In chemistry, the molar mass M is a physical property defined as the
mass of a given substance (chemical element or chemical compound)
divided by the amount of substance. The base
1 Molar masses of elements 2 Molar masses of compounds 3 Average molar mass of mixtures 4 Related quantities
4.1 Molecular mass
5 Precision and uncertainties 6 Measurement
6.1 Vapour density 6.2 Freezing-point depression 6.3 Boiling-point elevation
7 References 8 External links
Molar masses of elements Main articles: Relative atomic mass and Standard atomic weight The molar mass of atoms of an element is given by the Standard atomic weight of the element multiplied by the molar mass constant, M u = 1 × 10−3 kg/mol = 1 g/mol:
M(H) = 1.007 97(7) × 1 g/mol = 1.007 97(7) g/mol M(S) = 32.065(5) × 1 g/mol = 32.065(5) g/mol M(Cl) = 35.453(2) × 1 g/mol = 35.453(2) g/mol M(Fe) = 55.845(2) × 1 g/mol = 55.845(2) g/mol.
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/mole). Some elements are usually encountered as molecules, e.g. hydrogen (H 2), sulfur (S 8), chlorine (Cl 2). The molar mass of molecules of these elements is the molar mass of the atoms multiplied by the number of atoms in each molecule:
M(H 2) = 2 × 1.007 97(7) × 1 g/mol = 2.015 88(14) g/mol M(S 8) = 8 × 32.065(5) × 1 g/mol = 256.52(4) g/mol M(Cl 2) = 2 × 35.453(2) × 1 g/mol = 70.906(4) g/mol.
Molar masses of compounds The molar mass of a compound is given by the sum of the standard atomic weight (namely, the standard relative atomic mass) of the atoms which form the compound multiplied by the molar mass constant, M u:
M(NaCl) = [22.989 769 28(2) + 35.453(2)] × 1 g/mol = 58.443(2) g/mol M(C 12H 22O 11) = ([12 × 12.0107(8)] + [22 × 1.007 94(7)] + [11 × 15.9994(3)]) × 1 g/mol = 342.297(14) g/mol.
An average molar mass may be defined for mixtures of compounds. This is particularly important in polymer science, where different polymer molecules may contain different numbers of monomer units (non-uniform polymers). Average molar mass of mixtures The average molar mass of mixtures
displaystyle bar M
can be calculated from the mole fractions
displaystyle x_ i
of the components and their molar masses
displaystyle M_ i
displaystyle bar M =sum _ i x_ i M_ i ,
It can also be calculated from the mass fractions
displaystyle w_ i
of the components:
displaystyle 1/ bar M =sum _ i frac w_ i M_ i ,
As an example, the average molar mass of dry air is 28.97 g/mol.
Molar mass is closely related to the relative molar mass (M
r) of a compound, to the older term formula weight (F.W.), and to the
standard atomic masses of its constituent elements. However, it should
be distinguished from the molecular mass (also known as molecular
weight), which is the mass of one molecule (of any single isotopic
composition) and is not directly related to the atomic mass, 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 =
1.660 538 921(73)×10−27 kg).
Gram atomic mass is another term for the mass, in grams, of one mole
of atoms of that element. "Gram atom" is a former term for a mole.
Molecular weight (M.W.) is an older term for what is now more
correctly called the relative molar mass (M
r). This is a dimensionless quantity (i.e., a pure number, without
units) equal to the molar mass divided by the molar mass constant.
Main article: Molecular mass
The molecular mass (m) is the mass of a given molecule: it is measured
in atomic mass units (u) or daltons (Da). Different molecules of
the same compound may have different molecular masses because they
contain different isotopes of an element. The molar mass 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 standard atomic weights
of each nuclide, while molar masses are calculated from the atomic
mass of each element. The atomic mass takes into account the isotopic
distribution of the element in a given sample (usually assumed to be
"normal"). For example, water has a molar mass of
18.0153(3) g/mol, but individual water molecules have molecular
masses which range between 18.010 564 6863(15) u (1H
216O) and 22.027 7364(9) u (D
The distinction between molar mass and molecular mass is important
because relative molecular masses can be measured directly by mass
spectrometry, often to a precision of a few parts per million. This is
accurate enough to directly determine the chemical formula of a
This section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. (December 2008) (Learn how and when to remove this template message)
The term formula weight (F.W.) has a specific meaning when used in the
1–238 g/mol for atoms of naturally occurring elements;
10–1000 g/mol for simple chemical compounds;
1000–5,000,000 g/mol for polymers, proteins,
While molar masses are almost always, in practice, calculated from atomic weights, they can also be measured in certain cases. Such measurements are much less precise than modern mass spectrometric measurements of atomic weights and molecular masses, and are of mostly historical interest. All of the procedures rely on colligative properties, and any dissociation of the compound must be taken into account. Vapour density Main article: Vapour density The measurement of molar mass by vapour density relies on the principle, first enunciated by Amedeo Avogadro, that equal volumes of gases under identical conditions contain equal numbers of particles. This principle is included in the ideal gas equation:
p V = n R T
where n is the amount of substance. The vapour density (ρ) is given by
displaystyle rho = nM over V .
Combining these two equations gives an expression for the molar mass in terms of the vapour density for conditions of known pressure and temperature.
R T ρ
displaystyle M= RTrho over p
Freezing-point depression Main article: Freezing-point depression The freezing point of a solution is lower than that of the pure solvent, and the freezing-point depression (ΔT) is directly proportional to the amount concentration for dilute solutions. When the composition is expressed as a molality, the proportionality constant is known as the cryoscopic constant (K f) and is characteristic for each solvent. If w represents the mass fraction of the solute in solution, and assuming no dissociation of the solute, the molar mass is given by
displaystyle M= wK_ f over Delta T .
Boiling-point elevation Main article: Boiling-point elevation The boiling point of a solution of an involatile solute is higher than that of the pure solvent, and the boiling-point elevation (ΔT) is directly proportional to the amount concentration for dilute solutions. When the composition is expressed as a molality, the proportionality constant is known as the ebullioscopic constant (K b) and is characteristic for each solvent. If w represents the mass fraction of the solute in solution, and assuming no dissociation of the solute, the molar mass is given by
displaystyle M= wK_ b over Delta T .
^ a b International Union of Pure and Applied