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In chemistry , the MOLAR MASS _M_ is a physical property defined as the mass of a given substance (chemical element or chemical compound ) divided by the amount of substance . The base SI unit
SI unit
for molar mass is kg /mol . However, for historical reasons, molar masses are almost always expressed in g/mol.

As an example, the molar mass of water: _M_(H2O) ≈ 6998180000000000000♠18 g/mol.

CONTENTS

* 1 Molar masses of elements * 2 Molar masses of compounds * 3 Average molar mass of mixtures

* 4 Related quantities

* 4.1 Molecular mass * 4.2 DNA
DNA
synthesis usage

* 5 Precision and uncertainties

* 6 Measurement

* 6.1 Vapour density * 6.2 Freezing-point depression
Freezing-point depression
* 6.3 Boiling-point elevation
Boiling-point elevation

* 7 References * 8 External links

MOLAR MASSES OF ELEMENTS

Main articles: Relative atomic mass
Relative atomic mass
and Standard atomic weight
Standard atomic weight

The molar mass of atoms of an element is given by the Standard atomic weight of the element multiplied by the molar mass constant , _M_ u = 1 × 10−3 kg/mol = 1 g/mol: _M_(H) = 1.007 97(7) × 1 g/mol = 1.007 97(7) g/mol _M_(S) = 32.065(5) × 1 g/mol = 32.065(5) g/mol _M_(Cl) = 35.453(2) × 1 g/mol = 35.453(2) g/mol _M_(Fe) = 55.845(2) × 1 g/mol = 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) whereas molar masses have units (in this case, grams/mole).

Some elements are usually encountered as molecules , e.g. hydrogen (H 2), sulfur (S 8), chlorine (Cl 2). 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) = 2 × 1.007 97(7) × 1 g/mol = 2.015 88(14) g/mol _M_(S 8) = 8 × 32.065(5) × 1 g/mol = 256.52(4) g/mol _M_(Cl 2) = 2 × 35.453(2) × 1 g/mol = 70.906(4) g/mol.

MOLAR MASSES OF COMPOUNDS

The molar mass of a compound is given by the sum of the standard atomic weight (namely, the standard relative atomic mass) of the atoms which form the compound multiplied by the molar mass constant , _M_ u: _M_(NaCl) = × 1 g/mol = 58.443(2) g/mol _M_(C 12H 22O 11) = ( + + ) × 1 g/mol = 342.297(14) g/mol.

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 units (non-uniform polymers).

AVERAGE MOLAR MASS OF MIXTURES

The average molar mass of mixtures M {displaystyle {bar {M}}} can be calculated from the mole fractions x i {displaystyle x_{i}} of the components and their molar masses M i {displaystyle M_{i}} : M = i x i M i {displaystyle {bar {M}}=sum _{i}x_{i}M_{i},}

It can also be calculated from the mass fractions w i {displaystyle w_{i}} of the components: 1 / M = i w i M i , {displaystyle 1/{bar {M}}=sum _{i}{frac {w_{i}}{M_{i}}},}

As an example, the average molar mass of dry air is 28.97 g/mol.

RELATED QUANTITIES

Molar mass
Molar mass
is closely related to the RELATIVE MOLAR MASS (_M_ r) 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 (also 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 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 , with the definition 1 Da = 1 g/mol, despite the fact that it is strictly a unit of mass (1 Da = 1 u = 1.660 538 921(73)×10−27 kg).

MOLECULAR WEIGHT (M.W.) is an older term for what is now more correctly called the RELATIVE MOLAR MASS (_M_ r). This is a dimensionless quantity (i.e., a pure number, without units) equal to the molar mass divided by the molar mass constant .

MOLECULAR MASS

Main article: Molecular mass

The molecular mass (_m_) is the mass of a given molecule: it is measured in atomic mass units (u) or daltons (Da). Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The molar mass 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 standard atomic weights of each nuclide , while molar masses are calculated from the atomic mass of each element . The atomic mass takes into account the isotopic distribution of the element in a given sample (usually assumed to be "normal"). For example, water has a molar mass of 18.0153(3) g/mol, but individual water molecules have molecular masses which range between 18.010 564 6863(15) u (1H 216O) and 22.027 7364(9) u (D 218O).

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
DNA
SYNTHESIS USAGE

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The term FORMULA WEIGHT (F.W.) has a specific meaning when used in the context of DNA
DNA
synthesis: whereas an individual phosphoramidite nucleobase to be added to a DNA
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
DNA
polymer, minus protecting groups).

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 (the atomic mass of lithium 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 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.

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; 10–1000 g/mol for simple chemical compounds ; 1000–5,000,000 g/mol for polymers , proteins , DNA
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 , and any dissociation of the compound must be taken into account.

VAPOUR DENSITY

Main article: Vapour density

The measurement of molar mass by vapour density relies on the principle, first enunciated by Amedeo Avogadro
Amedeo Avogadro
, that equal volumes of gases under identical conditions contain equal numbers of particles. This principle is included in the ideal gas equation : p V = n R T {displaystyle pV=nRT }

where _n_ is the amount of substance . The vapour density (ρ) is given by = n M V . {displaystyle rho ={{nM} over {V}}. }

Combining these two equations gives an expression for the molar mass in terms of the vapour density for conditions of known pressure and temperature . M = R T p {displaystyle M={{RTrho } over {p}} }

FREEZING-POINT DEPRESSION

Main article: Freezing-point depression
Freezing-point depression

The freezing point of a solution is lower than that of the pure solvent , and the freezing-point depression (Δ_T_) is directly proportional to the amount concentration for dilute solutions. When the composition is expressed as a 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 M = w K f T . {displaystyle M={{wK_{f}} over {Delta T}}. }

BOILING-POINT ELEVATION

Main article: Boiling-point elevation
Boiling-point elevation

The boiling point of a solution of an involatile solute is higher than that of the pure solvent , and the boiling-point elevation (Δ_T_) is directly proportional to the amount concentration for dilute solutions. When the composition is expressed as a 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 M = w K b T . {displaystyle M={{wK_{b}} over {Delta T}}. }

REFERENCES

* ^ _A_ _B_ International Union of Pure and Applied Chemistry (1993). _Quantities, Units and Symbols in Physical Chemistry
Chemistry
_, 2nd edition, Oxford: Blackwell Science. ISBN 0-632-03583-8 . p. 41. Electronic version. * ^ _A_ _B_ Wieser, M. E. (2006), "Atomic Weights of the Elements 2005" (PDF), _Pure and Applied Chemistry
Chemistry
_, 78 (11): 2051–66, doi :10.1351/pac200678112051  _ * ^ A_ _B_ Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2011). "CODATA Recommended Values of the Fundamental Physical Constants: 2010". Database developed by J. Baker, M. Douma, and S. Kotochigova. National Institute of Standards and Technology
National Institute of Standards and Technology
, Gaithersburg, MD 20899. * ^ International Union of Pure and Applied Chemistry
Chemistry
(1984). "Note on the terminology for molar masses in polymer science". _J. Polym. Sci., Polym. Lett. Ed_. 22 (1): 57. Bibcode :1984JPoSL..22...57.. doi :10.1002/pol.1984.130220116 . * ^ Metanomski, W. V. (1991). _Compendium of Macromolecular Nomenclature_. Oxford: Blackwell Science. pp. 47–73. ISBN 0-632-02847-5 . * ^ The Engineering ToolBox Molecular Mass
Mass
of Air * ^ _A_ _B_ International Bureau of Weights and Measures
International Bureau of Weights and Measures
(2006), _The International System of Units (SI)_ (PDF) (8th ed.), p. 126, ISBN 92-822-2213-6 * ^ IUPAC , _ Compendium of Chemical Terminology _, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "relative molar mass". * ^ The technical definition is that the relative molar mass is the molar mass measured on a scale where the molar mass of unbound carbon 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 the molar mass constant is itself defined. * ^ "Atomic Weights and Isotopic Compositions for All Elements". NIST
NIST
. Retrieved 2007-10-14. * ^ "Author Guidelines – Article Layout". RSC Publishing . Retrieved 2007-10-14. * ^ Greenwood, Norman N. ; Earnshaw, Alan (1997). _ Chemistry
Chemistry
of the Elements_ (2nd ed.). Butterworth-Heinemann . p. 21. ISBN 0-08-037941-9 . * ^ See, e.g., Weast, R. C., ed. (1972). _Handbook of Chemistry
Chemistry
and Physics_ (53rd ed.). Cleveland, OH: Chemical Rubber Co.

EXTERNAL LINKS

* HTML5 Molar Mass

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