Molar mass
In chemistry, the molar mass of a chemical substance is defined as the ratio between the mass and the amount of substance of any sample of the substance:. The molar mass is a bulk, not molecular, property of a substance. The molar mass is a weighted ''average of many instances of the element or 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 molecular mass and formula mass are commonly used as synonyms of molar mass, as the numerical values are identical, differing only in units. 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 an intensive property of the substance, that does not depend on the size of the sample. In the International System of Units, the coherent unit of molar mass is kg/mol. However, for historical reasons, molar masses are almost always expressed with the unit 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, with the dalton defined as of the mass of a carbon-12 atom. Thus, during that period, the numerical value of the molar mass of a substance expressed in g/mol was exactly'' equal to the numerical value of the average mass of an entity of the substance expressed in daltons.
Since 2019, the mole has been redefined in the SI as the amount of any substance containing exactly entities, fixing the numerical value of the Avogadro constant when expressed in the unit mol−1, but because the dalton is still defined in terms of the experimentally determined mass of a carbon-12 atom, the numerical equivalence between the molar mass of a substance and the average mass of an entity of the substance is now only approximate, but equality may still be assumed with high accuracy—.
Technical background
For a pure sample of a substance, the known molar mass,, is used for calculating the amount of the substance in the sample,, given the mass of the sample,, through the equation:. If is the number of entities of the substance in the sample, and is the mass of each entity of the substance, then the mass of the sample is, and the amount of substance is ⋅, where is the elementary amount, an amount consisting of exactly one atomic-scale entity of any kind, analogous to the elementary charge. Since the elementary amount is the reciprocal of the Avogadro constant, using the relationship, the molar mass is then given by , i.e. the atomic-scale mass of one entity of the substance per elementary amount.Given the relative atomic-scale mass of an entity of a substance, its mass expressed in daltons is, where the atomic-scale unit of mass is defined as 1 Da = = /12. The corresponding atomic-scale unit of amount of substance is the entity, defined as 1 ent = . So, with known, the molar mass can be expressed in daltons per entity as. Thus, the molar mass of a substance can be calculated as, with the molar mass constant equal to exactly 1 Da/ent, which is equal to 1 g/mol, as the mole was historically defined such that the Avogadro number was exactly equal to the number of daltons in a gram. This means that : 1 mol = ent.
The relationship between the molar mass of carbon-12,, and its atomic mass,, can be expressed as. Rearranging and substituting the given values into the equation yields the following expression for the Avogadro constant:, making the Avogadro number equal to the number of daltons in a gram, and equivalently the number of atoms in 12 grams of carbon-12.
The mole was defined in such a way that the numerical value of the molar mass of a substance in g/mol, i.e., was equal to the numerical value of the average mass of one entity in Da, i.e., so that. The equivalence was exact before the redefinition of the mole in 2019, and is now only approximate, but equality may still be assumed with high accuracy. Thus, for example, the average mass of a molecule of water is about 18.0153 Da, 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 calculated using the relative atomic mass of the element, usually given by the standard atomic weight indicated in the periodic table. Thus, for example, the molar mass of iron is about 55.845 g/mol.
Calculation
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,, which is equal to 1 g/mol:. 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.Multiplying by the molar mass constant ensures that the calculation is dimensionally correct: relative atomic masses and standard atomic weights are dimensionless quantities, whereas molar masses have units.
Some elements are usually encountered as molecules, e.g. hydrogen, nitrogen, oxygen, sulfur, chlorine. The molar mass of molecules of these elements is the molar mass of the atoms multiplied by the number of atoms in each molecule:
Molar masses of compounds
The molar mass of a compound is given by the sum of the relative atomic masses of the elements which form the compound multiplied by the molar mass constant, :Here, is the relative molar mass, also called molecular weight or 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:
Average molar mass of mixtures
An average molar mass may be defined for mixtures of substances. 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. 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 28.9647 g/mol.
Related quantities
Molar mass is closely related to the molecular weight and formula weight , older terms for what is now more correctly called the relative molar mass, a dimensionless quantity equal to the molar mass divided by the molar mass constant, calculated from the standard atomic weights of its constituent elements. However, it should be distinguished from the molecular mass, which is the mass of one molecule, and to the atomic mass, which is the mass of one atom. The dalton, symbol Da, is also sometimes used as a unit of molecular weight and formula weight, especially in biochemistry, despite the fact that the quantities are dimensionless as relative masses.Obsolete terms for molar mass include gram atomic mass for the mass, in grams, of one mole of atoms of an element, and gram molecular mass for the mass, in grams, of one mole of molecules of a compound. The gram-atom is a former term for a mole of atoms, and gram-molecule for a mole of molecules.
Molecular mass
The molecular mass is the mass of a given molecule: it is usually measured in daltons. 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 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 of each element. The standard atomic weight takes into account the isotopic distribution of the element in a given sample. For example, water has a molar mass of, but individual water molecules have molecular masses which range between and .
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.
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.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. Most atomic masses are known to a precision of at least one part in ten-thousand, often much better. 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.