Mole (unit)

This article is about physical quantity measurement unit. For other uses, see Mole (disambiguation).

The mole (symbol mol) is the SI base unit of amount of substance, one of a few units used to measure this physical quantity. The name "mole" is an 1897 translation of the German Mol, coined by Wilhelm Ostwald in 1893, 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 German word Molekül (molecule).

The mole is commonly used in medicine to measure small amounts of a substance in blood or other liquids. In this context, millimoles per litre (mmol/L), micromoles/litre (µmol/L), or nanomoles/L (nmol/L) are often used.

The mole is defined as the amount of substance of a system that contains as many "elementary entities" (e.g. atoms, molecules, ions, electrons) as there are atoms in 12 g of carbon-12 (¹²C). A mole has 6.0221415×10²³ atoms or molecules of the pure substance being measured. A mole of a substance has mass in grams exactly equal to the substance's molecular or atomic weight, e. g. 1 mol of Calcium-40 is equal to 40 grams. That is to say, a substance's atomic or molecular mass in atomic mass units is the same as its molar mass in grams. Because of this, one can measure the number of moles in a pure substance by weighing it and comparing the result to its molecular or atomic weight.

The current definition of the mole was approved during the 1960s: Prior to that, there had been definitions based on the atomic weight 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 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. 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.

The names gram-atom (abbreviated gat.) and gram-molecule have also been used in the same sense as "mole". 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.

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. These criticisms may be briefly summarized 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.

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

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 453.59237 mol. Chemical engineers also use * moles( star moles) to denote two amounts of mass(or more) that has the same latent heat. This allows the assumption of equal-mole overflow to hold true in distillation columns.

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. 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.

Proposed future definition

Kilogram

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:

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.

Holiday

October the 23rd (10/23), "Mole Day", is an informal holiday in honor of the unit among chemists in North America. The date is derived from the Avogadro constant, which is approximately 6.02×10²³.

See also

• Einstein (unit)
• Faraday (unit)
• Stoichiometry
• Molar concentration
• Molarity
• Molar volume

External links

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