In
chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, proper ...
, the molar mass of a
chemical compound
A chemical compound is a chemical substance composed of many identical molecules (or molecular entities) containing atoms from more than one chemical element held together by chemical bonds. A molecule consisting of atoms of only one element ...
is defined as the
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different ele ...
of a sample of that compound divided by the
amount of substance which is the number of moles in that sample, measured in
moles Moles can refer to:
* Moles de Xert, a mountain range in the Baix Maestrat comarca, Valencian Community, Spain
*The Moles (Australian band)
*The Moles, alter ego of Scottish band Simon Dupree and the Big Sound
People
* Abraham Moles, French engin ...
.
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
isotope
Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers ( mass num ...
s. Most commonly, the molar mass is computed from the
standard atomic weight
The standard atomic weight of a chemical element (symbol ''A''r°(E) for element "E") is the weighted arithmetic mean of the relative isotopic masses of all isotopes of that element weighted by each isotope's abundance on Earth. For example, ...
s 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
The molecular mass (''m'') is the mass of a given molecule: it is measured in daltons (Da or u). Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The related quant ...
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
Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...
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
Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent—its atom making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Carbon ma ...
and metals, the molar mass is computed dividing by the number of moles of atoms instead. Thus, for example, the molar mass of
iron
Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in ...
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, . 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
atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons.
Every solid, liquid, gas, a ...
s of an
element is given by the relative atomic mass of the element multiplied by the
molar mass constant, For normal samples from earth with typical isotope composition, the atomic weight can be approximated by the standard atomic weight
or the conventional atomic weight.
:''M''(H) = × ''M'' =
:''M''(S) = × ''M'' =
:''M''(Cl) = × ''M'' =
:''M''(Fe) = × ''M'' = .
Multiplying by the molar mass constant ensures that the calculation is
dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coord ...
ally 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
molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and b ...
s, e.g.
hydrogen
Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-to ...
(H),
sulfur (S),
chlorine
Chlorine is a chemical element with the symbol Cl and atomic number 17. The second-lightest of the halogens, it appears between fluorine and bromine in the periodic table and its properties are mostly intermediate between them. Chlorine i ...
(Cl). 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 × 1.007 97(7) × ''M'' =
:''M''(S) = 8 × 32.065(5) × ''M'' =
:''M''(Cl) = 2 × 35.453(2) × ''M'' = .
Molar masses of compounds
The molar mass of a
compound is given by the sum of the
relative atomic mass
Relative atomic mass (symbol: ''A''; sometimes abbreviated RAM or r.a.m.), 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 ...
''A'' of the
atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons.
Every solid, liquid, gas, a ...
s which form the compound multiplied by the
molar mass constant ''M'':
:
Here, ''M'' is the relative molar mass, also called formula weight. For normal samples from earth with typical isotope composition, the
standard atomic weight
The standard atomic weight of a chemical element (symbol ''A''r°(E) for element "E") is the weighted arithmetic mean of the relative isotopic masses of all isotopes of that element weighted by each isotope's abundance on Earth. For example, ...
or the conventional atomic weight can be used as an approximation of the relative atomic mass of the sample. Examples are:
:''M''(NaCl) =
+ nbsp;× =
:''M''(CHO) = (
2 × nbsp;+
2 × nbsp;+
1 × × = .
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
In chemistry, a monomer ( ; '' mono-'', "one" + '' -mer'', "part") is a molecule that can react together with other monomer molecules to form a larger polymer chain or three-dimensional network in a process called polymerization.
Classification
...
units (non-uniform polymers).
Average molar mass of mixtures
The average molar mass of mixtures
can be calculated from the
mole fractions
of the components and their molar masses
:
:
It can also be calculated from the
mass fractions of the components:
:
As an example, the average molar mass of dry air is 28.97 g/mol.
Related quantities
Molar mass is closely related to the relative molar mass (''M'') 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
The molecular mass (''m'') is the mass of a given molecule: it is measured in daltons (Da or u). Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The related quant ...
(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 atomic mass (''m''a 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&n ...
, 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
Biochemistry or biological chemistry is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology and ...
, with the definition 1 Da = 1 g/mol, despite the fact that it is strictly a unit of mass (1 Da = 1 u = , 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''). This is a
dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coord ...
less quantity (i.e., a pure number, without units) equal to the molar mass divided by the
molar mass constant.
Molecular mass
The molecular mass (''m'') is the mass of a given molecule: it is usually measured in
daltons (Da or u).
Different molecules of the same compound may have different molecular masses because they contain different
isotope
Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers ( mass num ...
s 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 mass
The atomic mass (''m''a 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&n ...
es of each
nuclide, while molar masses are calculated from the
standard atomic weight
The standard atomic weight of a chemical element (symbol ''A''r°(E) for element "E") is the weighted arithmetic mean of the relative isotopic masses of all isotopes of that element weighted by each isotope's abundance on Earth. For example, ...
s 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
Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...
has a molar mass of , but individual water molecules have molecular masses which range between (
1H
16O) and (
2H
18O).
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
In chemistry, a chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, ...
of a molecule.
DNA synthesis usage
The term formula weight has a specific meaning when used in the context of DNA synthesis: whereas an individual
phosphoramidite
A phosphoramidite (RO)2PNR2 is a monoamide of a phosphite diester. The key feature of phosphoramidites is their markedly high reactivity towards nucleophiles catalyzed by weak acids ''e.c''., triethylammonium chloride or 1''H''-tetrazole. In these ...
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).
Precision and uncertainties
The precision to which a molar mass is known depends on the precision of the
atomic mass
The atomic mass (''m''a 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&n ...
es 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
(the atomic mass of
lithium
Lithium (from el, λίθος, lithos, lit=stone) is a chemical element with the symbol Li and atomic number 3. It is a soft, silvery-white alkali metal. Under standard conditions, it is the least dense metal and the least dense soli ...
is a notable, and serious, 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
isotope
Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers ( mass num ...
s 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.
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;
: for
simple chemical compounds;
: for
polymer
A polymer (; Greek '' poly-'', "many" + '' -mer'', "part")
is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...
s,
protein
Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, res ...
s,
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
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 ...
, 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:
:
where ''n'' is the
amount of substance. The vapour density (''ρ'') is given by
:
Combining these two equations gives an expression for the molar mass in terms of the vapour density for conditions of known
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
and
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
:
:
Freezing-point depression
The
freezing point of a
solution
Solution may refer to:
* Solution (chemistry), a mixture where one substance is dissolved in another
* Solution (equation), in mathematics
** Numerical solution, in numerical analysis, approximate solutions within specified error bounds
* Solutio ...
is lower than that of the pure
solvent
A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...
, and the freezing-point depression (Δ''T'') is directly proportional to the
amount concentration
Quantity or amount is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a un ...
for dilute solutions. When the composition is expressed as a
molality
Molality is a measure of the number of moles of solute in a solution corresponding to 1 kg or 1000 g of solvent. This contrasts with the definition of molarity which is based on a specified volume of solution.
A commonly used unit for molali ...
, the proportionality constant is known as the
cryoscopic constant (''K'') 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
:
Boiling-point elevation
The
boiling point of a
solution
Solution may refer to:
* Solution (chemistry), a mixture where one substance is dissolved in another
* Solution (equation), in mathematics
** Numerical solution, in numerical analysis, approximate solutions within specified error bounds
* Solutio ...
of an involatile
solute is higher than that of the pure
solvent
A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...
, and the boiling-point elevation (Δ''T'') is directly proportional to the
amount concentration
Quantity or amount is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a un ...
for dilute solutions. When the composition is expressed as a
molality
Molality is a measure of the number of moles of solute in a solution corresponding to 1 kg or 1000 g of solvent. This contrasts with the definition of molarity which is based on a specified volume of solution.
A commonly used unit for molali ...
, the proportionality constant is known as the
ebullioscopic constant (''K'') 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
:
See also
*
Mole map (chemistry)
References
External links
HTML5 Molar Mass Calculator web and mobile application.
with the uncertainty of ''M'' and all the calculations shown
Molar Mass CalculatorOnline Molar Mass and Elemental Composition Calculator
Stoichiometry Add-In for Microsoft Excel for calculation of molecular weights, reaction coefficients and stoichiometry. It includes both average atomic weights and isotopic weights.
{{Mole concepts
Mass