Mole (unit)

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The mole (symbol: mol) is a unit of amount of substance: it is an SI base unit,^[1] and one of the few units used to measure this physical quantity. The name "mole" was coined in German (as Mol) by Wilhelm Ostwald in 1893,^[2] although the related concept of equivalent mass had been in use at least a century earlier. The name is assumed to be derived from the word Molekül (molecule). The first usage in English dates from 1897, in a work translated from German.^[3][4] The names gram-atom and gram-molecule have also been used in the same sense as "mole",^[1][5] but these names are now obsolete.

The mole is defined as the amount of substance of a system that contains as many "elemental entities" (e.g., atoms, molecules, ions, electrons) as there are atoms in 12 g of carbon-12.^[1] Hence:

• one mole of iron contains the same number of atoms as one mole of gold;
• one mole of benzene contains the same number of molecules as one mole of water;
• the number of atoms in one mole of iron is equal to the number of molecules in one mole of water.

It is a common misconception that the mole is defined in terms of the Avogadro constant (also known as "Avogadro's number"). It is not necessary to know the number of atoms or molecules that are present in order to use the mole as a unit of measurement,^[5] and indeed the first measurements of amount of substance predate modern atomic theory and any measurements of atomic weight.^[6] The current definition of the mole was approved during the 1960s:^[1][5] Prior to that, there had been definitions based on the atomic weight of hydrogen, the atomic weight of oxygen, and the relative atomic mass of oxygen-16: the four different definitions are equivalent to within 1%.

The most common method of measuring an amount of substance is to measure its mass and then to divide by the molar mass of the substance.^[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]

Contents 1 The mole as a unit 2 History 3 Other units called "mole" 4 Proposed future definition 4.1 Kilogram 5 See also 6 References

[edit] 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 being a unit like the metre or the second.^[5] These criticisms may be briefly summarised as:

• amount of substance is not a true physical quantity (or dimension), and is redundant to mass, so should not have its own base unit;
• the mole is simply a shorthand way of referring to a large number.

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.

The second misconception, that the mole is simply a counting aid, has even found its way into elementary chemistry textbooks.^[8] It contends that the mole is defined in terms of the Avogadro constant, rather than the other way around, and so is equal to 6.02214179×10²³ elementary entities.

Consider the measurement of one mole of silicon. As silicon is a solid at room temperature, the convenient method of measurement is weighing. By consulting published tables, it can easily be found that the atomic weight of silicon is 28.0855.^[9] Multiplying by the molar mass constant M_u gives the molar mass in any desired mass units: assuming the measurement is to be made in grams, M_u = 1 g/mol, and so the molar mass of silicon is 28.0855 g/mol. Hence, 28.0855 g of silicon is equivalent to one mole of silicon, without the Avogadro constant ever having come into play.

Counting (or calculating) the number of atoms in 28.0855 g of silicon is one way of determining the Avogadro constant, N_A, and a way which is currently receiving a lot of attention (see below) although, as of the 2006 CODATA values of the physical constants, it is not the most accurate. It is only a method of determining N_A because it is known by other means that 28.0855 g of silicon is equivalent to one mole. Those other means are:

• the very accurate determination of the ratios of the masses of each of the three silicon nuclides to the mass of an atom of carbon-12, in such a way that it is known that a silicon-28 atom is [27.976 926 5327(20)/12] times as massive as a carbon-12 atom;^[9][10]
• the determination of the isotopic abundance of silicon in the samples used to make the measurements, allowing the calculation of the atomic weight of silicon in each individual sample;
• the definition of 12 g of carbon-12 atoms to be equivalent to one mole.

[edit] History

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' work, 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	1.007 94(7)	−0.788%
Atomic weight of oxygen = 16	15.9994(3)	+37.5 ppm
Relative atomic mass of 16O = 16	15.994 914 6221(15)	+318 ppm

[edit] Other units called "mole"

Chemical engineers use the concept extensively, but the unit is rather small for industrial use. For convenience in avoiding conversions, American engineers adopted the pound-mole or lb-mol, which is defined is the number of entities in 12 lb of 12-C. One lb-mol is equal to 453.59237 mol.^[11]

In the metric system, chemical engineers once used the kilogram-mole or kg-mol, which is defined as the number of entities in 12 kg of 12-C, and often referred to the mole as the gram-mole, written g-mol, when dealing with laboratory data.^[11]

However modern chemical engineering practice is to use the kilomole, (kmol) which is identical to the kilogram-mole.

[edit] Proposed future definition

[edit] Kilogram

As with other SI base units, there have been proposals to redefine the kilogram in such a way as to define some presently measured physical constants to fixed values. One proposed definition of the kilogram is:^[12]

The kilogram is the mass of exactly (^{6.0221415×1023}⁄_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 6.0221415×10²³ elementary entities per mole.

[edit] See also

[edit] References

• The Origin of the Word 'Mole' ChemTeam.