# Molar mass

Last updated
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 MN−1

In chemistry, the molar mass (or molecular weight) (M) 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.

## Contents

The molecular mass and formula mass are commonly used as a synonym of molar mass, particularly for molecular compounds; 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 formula weight is a synonym of molar mass that is frequently used for non-molecular compounds, such as ionic salts.

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, 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, Mu  1×10−3 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.

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

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:

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

## Molar masses of compounds

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

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

Here, Mr 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:

${\displaystyle {\begin{array}{ll}M({\ce {NaCl}})&={\bigl [}22.98976928(2)+35.453(2){\bigr ]}\times 1{\text{ g/mol}}\\&=58.443(2){\text{ g/mol}}\\[4pt]M({\ce {C12H22O11}})&={\bigl [}12\times 12.0107(8)+22\times 1.00794(7)+11\times 15.9994(3){\bigr ]}\times 1{\text{ g/mol}}\\&=342.297(14){\text{ g/mol}}\end{array}}}$

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. [4] [5]

## Average molar mass of mixtures

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

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

It can also be calculated from the mass fractions wi of the components:

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

As an example, the average molar mass of dry air is 28.96 g/mol. [6]

Molar mass is closely related to the relative molar mass (Mr) 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 (Mr). [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]

### Molecular mass

The molecular mass (m) is the mass of a given molecule: it is usually measured in daltons (Da or u). [9] 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 nuclide, while molar masses are calculated from the standard atomic weights [10] of each element. The standard atomic weight 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 18.0105646863(15) Da (1H216O) and 22.0277364(9) Da (2H218O).

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 molecule. [11]

### DNA synthesis usage

The term formula weight has a specific meaning when used in the context of DNA synthesis: whereas an individual phosphoramidite nucleobase to be added to a DNA polymer has protecting groups and has its molecular weight quoted including these groups, the amount of molecular weight that is ultimately added by this nucleobase to a DNA polymer is referred to as the nucleobase's formula weight (i.e., the molecular weight of this nucleobase within the DNA polymer, minus protecting groups).[ citation needed ]

## Precision and uncertainties

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]

## Measurement

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.

### 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:

${\displaystyle pV=nRT,}$

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:

${\displaystyle M={{RT\rho } \over {p}}.}$

### 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 (Kf) 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

${\displaystyle M={{wK_{\text{f}}} \over {\Delta T}}.\ }$

### 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 (Kb) 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

${\displaystyle M={{wK_{\text{b}}} \over {\Delta T}}.\ }$

## Related Research Articles

The molecular mass (m) is the mass of a given molecule. The unit dalton (Da) is often used. Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The derived quantity relative molecular mass is the unitless ratio of the mass of a molecule to the atomic mass constant (which is equal to one dalton).

In thermodynamics, the specific heat capacity of a substance is the amount of heat that must be added to one unit of mass of the substance in order to cause an increase of one unit in temperature. It is also referred to as massic heat capacity or as the specific heat. More formally it is the heat capacity of a sample of the substance divided by the mass of the sample. The SI unit of specific heat capacity is joule per kelvin per kilogram, J⋅kg−1⋅K−1. For example, the heat required to raise the temperature of 1 kg of water by 1 K is 4184 joules, so the specific heat capacity of water is 4184 J⋅kg−1⋅K−1.

Stoichiometry is the relationship between the weights of reactants and products before, during, and following chemical reactions.

The mole (symbol mol) is a unit of measurement, the base unit in the International System of Units (SI) for amount of substance, a quantity proportional to the number of elementary entities of a substance. One mole contains exactly 6.02214076×1023 elementary entities (approximately 602 sextillion or 602 billion times a trillion), which can be atoms, molecules, ions, or other particles. The number of particles in a mole is the Avogadro number (symbol N0) and the numerical value of the Avogadro constant (symbol NA) expressed in mol-1. The value was chosen based on the historical definition of the mole as the amount of substance that corresponds to the number of atoms in 12 grams of 12C, which made the mass of a mole of a compound expressed in grams, numerically equal to the average molecular mass of the compound expressed in daltons. With the 2019 redefinition of the SI base units, the numerical equivalence is now only approximate but may be assumed for all practical purposes.

The Avogadro constant, commonly denoted NA or L, is an SI defining constant with an exact value of 6.02214076×1023 mol−1 (reciprocal moles). It is defined as the number of constituent particles (usually molecules, atoms, or ions) per mole (SI unit) and used as a normalization factor in the amount of substance in a sample. The constant is named after the physicist and chemist Amedeo Avogadro (1776–1856).

The dalton or unified atomic mass unit is a non-SI unit of mass defined as 1/12 of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest. The atomic mass constant, denoted mu, is defined identically, giving mu = 1/12m(12C) = 1 Da.

In chemistry and related fields, the molar volume, symbol Vm, or of a substance is the ratio of the volume occupied by a substance to the amount of substance, usually at a given temperature and pressure. It is equal to the molar mass (M) divided by the mass density (ρ):

Graham's law of effusion was formulated by Scottish physical chemist Thomas Graham in 1848. Graham found experimentally that the rate of effusion of a gas is inversely proportional to the square root of the molar mass of its particles. This formula is stated as:

Relative atomic mass, also known by the deprecated synonym atomic weight, is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a given sample to the atomic mass constant. The atomic mass constant is defined as being 1/12 of the mass of a carbon-12 atom. Since both quantities in the ratio are masses, the resulting value is dimensionless. These definitions remain valid even after the 2019 redefinition of the SI base units.

Avogadro's law or Avogadro-Ampère's hypothesis is an experimental gas law relating the volume of a gas to the amount of substance of gas present. The law is a specific case of the ideal gas law. A modern statement is:

Avogadro's law states that "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules."

For a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant.

In chemistry, colligative properties are those properties of solutions that depend on the ratio of the number of solute particles to the number of solvent particles in a solution, and not on the nature of the chemical species present. The number ratio can be related to the various units for concentration of a solution such as molarity, molality, normality (chemistry), etc. The assumption that solution properties are independent of nature of solute particles is exact only for ideal solutions, which are solutions that exhibit thermodynamic properties analogous to those of an ideal gas, and is approximate for dilute real solutions. In other words, colligative properties are a set of solution properties that can be reasonably approximated by the assumption that the solution is ideal.

In chemistry, the amount of substance (symbol n) in a given sample of matter is defined as a ratio (n = N/NA) between the number of elementary entities (N) and the Avogadro constant (NA). The entities are usually molecules, atoms, or ions of a specified kind. The particular substance sampled may be specified using a subscript, e.g., the amount of sodium chloride (NaCl) would be denoted as nNaCl. The unit of amount of substance in the International System of Units is the mole (symbol: mol), a base unit. Since 2019, the value of the Avogadro constant NA is defined to be exactly 6.02214076×1023 mol−1. Sometimes, the amount of substance is referred to as the chemical amount or, informally, as the "number of moles" in a given sample of matter.

The molar heat capacity of a chemical substance is the amount of energy that must be added, in the form of heat, to one mole of the substance in order to cause an increase of one unit in its temperature. Alternatively, it is the heat capacity of a sample of the substance divided by the amount of substance of the sample; or also the specific heat capacity of the substance times its molar mass. The SI unit of molar heat capacity is joule per kelvin per mole, J⋅K−1⋅mol−1.

In chemistry, equivalent weight is the mass of one equivalent, that is the mass of a given substance which will combine with or displace a fixed quantity of another substance. The equivalent weight of an element is the mass which combines with or displaces 1.008 gram of hydrogen or 8.0 grams of oxygen or 35.5 grams of chlorine. These values correspond to the atomic weight divided by the usual valence; for oxygen as example that is 16.0 g / 2 = 8.0 g.

In polymer chemistry, the molar mass distribution describes the relationship between the number of moles of each polymer species and the molar mass of that species. In linear polymers, the individual polymer chains rarely have exactly the same degree of polymerization and molar mass, and there is always a distribution around an average value. The molar mass distribution of a polymer may be modified by polymer fractionation.

A chemical substance is a unique form of matter with constant chemical composition and characteristic properties. Chemical substances may take the form of a single element or chemical compounds. If two or more chemical substances can be combined without reacting, they may form a chemical mixture. If a mixture is separated to isolate one chemical substance to a desired degree, the resulting substance is said to be chemically pure.

The mass recorded by a mass spectrometer can refer to different physical quantities depending on the characteristics of the instrument and the manner in which the mass spectrum is displayed.

The molar mass constant, usually denoted by Mu, is a physical constant defined as one twelfth of the molar mass of carbon-12: Mu = M(12C)/12. The molar mass of any element or compound is its relative atomic mass multiplied by the molar mass constant.

This glossary of chemistry terms is a list of terms and definitions relevant to chemistry, including chemical laws, diagrams and formulae, laboratory tools, glassware, and equipment. Chemistry is a physical science concerned with the composition, structure, and properties of matter, as well as the changes it undergoes during chemical reactions; it features an extensive vocabulary and a significant amount of jargon.

The atomic mass (ma or m) is the mass of an atom. Although the SI unit of mass is the kilogram (symbol: kg), atomic mass is often expressed in the non-SI unit dalton (symbol: Da) – equivalently, unified atomic mass unit (u). 1 Da is defined as 112 of the mass of a free carbon-12 atom at rest in its ground state. The protons and neutrons of the nucleus account for nearly all of the total mass of atoms, with the electrons and nuclear binding energy making minor contributions. Thus, the numeric value of the atomic mass when expressed in daltons has nearly the same value as the mass number. Conversion between mass in kilograms and mass in daltons can be done using the atomic mass constant .

## References

1. International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry , 2nd edition, Oxford: Blackwell Science. ISBN   0-632-03583-8 . p. 41. Electronic version.
2. "2022 CODATA Value: molar mass constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 2024-05-18.
3. Wieser, M. E. (2006), "Atomic Weights of the Elements 2005" (PDF), Pure and Applied Chemistry , 78 (11): 2051–66, doi:
4. "International union of pure and applied chemistry, commission on macromolecular nomenclature, note on the terminology for molar masses in polymer science". Journal of Polymer Science: Polymer Letters Edition. 22 (1): 57. 1984. Bibcode:1984JPoSL..22...57.. doi:10.1002/pol.1984.130220116.
5. Metanomski, W. V. (1991). Compendium of Macromolecular Nomenclature. Oxford: Blackwell Science. pp. 47–73. ISBN   0-632-02847-5.
6. The Engineering ToolBox Molecular Mass of Air
7. IUPAC , Compendium of Chemical Terminology , 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006) " relative molar mass ". doi : 10.1351/goldbook.R05270
8. The technical definition is that the relative molar mass is the molar mass measured on a scale where the molar mass of unbound carbon 12 atoms, at rest and in their electronic ground state, is 12. The simpler definition given here is equivalent to the full definition because of the way the molar mass constant is itself defined.
9. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 126, ISBN   92-822-2213-6, archived (PDF) from the original on 2021-06-04, retrieved 2021-12-16
10. "Atomic Weights and Isotopic Compositions for All Elements". NIST . Retrieved 2007-10-14.
11. "Author Guidelines – Article Layout". RSC Publishing . Retrieved 2007-10-14.
12. Greenwood, Norman N.; Earnshaw, Alan (1997). Chemistry of the Elements (2nd ed.). Butterworth-Heinemann. p. 21. ISBN   978-0-08-037941-8.
13. See, e.g., Weast, R. C., ed. (1972). Handbook of Chemistry and Physics (53rd ed.). Cleveland, OH: Chemical Rubber Co.
14. Possolo, Antonio; van der Veen, Adriaan M. H.; Meija, Juris; Hibbert, D. Brynn (2018-01-04). "Interpreting and propagating the uncertainty of the standard atomic weights (IUPAC Technical Report)". Pure and Applied Chemistry. 90 (2): 395–424. doi:. S2CID   145931362.