# Molar Mass

In chemistry , the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance in that sample, measured in moles . [1] It is the mass of 1 mole of the substance or6.022 × 10 23 particles, expressed in grams. Molar mass is a bulk, not a molecular, property of a substance. The molar mass is the average of several instances of a compound , which often varies in mass due to the presence of isotopes . Typically, the molarmass is calculated from the standard atomic mass and is thus a topological average and a function of the relative abundance of the isotopes of the constituent atoms on Earth. Molarmass is suitable for converting large quantities between the mass of a substance and the amount of a substance.

Molecular weight is usually used as a synonym of molar mass, especially for molecular compounds; However, most authoritative sources define it differently ( see molecular mass ).

The formula weight is a synonym of molar mass that is often used for nonmolecular compounds, such as ionic salts .

Molar mass is an intensive property of matter, which does not depend on the size of the sample. In the International System of Units (SI), the favorable unit of molar mass is kg / mol . However, for historical reasons, the molar mass is almost always expressed in g /mol.

The mole was defined in such a way that the molarmass of a compound, in g/mol, is numerically equal (for all practical purposes) to the average mass of a molecule , in daltons . Thus, for example, the average mass of a molecule of water is about 18.0153 daltons, and the molarmass of water is about 18.0153 g/mol.

For chemical elements without isolated molecules, such as carbon and metals, the molarmass is calculated by dividing by the number of moles of atoms. Thus, for example, the molarmass of iron is approximately 55.845 g/mol.

Since 1971, the SI defined “amount of matter” as a separate dimension of measurement . As of 2019, the mole was defined as the amount of matter that contains as many constituent particles as an atom in 12 grams of carbon -12. During that period, the molarmass of carbon-12 was by definition exactly 12 g/mol. Since 2019, one 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 . Thus the molarmass of a compound in g/mol is equal to the mass of this number of molecules of the compound in g.

## molar mass of elements

The molar mass of atoms of an element is given by multiplying the relative atomic mass of that element by the molar mass constant , M u = 0.999 999 999 65 (30) × 10 −3 kg⋅mol −1 . [2] For normal samples from Earth with specific isotope composition, the atomic weight can be estimated by the standard atomic weight [3] or by the conventional atomic weight.

m (h) =1.007 97 (7) × m u =1.007 97 (7) g/mol
m (s) =32.065(5) × m u =32.065(5) g/mol
M (Cl) =35.453(2) × m u =35.453(2) g/mol
M (Fe) =55.845(2) × m u =55.845(2) g/mol .

Multiplying by the molar mass constant ensures that the calculation is dimensionally correct: standard relative atomic masses are dimensionless quantities (i.e. pure numbers) while molar masses have units (in this case, grams per mole).

Some elements are usually found in the form of molecules , such as hydrogen (H.)2), sulfur (S.)8), chlorine (Cl.)2) The molarmass of the molecules of these elements is the molarmass of the atoms multiplied by the number of atoms in each molecule:

m (h2) = 2 × 1.007 97 (7) × u  =2.015 88 (14) g/molem (s)
8) = 8 × 32.065(5) × u  =256.52(4) g/molm (cli)
2) = 2 × 35.453(2) × u  =70.906(4) g/mol .

## molar mass of compounds

The molar mass of a compound is given by the sum of the relative atomic masses AR By which pair of atoms multiply form the molar mass constant m

{\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 specific isotopic compositions, the standard atomic weight or conventional atomic weight can be used as an approximation to the relative atomic mass of the sample. Examples are:

m (NaCl) = [22.98 9 76 9 28 (2) + 35.453(2) ] × 1.000 000  g/mol  =58.443(2) g/mole

An average molar mass can be defined for a mixture of compounds. [1] This is particularly important in polymer science , where different polymer molecules may contain different numbers of monomer units (non-identical polymers).

## average molar mass of the mixture

The average molar mass of a mixture can be calculated from the mole fractions

{\bar {M}} x_{i}

of the components and their molar mass :Mi

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


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

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


For example, the average molarmass of dry air is 28.97  g/mol. [6]

## related quantity

Molar mass is closely related to relative molar mass ( MR) of a compound, for the old term formula weight (FW), and the standard atomic mass of its constituent elements. However, it must be distinguished from molecular mass (which is also doubtful, also sometimes referred to as molecular weight), which is the mass of a molecule (any one isotopic composition) and is not directly related to the atom. The mass of an atom (of a single isotope), of mass. Dalton, symbol Da, is also sometimes used as a unit of molar mass, especially in biochemistry, with the definition 1  Da  = 1  g/mol, the fact that it is strictly a unit of mass. Despite the unit is (1  Da  = 1  U  =1.660 539 066 60 (50) × 10 -27  kg , CODATA Recommendation Values ​​as of 2018).

Gram atomic mass is another term for the mass, in grams, of a mole of atoms of that element. “Gram atom” is a former term for a mole.

Molecular weight (MW) is an older term now more correctly called relative molarmass ( MR[7] It is a dimensionless quantity (ie, a pure number, without units) equal to the molarmass divided by the molarmass constant. [8]

### molecular mass

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. It is different from but related to molarmass, which is a measure of the average molecular mass of all molecules in a sample and is usually a more appropriate measure when dealing with macroscopic (weighable) amounts of a substance.

The molecular mass is calculated from the atomic mass of each nuclide, while the molar mass is calculated from the standard atomic mass of each element [10] . The standard atomic weight takes into account the isotopic distribution of the element in a given sample (usually considered “normal”). For example, the molar mass of water is18.0153(3) g/mol , but individual water molecules have molecular masses that are . occur between18.010 564 6863 (15 ) of ( 1H1216 o) and22.027 7364 (9) da ( 2 h218 o).

The distinction between molar mass and molecular mass is important because relative molecular mass can be directly measured by mass spectrometry, often to an accuracy of a few parts per million. It is accurate enough to directly determine the chemical formula of a molecule. [11 1]

### DNA synthesis usage

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

## accuracy and uncertainty

The accuracy with which a molar mass is known depends on the accuracy of the atomic mass from which it was calculated, and the value of the molar mass constant. Most atomic masses are known to have an accuracy 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 sufficient for almost all common uses in chemistry: it is more accurate than most chemical analyses, and exceeds the purity of most laboratory reagents.

The accuracy of the atomic mass, and therefore the molar mass, is limited by the knowledge of the element’s isotopic distribution. If a more precise value of the molar mass is required, it is necessary to determine the isotopic distribution of the sample in question, which may differ from the standard distribution used to calculate the standard atomic mass. The isotopic distributions of different elements in a sample are not necessarily independent of each other: for example, a sample that has been distilled will be rich in mild isotopes of all elements present. This complicates the calculation of the standard uncertainty in the molar mass.

A useful convention for general laboratory work is to quote the molar mass to two decimal places for all calculations. This is usually more accurate than necessary, 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 tabular values ​​of molar mass. [13] [14]

## measurement

Molar mass is almost never measured directly. They can be calculated from the standard atomic mass, and are often listed in chemical catalogs and safety data sheets (SDS). Molar masses generally differ in:

1-238 g/mol for atoms of naturally occurring elements;
10 – 1000 g/mol for simple chemical compounds ;
1000-5 000 000 g/mol for polymers, proteins, DNA fragments, etc.

While molar masses are almost always, in practice, calculated from atomic mass, they can also be measured in some cases. Such measurements are much less accurate than modern mass spectrometric measurements of atomic mass and molecular mass, and are mostly of historical interest. All processes depend on collinear properties, and any dissociation of the compound must be taken into account.

### vapor density

Vapor density by molar mass and the measurement principle, previously propounded by Amedeo Avogadro, that equal volumes of gases under similar 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 vapor density ( ) is given by

{\displaystyle \rho ={{nM} \over {V}}.}

Combining these two equations gives an expression for the molar mass in terms of vapor density for known pressure and temperature conditions:

{\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 the dilute solution. When the composition is expressed as molality, the proportionality constant is known as the cryoscopic constant ( K.)F) 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 height

The boiling point of a solution of an involatile solute is higher than that of the pure solvent, and the boiling point height (ΔT ) is directly proportional to the amount concentration for the dilute solution. When the structure is expressed as molality, the proportionality constant is known as the ebullioscopic constant ( K.)b) 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}}.\ }