Molar mass

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 = 0.99999999965(30)×10⁻³ kg⋅mol⁻¹.[2] For normal samples from earth with typical isotope composition, the atomic weight can be approximated by the standard atomic weight[3] or the conventional atomic weight.

M(H) = 1.00797(7) × M_u = 1.00797(7) g/mol

M(S) = 32.065(5) × M_u = 32.065(5) g/mol

M(Cl) = 35.453(2) × M_u = 35.453(2) g/mol

M(Fe) = 55.845(2) × M_u = 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 per 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) × M_u = 2.01588(14) g/mol

M(S
₈) = 8 × 32.065(5) × M_u = 256.52(4) g/mol

M(Cl
₂) = 2 × 35.453(2) × M_u = 70.906(4) g/mol.

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:

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

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:

M(NaCl) = [22.98976928(2) + 35.453(2)] × 1.000000 g/mol = 58.443(2) g/mol

M(C
₁₂H
₂₂O
₁₁) = ([12 × 12.0107(8)] + [22 × 1.00794(7)] + [11 × 15.9994(3)]) × 1.000000 g/mol = 342.297(14) g/mol.

An average molar mass may be defined for mixtures of compounds.[1] This is particularly important in polymer science, where different polymer molecules may contain different numbers of monomer units (non-uniform polymers).[4][5]

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:

${\displaystyle {\frac {1}{\bar {M}}}=\sum _{i}{\frac {w_{i}}{M_{i}}}.}$

As an example, the average molar mass of dry air is 28.97 g/mol.[6]

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 (which is confusingly also sometimes 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 = 1.66053906660(50)×10⁻²⁷ kg, as of 2018 CODATA recommended values).

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).[7] This is a dimensionless quantity (i.e., a pure number, without units) equal to the molar mass divided by the molar mass constant.[8]

The precision to which a molar mass is known depends on the precision of the atomic masses from which it was calculated, and value of the molar mass constant. Most atomic masses are known to a precision of at least one part in ten-thousand, often much better[3] (the atomic mass of lithium is a notable, and serious,[12] exception). This is adequate for almost all normal uses in chemistry: it is more precise than most chemical analyses, and exceeds the purity of most laboratory reagents.

The precision of atomic masses, and hence of molar masses, is limited by the knowledge of the isotopic distribution of the element. If a more accurate value of the molar mass is required, it is necessary to determine the isotopic distribution of the sample in question, which may be different from the standard distribution used to calculate the standard atomic mass. The isotopic distributions of the different elements in a sample are not necessarily independent of one another: for example, a sample which has been distilled will be enriched in the lighter isotopes of all the elements present. This complicates the calculation of the standard uncertainty in the molar mass.

A useful convention for normal laboratory work is to quote molar masses to two decimal places for all calculations. This is more accurate than is usually required, but avoids rounding errors during calculations. When the molar mass is greater than 1000 g/mol, it is rarely appropriate to use more than one decimal place. These conventions are followed in most tabulated values of molar masses.[13][14]

Molar masses are almost never measured directly. They may be calculated from standard atomic masses, and are often listed in chemical catalogues and on safety data sheets (SDS). Molar masses typically vary between:

1–238 g/mol for atoms of naturally occurring elements;

10–1000 g/mol for simple chemical compounds;

1000–5000000 g/mol for polymers, proteins, DNA fragments, etc.

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.

• Mole map (chemistry)

• HTML5 Molar Mass Calculator Archived 2017-04-25 at the Wayback Machine web and mobile application.
• Online Molar Mass Calculator with the uncertainty of M and all the calculations shown
• Molar Mass Calculator Online Molar Mass and Elemental Composition Calculator
• Stoichiometry Add-In for Microsoft Excel Archived 2011-05-11 at the Wayback Machine for calculation of molecular weights, reaction coefficients and stoichiometry. It includes both average atomic weights and isotopic weights.
• Molar mass: chemistry second-level course.