Mole (unit)

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The mole is a unit of measurement for the amount of substance or chemical amount. It is one of the base units in the International System of Units, and has the unit symbol mol.[1]

The name mole is an 1897 translation[2][3] of the German unit Mol, coined by the chemist Wilhelm Ostwald in 1893,[4] although the related concept of equivalent mass had been in use at least a century earlier. The name is derived[5] from the German word Molekül (molecule).

The mole is defined as the amount of substance that contains as many elementary entities (e.g., atoms, molecules, ions, electrons) as there are atoms in 12 g of the isotope carbon-12 (12C).[1] Thus, by definition, one mole of pure 12C has a mass of exactly 12 g. The amount of substance n (in mol) and the number of atoms or molecules contained in it, N, are proportional, and the proportionality constant N/n is known as the Avogadro constant. By definition it has the dimension of the inverse of amount of substance (unit mol−1) and its experimentally determined value is .[6]

By this definition, a mole of any pure substance has a mass in grams exactly equal to that substance's molecular or atomic mass; e.g., of calcium-40 is approximately equal to , because the Ca-40 isotope has a mass of 39.9625906 amu on the C-12 scale. In other words, the numerical value of a substance's molecular or atomic mass in atomic mass units is the same as that of its molar mass—the mass of one mole of that substance—in grams.

The most common method of determining the amount, expressed in moles, of pure substance the value of whose molar mass is known, is to measure its mass in grams and then to divide by its molar mass (expressed in g/mol).[7] Molar masses may be easily calculated from tabulated values of atomic weights and the molar mass constant (which has a convenient defined value of 1 g/mol). Other methods include the use of the molar volume or the measurement of electric charge.[7]

The current definition of the mole was approved during the 1960s.[1][8] Earlier definitions had been based on the atomic mass of hydrogen (about one gram of hydrogen-1 gas, excluding its heavy isotopes), the atomic weight of oxygen, and the relative atomic mass of oxygen-16; the four different definitions were equivalent to within 1%.

The names gram-atom (abbreviated gat.) and gram-molecule have also been used in the same sense as "mole".[1] However, modern conventions define the gram-atom and the mole differently. While the elementary entity defining a mole will vary depending on the substance, the elementary entity for the gram-atom is always the atom. For example, 1 mole of He is equivalent to 1 gram-atom of He, but 1 mole of MgB2 is equivalent to 3 gram-atoms of MgB2.[9][10]



The first table of atomic weights was published by John Dalton (1766–1844) in 1805, based on a system in which the atomic weight of hydrogen was defined as 1. These atomic weights were based on the stoichiometric proportions of chemical reactions and compounds, a fact which greatly aided their acceptance: it was not necessary for a chemist to subscribe to atomic theory (an unproven hypothesis at the time) to make practical use of the tables. This would lead to some confusion between atomic weights (promoted by proponents of atomic theory) and equivalent weights (promoted by its opponents and which sometimes differed from atomic weights by an integer factor), which would last throughout much of the nineteenth century.

Jöns Jacob Berzelius (1779–1848) was instrumental in the determination of atomic weights to ever increasing accuracy. He was also the first chemist to use oxygen as the standard to which other weights were referred. Oxygen is a useful standard, as, unlike hydrogen, it forms compounds with most other elements, especially metals. However he chose to fix the atomic weight of oxygen as 100, an innovation which did not catch on.

Charles Frédéric Gerhardt (1816–56), Henri Victor Regnault (1810–78) and Stanislao Cannizzaro (1826–1910) expanded on Berzelius' works, resolving many of the problems of unknown stoichiometry of compounds, and the use of atomic weights attracted a large consensus by the time of the Karlsruhe Congress (1860). The convention had reverted to defining the atomic weight of hydrogen as 1, although at the level of precision of measurements at that time—relative uncertainties of around 1%—this was numerically equivalent to the later standard of oxygen = 16. However the chemical convenience of having oxygen as the primary atomic weight standard became ever more evident with advances in analytical chemistry and the need for ever more accurate atomic weight determinations.

Scale basis Scale basis
relative to 12C = 12
Relative deviation
from the 12C = 12 scale
Atomic weight of hydrogen = 1 1.00794(7) −0.788%
Atomic weight of oxygen = 16 15.9994(3) +0.00375%
Relative atomic mass of 16O = 16 15.9949146221(15) +0.0318%

The mole as a unit

Since its adoption into the International System of Units, there have been a number of criticisms of the concept of the mole as a unit like the meter or the second:

  • the number of molecules etc. in a given lump of material is a fixed dimensionless quantity which can be expressed simply as a number, so does not require its own base unit[8];
  • the SI thermodynamic mole is irrelevant to analytical chemistry and is causing avoidable costs to advanced economies[11];
  • the concepts of the SI quantity 'amount of substance' and unit 'mole' are confusing and difficult to teach[12].

In chemistry, it has been known since Proust's law of definite proportions (1794) that knowledge of the mass of each of the components in a chemical system is not sufficient to define the system. Amount of substance can be described as mass divided by Proust's "definite proportions", and contains information which is missing from the measurement of mass alone. As demonstrated by Dalton's law of partial pressures (1803), a measurement of mass is not even necessary to measure the amount of substance (although in practice it is usual). There are many physical relationships between amount of substance and other physical quantities, most notably the ideal gas law (where the relationship was first demonstrated in 1857). The term "mole" was first used in a textbook describing these colligative properties.

Other units called "mole"

Chemical engineers use the concept extensively, but the unit is rather small for industrial use. For convenience in avoiding conversions, some American engineers adopted the pound-mole (noted lb-mol or lbmol), which is defined as the number of entities in 12 lb of 12C. One lb-mol is equal to .[13] In the metric system, chemical engineers once used the kilogram-mole (noted kg-mol), which is defined as the number of entities in 12 kg of 12C, and often referred to the mole as the gram-mole (noted g-mol), when dealing with laboratory data.[13] However modern chemical engineering practice is to use the kilomole (kmol), which is identical to the kilogram-mole, but whose name and symbol adopt the SI convention for standard multiples of metric units.


As with other SI base units, there have been proposals to redefine the kilogram in such a way as to define some currently measured physical constants to fixed values. One proposed definition of the kilogram is:[14]

The kilogram is the mass of exactly (0.012) unbound carbon-12 atoms at rest and in their ground state.

This would have the effect of defining the Avogadro constant to be precisely elementary entities per mole.

A decision on this proposal is expected by the CGPM in October 2011.[15]

Related units

The SI units for molar concentration are mol/m3. However, most chemical literature traditionally uses mol/dm3, or mol dm−3, which is the same as mol/L. These traditional units are often denoted by a capital letter M (pronounced "molar"), sometimes preceded by an SI prefix, for example millimoles per litre (mmol/L) or millimolar (mM), micromoles/litre (µmol/L) or micromolar (µM), or nanomoles/L (nmol/L) or nanomolar (nM).

The unit's holiday

October 23 is called Mole Day.[16] It is an informal holiday in honor of the unit among chemists in North America. The date is derived from Avogadro's number, which is approximately 6.02×1023. It officially starts at 6:02 A.M. and ends at 6:02 P.M.

See also


  1. a b c d International Bureau of Weights and Measures (2006), (8th ed.), pp. 114–15, , 
  2. Some sources place the date of first usage in English as 1902. Merriam–Webster proposes an etymology from Molekulärgewicht (molecular weight).
  3. Ostwald, Wilhelm (1893). . Leipzig. p. 119. 
  4. mole, n.8, Oxford English Dictionary, Draft Revision Dec. 2008
  5. Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). . Rev. Mod. Phys. 80: 633–730. .  Direct link to value.
  6. a b International Bureau of Weights and Measures. "Realising the mole." Retrieved 25 September 2008.
  7. a b de Bièvre, P.; Peiser, H.S. (1992). . Pure Appl. Chem. 64 (10): 1535–43. . 
  8. Wang, Yuxing et al.; Bouquet, Fr d ric; Sheikin, Ilya; Toulemonde, Pierre; Revaz, Bernard; Eisterer, Michael; Weber, Harald W; Hinderer, Joerg et al. (2003). . Journal of Physics: Condensed Matter 15: 883–893. . 
  9. Lortz, R. et al.; Wang, Y.; Abe, S.; Meingast, C.; Paderno, Yu.; Filippov, V.; Junod, A. (2005). . Phys. Rev. B 72: 024547. . 
  10. Price, Gary (2010). . Accreditation and Quality Assurance 15 (7): 421-427. .
  11. Furio, C; Azcona, R;Guisasola, J. (2002). . Chemistry Education: Research and Practice in Europe 3 (3): 277-292.
  12. a b Himmelblau, David (1996). (6 ed.). pp. 17–20. . 
  13. Mills, Ian M.; Mohr, Peter J.; Quinn, Terry J.; Taylor, Barry N.; Williams, Edwin R. (2005). . Metrologia 42: 71–80. .  Abstract.
  14. Ian Mills (29 September 2010). . CCU. Retrieved 2011-01-01. 
  15. History of National Mole Day Foundation, Inc