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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 eleme ...
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 In chemistry, the amount of substance ''n'' in a given sample of matter is defined as the quantity or number of discrete atomic-scale particles in it divided by the Avogadro constant ''N''A. The particles or entities may be molecules, atoms, ions ...
which is the number of moles in that sample, measured in moles. 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 Physical properties of materials and systems can often be categorized as being either intensive or extensive, according to how the property changes when the size (or extent) of the system changes. According to IUPAC, an intensive quantity is one ...
of the substance, that does not depend on the size of the sample. In the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...
(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 a ...
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 m ...
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 i ...
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 Carbon-12 (12C) is the most abundant of the two stable isotopes of carbon ( carbon-13 being the other), amounting to 98.93% of element carbon on Earth; its abundance is due to the triple-alpha process by which it is created in stars. Carbon-12 i ...
. 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, g ...
s of an
element Element or elements may refer to: Science * Chemical element, a pure substance of one type of atom * Heating element, a device that generates heat by electrical resistance * Orbital elements, parameters required to identify a specific orbit of o ...
is given by the relative atomic mass of the element multiplied by the
molar mass constant The molar mass constant, usually denoted by ''M''u, is a physical constant defined as one twelfth of the molar mass of carbon-12: ''M''u = ''M''(12C)/12. The molar mass of any element or compound is its relative atomic mass (atomic weight) mu ...
, 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 bio ...
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-toxi ...
(H),
sulfur Sulfur (or sulphur in British English) is a chemical element with the symbol S and atomic number 16. It is abundant, multivalent and nonmetallic. Under normal conditions, sulfur atoms form cyclic octatomic molecules with a chemical formula ...
(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 Compound may refer to: Architecture and built environments * Compound (enclosure), a cluster of buildings having a shared purpose, usually inside a fence or wall ** Compound (fortification), a version of the above fortified with defensive struc ...
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, g ...
s which form the compound multiplied by the
molar mass constant The molar mass constant, usually denoted by ''M''u, is a physical constant defined as one twelfth of the molar mass of carbon-12: ''M''u = ''M''(12C)/12. The molar mass of any element or compound is its relative atomic mass (atomic weight) mu ...
''M'': :$M = M_ M_ = M_ \sum_i _i.$ 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 Polymer science or macromolecular science is a subfield of materials science concerned with polymers, primarily synthetic polymers such as plastics and elastomers. The field of polymer science includes researchers in multiple disciplines inclu ...
, 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. Classificati ...
units (non-uniform polymers).

# Average molar mass of mixtures

The average molar mass of mixtures $\bar$ can be calculated from the
mole fraction In chemistry, the mole fraction or molar fraction (''xi'' or ) is defined as unit of the amount of a constituent (expressed in moles), ''ni'', divided by the total amount of all constituents in a mixture (also expressed in moles), ''n''tot. This ...
s $x_i$ of the components and their molar masses $M_i$: :$\bar = \sum_i x_i M_i.$ It can also be calculated from the mass fractions $w_i$ of the components: :$\frac = \sum_i\frac.$ 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&nb ...
, 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 ...
, 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 The molar mass constant, usually denoted by ''M''u, is a physical constant defined as one twelfth of the molar mass of carbon-12: ''M''u = ''M''(12C)/12. The molar mass of any element or compound is its relative atomic mass (atomic weight) mu ...
.

## 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&nb ...
es of each
nuclide A nuclide (or nucleide, from nucleus, also known as nuclear species) is a class of atoms characterized by their number of protons, ''Z'', their number of neutrons, ''N'', and their nuclear energy state. The word ''nuclide'' was coined by Tru ...
, 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 Element or elements may refer to: Science * Chemical element, a pure substance of one type of atom * Heating element, a device that generates heat by electrical resistance * Orbital elements, parameters required to identify a specific orbit of o ...
. 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 a ...
has a molar mass of , but individual water molecules have molecular masses which range between (1H16O) and (2H18O). The distinction between molar mass and molecular mass is important because relative molecular masses can be measured directly by
mass spectrometry Mass spectrometry (MS) is an analytical technique that is used to measure the mass-to-charge ratio of ions. The results are presented as a '' mass spectrum'', a plot of intensity as a function of the mass-to-charge ratio. Mass spectrometry is u ...
, often to a precision of a few
parts per million In science and engineering, the parts-per notation is a set of pseudo-units to describe small values of miscellaneous dimensionless quantities, e.g. mole fraction or mass fraction. Since these fractions are quantity-per-quantity measures, th ...
. 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&nb ...
es from which it was calculated, and value of the
molar mass constant The molar mass constant, usually denoted by ''M''u, is a physical constant defined as one twelfth of the molar mass of carbon-12: ''M''u = ''M''(12C)/12. The molar mass of any element or compound is its relative atomic mass (atomic weight) mu ...
. 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 solid ...
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 Distillation, or classical distillation, is the process of separating the components or substances from a liquid mixture by using selective boiling and condensation, usually inside an apparatus known as a still. Dry distillation is the heating ...
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 error A roundoff error, also called rounding error, is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. Rounding errors are d ...
s 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 sheet A safety data sheet (SDS), material safety data sheet (MSDS), or product safety data sheet (PSDS) is a document that lists information relating to occupational safety and health for the use of various substances and products. SDSs are a widel ...
s (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 ...
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 Lorenzo Romano Amedeo Carlo Avogadro, Count of Quaregna and Cerreto (, also , ; 9 August 17769 July 1856) was an Italian scientist, most noted for his contribution to molecular theory now known as Avogadro's law, which states that equal volum ...
, that equal volumes of gases under identical conditions contain equal numbers of particles. This principle is included in the ideal gas equation: :$pV = nRT ,$ where ''n'' is the
amount of substance In chemistry, the amount of substance ''n'' in a given sample of matter is defined as the quantity or number of discrete atomic-scale particles in it divided by the Avogadro constant ''N''A. The particles or entities may be molecules, atoms, ions ...
. The vapour density (''ρ'') is given by :$\rho = .$ 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 ...
: :$M = .$

## Freezing-point depression

The
freezing point The melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depends ...
of a solution 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 uni ...
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 molal ...
, 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 chemistry, a solution is a special type of homogeneous mixture composed of two or more substances. In such a mixture, a solute is a substance dissolved in another substance, known as a solvent. If the attractive forces between the solvent ...
in solution, and assuming no dissociation of the solute, the molar mass is given by :$M = .\$

## Boiling-point elevation

The
boiling point The boiling point of a substance is the temperature at which the vapor pressure of a liquid equals the pressure surrounding the liquid and the liquid changes into a vapor. The boiling point of a liquid varies depending upon the surrounding en ...
of a solution of an involatile
solute In chemistry, a solution is a special type of homogeneous mixture composed of two or more substances. In such a mixture, a solute is a substance dissolved in another substance, known as a solvent. If the attractive forces between the solvent ...
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 uni ...
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 molal ...
, 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 :$M = .\$

* Mole map (chemistry)