Molar mass

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. The molar mass is appropriate for converting between the mass of a substance and the amount of a substance for bulk quantities.

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 (daltons vs 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 molar mass of a compound, in g/mol, is numerically equal to the average mass of one molecule or formula unit, in daltons. 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 daltons, 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 computed dividing by the number of moles of atoms instead. 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. During that period, the molar mass of carbon-12 was thus exactly 12 g/mol, by definition. 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 particles, 6.02214076×10²³. The molar mass of a compound in g/mol thus is equal to the mass of this number of molecules of the compound in grams.

Molar masses of elements

The molar mass of atoms of an element is given by the relative atomic mass of the element multiplied by the molar mass constant, M_u ≈ 1.000000×10⁻³ kg/mol = 1 g/mol. For normal samples from earth with typical isotope composition, the atomic weight can be approximated by the standard atomic weight^[2] or the conventional atomic weight.

{\begin{array}{lll}M({\ce {H}})&=1.00797(7)\times M_{\mathrm {u} }&=1.00797(7){\text{ g/mol}}\\M({\ce {S}})&=32.065(5)\times M_{\mathrm {u} }&=32.065(5){\text{ g/mol}}\\M({\ce {Cl}})&=35.453(2)\times M_{\mathrm {u} }&=35.453(2){\text{ g/mol}}\\M({\ce {Fe}})&=55.845(2)\times M_{\mathrm {u} }&=55.845(2){\text{ g/mol}}\end{array}}

Multiplying by the molar mass constant ensures that the calculation is dimensionally correct: standard relative atomic masses are dimensionless quantities (i.e., pure numbers) whereas molar masses have units (in this case, grams per mole).

Some elements are usually encountered as molecules, e.g. hydrogen (H₂), sulfur (S₈), chlorine (Cl₂). The molar mass of molecules of these elements is the molar mass of the atoms multiplied by the number of atoms in each molecule:

{\begin{array}{lll}M({\ce {H2}})&=2\times 1.00797(7)\times M_{\mathrm {u} }&=2.01595(4){\text{ g/mol}}\\M({\ce {S8}})&=8\times 32.065(5)\times M_{\mathrm {u} }&=256.52(4){\text{ g/mol}}\\M({\ce {Cl2}})&=2\times 35.453(2)\times M_{\mathrm {u} }&=70.906(4){\text{ g/mol}}\end{array}}

Molar masses of compounds

The molar mass of a compound is given by the sum of the relative atomic mass $A r$ of the atoms which form the compound multiplied by the molar mass constant $M_{u}\approx 1{\text{ g/mol}}$ :

M=M_{\rm {u}}M_{\rm {r}}=M_{\rm {u}}\sum _{i}{A_{\rm {r}}}_{i}.

Here, $M r$ is the relative molar mass, also called formula weight. For normal samples from earth with typical isotope composition, the standard atomic weight or the conventional atomic weight can be used as an approximation of the relative atomic mass of the sample. Examples are: ${\begin{array}{ll}M({\ce {NaCl}})&={\bigl [}22.98976928(2)+35.453(2){\bigr ]}\times 1{\text{ g/mol}}\\&=58.443(2){\text{ g/mol}}\\[4pt]M({\ce {C12H22O11}})&={\bigl [}12\times 12.0107(8)+22\times 1.00794(7)+11\times 15.9994(3){\bigr ]}\times 1{\text{ g/mol}}\\&=342.297(14){\text{ g/mol}}\end{array}}$

An average molar mass may be defined for mixtures of compounds.^[1] This is particularly important in polymer science, where there is usually a molar mass distribution of non-uniform polymers so that different polymer molecules contain different numbers of monomer units.^[3]^[4]

Average molar mass of mixtures

The average molar mass of mixtures ${\overline {M}}$ can be calculated from the mole fractions $x i$ of the components and their molar masses $M i$ :

{\overline {M}}=\sum _{i}x_{i}M_{i}.

It can also be calculated from the mass fractions $w i$ of the components:

{\frac {1}{\overline {M}}}=\sum _{i}{\frac {w_{i}}{M_{i}}}.

As an example, the average molar mass of dry air is 28.96 g/mol.^[5]

Related quantities

Molar mass is closely related to the relative molar mass ( $M r$ ) of a compound and to the standard atomic weights of its constituent elements. However, it should be distinguished from the molecular mass (which is confusingly also sometimes known as molecular weight), which is the mass of one molecule (of any single isotopic composition), and to the atomic mass, which is the mass of one atom (of any single isotope). The dalton, symbol Da, is also sometimes used as a unit of molar mass, especially in biochemistry, with the definition 1 Da = 1 g/mol, despite the fact that it is strictly a unit of mass (1 Da = 1 u = 1.66053906892(52)×10⁻²⁷ kg, as of 2022 CODATA recommended values).^[6]

Obsolete terms for molar mass include gram atomic mass for the mass, in grams, of one mole of atoms of an element, and gram molecular mass for the mass, in grams, of one mole of molecules of a compound. The gram-atom is a former term for a mole of atoms, and gram-molecule for a mole of molecules.^[7]

Molecular weight (M.W.) (for molecular compounds) and formula weight (F.W.) (for non-molecular compounds), are older terms for what is now more correctly called the relative molar mass ( $M r$ ).^[8] This is a dimensionless quantity (i.e., a pure number, without units) equal to the molar mass divided by the molar mass constant.^{[notes 1]}

Molecular mass

The molecular mass ( $m$ ) is the mass of a given molecule: it is usually measured in daltons (Da or u).^[7] Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. This is distinct but related to the molar mass, which is a measure of the average molecular mass of all the molecules in a sample and is usually the more appropriate measure when dealing with macroscopic (weigh-able) quantities of a substance.

Molecular masses are calculated from the atomic masses of each