weight or formula weight, but see related quantities for usage) of a chemical compound is defined as the ratio between the mass and the amount of substance (measured in moles) of any sample of the compound.^[1] The molar mass is a bulk, not molecular, property of a substance. The molar mass is an average of many instances of the compound, which often vary in mass due to the presence of isotopes. Most commonly, the molar mass is computed from the standard atomic weights and is thus a terrestrial average and a function of the relative abundance of the isotopes of the constituent atoms on Earth.

For a sample of a substance X, the molar mass, M(X), is appropriate for converting between the mass of the substance, m(X), and the amount of the substance, n(X), for bulk quantities: M(X) = m(X)/n(X). If N(X) is the number of entities in the sample, m(X) = N(X)m_a(X) and n(X) = N(X)/N_A = N(X) ent, where ent is an atomic-scale unit of amount equal to one entity. So M(X) = m_a(X)/ent, the atomic-scale entity mass per entity, which is self evident. Since m_a(X) = A_r(X) Da, molar mass can be written in units of dalton per entity as M(X) = A_r(X) Da/ent. One mole is an aggregate of an Avogadro number of entities, and (for all practical purposes) the Avogadro number is g/Da. So (for all practical purposes) Da/ent = g/mol. And the molar mass can be calculated from M(X) = A_r(X) Da/ent = A_r(X) g/mol = A_r(X) kg/kmol.

The molecular mass (for molecular compounds) and formula mass (for non-molecular compounds, such as ionic salts) are commonly used as synonyms of molar mass, differing only in units (dalton vs Da/ent or g/mol); however, the most authoritative sources define it differently. The difference is that molecular mass is the mass of one specific particle or molecule, while the molar mass is an average over many particles or molecules.

The molar mass is an intensive property of the substance, that does not depend on the size of the sample. In the International System of Units (SI), the coherent unit of molar mass is kg/mol. However, for historical reasons, molar masses are almost always expressed in g/mol.

The mole was defined in such a way that the numerical value of the molar mass of a compound in g/mol, i.e. M(X)/(g/mol), was equal to the numerical value of the average atomic-scale mass of one entity (atom, molecule, formula unit, . . .) in Da, i.e. m_a(X)/Da = A_r(X). Specifically: M(X) = A_r(X) g/mol. It was exactly equal before the redefinition of the mole in 2019, and is now only approximately equal, but the difference is negligible for all practical purposes. Thus, for example, the average mass of a molecule of water is about 18.0153 Da, and the molar mass of water is about 18.0153 g/mol.

For chemical elements without isolated molecules, such as carbon and metals, the molar mass is still computed using M(X) = A_r(X) g/mol. Thus, for example, the molar mass of iron is about 55.845 g/mol.

Since 1971, SI defined the "amount of substance" as a separate dimension of measurement. Until 2019, the mole was defined as the amount of substance that has as many constituent particles as there are atoms in 12 grams of carbon-12. That meant that, during that period, the molar mass of carbon-12 was thus exactly 12 g/mol, by definition: M(¹²C) = 12 g/mol (exactly). Inverting this gives an expression for the (original) definition of the mole in terms of the international prototype of the kilogram (IPK) and the molar mass of carbon-12: 1 mol = (0.012 IPK)/M(¹²C). Because the dalton was (and still is) defined as 1 Da = m_a(¹²C)/12 and M(¹²C) = m_a(¹²C)N_A, the original mole definition can be written as 1 mol = (g/Da)(1/N_A), where (g/Da) is the (1971 definition of the) Avogadro number—the number of carbon-12 atoms in 12 grams of carbon-12—and (1/N_A) is an amount of one entity. Since 2019, a mole of any substance has been redefined in the SI as the amount of that substance containing an exactly defined number of entities: 1 mol = 6.02214076×10²³(1/N_A). This is still in the same form as the previous definition, one mole = (Avogadro number)(amount of one entity), but because the dalton is still defined in terms of the (now inexactly known) mass of the carbon-12 atom, the Avogadro number is no longer exactly equal to (g/Da). The numerical value of the molar mass of a substance expressed in g/mol thus is (for all practical purposes) still equal to the numerical value of the mass of this number of entities (i.e. an amount of one mole) of the substance expressed in grams—(the relative discrepancy is only of order 10^–9).