Inchemistry, themolar mass (M) (sometimes calledmolecular weight orformula weight, but seerelated quantities for usage) of achemical compound is defined as the ratio between themass and theamount of substance (measured inmoles) of any sample of the compound.[1] The molar mass is a bulk, not molecular,property of a substance. The molar mass is anaverage of many instances of the compound, which often vary in mass due to the presence ofisotopes. Most commonly, the molar mass is computed from thestandard atomic weights and is thus a terrestrial average and a function of the relative abundance of theisotopes 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.
Themolecular mass (for molecular compounds) and formula mass (for non-molecular compounds, such asionic salts) are commonly used as synonyms of molar mass, differing only in units (daltons vs g/mol); 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 molar mass is anintensive property of the substance, that does not depend on the size of the sample. In theInternational System of Units (SI), thecoherent 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 or formula unit, in daltons. It was exactly equal before theredefinition 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 ofwater is about 18.0153 daltons, and the molar mass of water is about 18.0153 g/mol.
For chemical elements without isolated molecules, such ascarbon and metals, the molar mass is computed dividing by the number of moles of atoms instead. Thus, for example, the molar mass ofiron is about 55.845 g/mol.
Since 1971, SI defined the "amount of substance" as a separatedimension 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 ofcarbon-12. During that period, the molar mass of carbon-12 was thusexactly 12 g/mol, by definition. Since 2019, a mole of any substance has beenredefined 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.
The molar mass ofatoms of anelement is given by the relative atomic mass of the element multiplied by themolar mass constant,Mu ≈ 1.000000×10−3 kg/mol ≈ 1 g/mol. For normal samples from Earth with typical isotope composition, the atomic weight can be approximated by the standard atomic weight[2] or the conventional atomic weight.
Multiplying by the molar mass constant ensures that the calculation isdimensionally 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 asmolecules, 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:
Here,Mr is the relative molar mass, also called formula weight. For normal samples from earth with typical isotope composition, thestandard atomic weight or the conventional atomic weight can be used as an approximation of the relative atomic mass of the sample. Examples are:
An average molar mass may be defined for mixtures of compounds.[1] This is particularly important inpolymer science, where there is usually amolar mass distribution of non-uniform polymers so that different polymer molecules contain different numbers ofmonomer units.[3][4]
Molar mass is closely related to therelative molar mass (Mr) of a compound and to thestandard atomic weights of its constituent elements. However, it should be distinguished from themolecular mass (which is confusinglyalso sometimes known as molecular weight), which is the mass ofone molecule (of anysingle isotopic composition), and to theatomic mass, which is the mass ofone atom (of anysingle isotope). Thedalton, symbol Da, is also sometimes used as a unit of molar mass, especially inbiochemistry, with the definition 1 Da = 1 g/mol, despite the fact that it is strictly a unit of mass (1 Da = 1 u =1.66053906892(52)×10−27 kg, as of 2022 CODATA recommended values).[6]
Obsolete terms for molar mass includegram atomic mass for the mass, in grams, of one mole of atoms of an element, andgram molecular mass for the mass, in grams, of one mole of molecules of a compound. Thegram-atom is a former term for a mole of atoms, andgram-molecule for a mole of molecules.[7]
Molecular weight (M.W.) (for molecular compounds) andformula weight (F.W.) (for non-molecular compounds), are older terms for what is now more correctly called therelative molar mass (Mr).[8] This is adimensionless quantity (i.e., a pure number, without units) equal to the molar mass divided by themolar mass constant.[notes 1]
The molecular mass (m) is the mass of a given molecule: it is usually measured indaltons (Da or u).[7] Different molecules of the same compound may have different molecular masses because they contain differentisotopes 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 theatomic masses of eachnuclide, while molar masses are calculated from thestandard atomic weights[9] of eachelement. The standard atomic weight takes into account theisotopic distribution of the element in a given sample (usually assumed to be "normal"). For example,water has a molar mass of18.0153(3) g/mol, but individual water molecules have molecular masses which range between18.0105646863(15) Da (1H216O) and22.0277364(9) Da (2H218O).
The distinction between molar mass and molecular mass is important because relative molecular masses can be measured directly bymass spectrometry, often to a precision of a fewparts per million. This is accurate enough to directly determine thechemical formula of a molecule.[10]
The termformula weight has a specific meaning when used in the context of DNA synthesis: whereas an individualphosphoramidite nucleobase to be added to a DNA polymer has protecting groups and has itsmolecular 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'sformula weight (i.e., the molecular weight of this nucleobase within the DNA polymer, minus protecting groups).[citation needed]
The precision to which a molar mass is known depends on the precision of theatomic masses from which it was calculated (and very slightly on the value of themolar mass constant, which depends on the measured value of thedalton). Most atomic masses are known to a precision of at least one part in ten-thousand, often much better[2] (the atomic mass oflithium is a notable, and serious,[11] exception). This is adequate for almost all normal uses in chemistry: it is more precise than mostchemical 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 theisotopic 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 beendistilled will beenriched in the lighterisotopes of all the elements present. This complicates the calculation of thestandard uncertainty in the molar mass.
A useful convention for normal laboratory work is to quote molar masses to twodecimal places for all calculations. This is more accurate than is usually required, but avoidsrounding 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.[12][13]
Molar masses are almost never measured directly. They may be calculated from standard atomic masses, and are often listed in chemical catalogues and onsafety data sheets (SDS). Molar masses typically vary between:
1–238 g/mol for atoms of naturally occurring elements;
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 modernmass spectrometric measurements of atomic weights and molecular masses, and are of mostly historical interest. All of the procedures rely oncolligative properties, and anydissociation of the compound must be taken into account.
The measurement of molar mass by vapour density relies on the principle, first enunciated byAmedeo Avogadro, that equal volumes of gases under identical conditions contain equal numbers of particles. This principle is included in theideal gas equation:
Thefreezing point of asolution is lower than that of the puresolvent, and the freezing-point depression (ΔT) is directly proportional to theamount concentration for dilute solutions. When the composition is expressed as amolality, the proportionality constant is known as thecryoscopic constant (Kf) and is characteristic for each solvent. Ifw represents themass fraction of thesolute in solution, and assuming no dissociation of the solute, the molar mass is given by
Theboiling point of asolution of an involatilesolute is higher than that of the puresolvent, and the boiling-point elevation (ΔT) is directly proportional to theamount concentration for dilute solutions. When the composition is expressed as amolality, the proportionality constant is known as theebullioscopic constant (Kb) and is characteristic for each solvent. Ifw represents themass fraction of the solute in solution, and assuming no dissociation of the solute, the molar mass is given by
^"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.
^The technical definition is that the relative molar mass is the molar mass measured on a scale where the molar mass of unboundcarbon 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 themolar mass constant is itself defined.
