Mole (unit)

The mole is a unit of measurement used in chemistry to express amounts of a chemical substance, defined as an amount of a substance that contains as many elementary entities (e.g., atoms, molecules, ions, electrons) as there are atoms in 12 grams of pure carbon-12 (12C), the isotope of carbon with atomic weight 12. This corresponds to a value of $6.022$ elementary entities of that substance. It is one of the base units in the International System of Units, and has the unit symbol mol.

The mole is widely used in chemistry, instead of units of mass or volume, as a convenient way to express the amounts of reagents and products of chemical reactions. For example, the chemical equation 2 H2 + O2 → 2 H2O implies that 2 mol of dihydrogen and 1 mol of dioxygen react to form 2 mol of water. The mole may also be used to express the number of atoms, ions, or other elementary entities in some sample. The concentration of a solution is commonly expressed by its molarity, the number of moles of the dissolved substance per liter of solution.

The number of molecules in a mole (known as Avogadro's number) is defined so that the mass of one mole of a substance, expressed in grams, is exactly equal to the substance's mean molecular weight. For example, the mean molecular weight of natural water is about 18.015, so one mole of water is about 18.015 grams. This property considerably simplifies many chemical and physical computations.

The name gram-molecule was formerly used for essentially the same concept. The name gram-atom (abbreviated gat.) has been used for related but distinct concept, namely a quantity of a substance that contains Avogadro's number of atoms, whether isolated or combined in molecules. Thus, for example, 1 mole of MgB2 is 1 gram-molecule of MgB2 but 3 gram-atoms of MgB2.

Definition and related concepts
, the mole is defined by BIPM to be an amount of a substance that contains as many elementary entities (e.g., atoms, molecules, ions, electrons) as there are atoms in 12 grams of pure carbon-12 (12C), the isotope of carbon with atomic weight 12. Thus, by definition, one mole of pure 12C has a mass of exactly 12 g. It also follows from the definition that X moles of any substance will contain the same number of molecules as X moles of any other substance.

The mass per mole of a substance is called its molar mass. Since the standard unit for expressing the mass of molecules or atoms (the dalton or atomic mass unit) is defined as 1/12 of the mass of a 12C atom, it follows that the molar mass of a substance, measured in grams per mole, is exactly equal to its mean molecular or atomic mass, measured in daltons; which is to say, to the substance's mean molecular or atomic weight.

The number of elementary entities in a sample of a substance is technically called its (chemical) amount. Therefore, the mole is a convenient unit for that physical quantity. One can determine the chemical amount of a known substance, in moles, by dividing the sample's mass by the substance's molar mass. Other methods include the use of the molar volume or the measurement of electric charge.

It should be noted that the mass of one mole of a substance depends not only on its molecular formula, but also on the proportion of the isotopes of each element present in it. For example, one mole of calcium-40 is $39.963$ ± $0$ grams, whereas one mole of calcium-42 is $41.959$ ± $0$ grams, and one mole of calcium with the normal isotopic mix is 40.078 ± 0.004 grams.

Since the definition of the gram is not mathematically tied to that of the dalton, the number NA of molecules in a mole (Avogadro's number) must be determined experimentally. The value adopted by CODATA in 2006 is NA = $6.022$ ± $0$. In 2011 the measurement was refined to $6.022$ ± $0$.

History
The history of the mole is intertwined with that of molecular mass, atomic mass unit, Avogadro's number and related concepts.

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 that 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 that 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.

Developments in mass spectrometry led to the adoption of oxygen-16 as the standard substance, in lieu of natural oxygen. The current definition of the mole, based on carbon-12, was approved during the 1960s. The four different definitions were equivalent to within 1%.

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

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 that can be expressed simply as a number, so does not require its own base unit;
 * the SI thermodynamic mole is irrelevant to analytical chemistry and is causing avoidable costs to advanced economies;
 * the mole is not a true metric (i.e measuring) unit, rather it is a parametric unit and amount of substance is a parametric base quantity;
 * the concepts of the SI quantity 'amount of substance' and unit 'mole' are confusing and difficult to teach.
 * the SI defines numbers of entities as quantities of dimension one, and thus ignores the ontological distinction between entities and units of continuous quantities.

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 that 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, the most notable one being 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 $12$. 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.

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 ($12$) unbound carbon-12 atoms at rest and in their ground state.

This would have the effect of defining the Avogadro constant to be precisely $16$ elementary entities per mole.

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

Related units
The SI units for molar concentration are mol/m3. However, most chemical literature traditionally uses mol/dm3, or mol dm&minus;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. 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 6.022×1023. It officially starts at 6:02 A.M. and ends at 6:01 P.M.