The mole

The mole is the unit of measurement for amount of substance in the International System of Units (SI). The unit is defined as the amount or sample of a chemical substance that contains as many constitutive particles, e.g., atoms, molecules, ions, electrons, or photons, as there are atoms in 12 grams of carbon-12 (12C), the isotope of carbon with standard atomic weight 12 by definition. This number is expressed by the Avogadro constant, which has a value of approximately 6.022140857×1023 mol−1. The mole is an SI base unit, with the unit symbol mol.

Mole

Unit system SI base unit

Unit of Amount of substance

Symbol mol 

The mole is widely used in chemistry as a convenient way to express amounts of reactants and products of chemical reactions. For example, the chemical equation 2 H2 + O2 → 2H2O implies that 2 mol dihydrogen (H2) and 1 mol dioxygen (O2) react to form 2 mol water (H2O). The mole may also be used to represent the number of atoms, ions, or other entities in a given sample of a substance. The concentration of a solution is commonly expressed by its molarity, defined as the amount of dissolved substance per unit volume of solution, for which the unit typically used is moles per litre(mol/l).

The term gram-molecule was formerly used for essentially the same concept.[1] The term gram-atom has been used for a 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 MgBr2 is 1 gram-molecule of MgBr2 but 3 gram-atoms of MgBr2.

As of 2011, the mole is defined by International Bureau of Weights and Measures to be the amount of substance of a system which contains the same number of constitutive entities (e.g. atoms, molecules, ions, electrons, photons) as atoms in 0.012 kilograms of carbon-12 (12C), the isotope of carbon with standard atomic weight 12.[1]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 contain the same number of molecules as Xmoles of any other substance. The basic, constitutive entities concerned may be atoms, molecules, ions, electrons, photons, or other elementary particles. When using the mole as unit, the entities must be specified. The concept applies only to homogeneous amounts of substances, that is, consisting of entities that all have practically the same physical properties.

The molar mass of a substance is its mass divided by its amount of substance, which is a constant for any given substance. Since the unified atomic mass unit (symbol: u, or Da) is defined as 1/12 of the mass of the 12C atom, it follows that the molar mass of a substance, measured in grams per mole, is numerically equal to its mean atomic or molecular mass measured in Da.

The number of constitutive entities in a sample of a substance is technically called its (chemical) amount. Therefore, the mole is a 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 volumeor the measurement of electric charge.

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 39.96259098±0.00000022 grams, whereas one mole of calcium-42 is 41.95861801±0.00000027 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 (as of 2011) mathematically tied to that of the atomic mass unit, the number of molecules per mole NA (the Avogadro constant) must be determined experimentally. The value adopted by CODATA in 2010 is NA = (6.02214129±0.00000027)×1023 mol−1. In 2011 the measurement was refined to (6.02214078±0.00000018)×1023 mol−1.

The number of moles of a sample is the sample mass divided by the molar mass of the material.

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 standard atomic weight(atomic weight) was published by John Dalton (1766–1844) in 1805, based on a system in which the relative atomic mass of hydrogen was defined as 1. These relative atomic masses were based on the stoichiometric proportions of chemical reaction 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 masses (promoted by proponents of atomic theory) and equivalent weights (promoted by its opponents and which sometimes differed from relative atomic masses by an integer factor), which would last throughout much of the nineteenth century.

Jöns Jacob Berzelius (1779–1848) was instrumental in the determination of relative atomic masses to ever-increasing accuracy. He was also the first chemist to use oxygenas the standard to which other masses 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 mass of oxygen as 100, 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 masses attracted a large consensus by the time of the Karlsruhe Congress (1860). The convention had reverted to defining the atomic mass 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 mass standard became ever more evident with advances in analytical chemistry and the need for ever more accurate atomic mass determinations.

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

Scale basisScale basis

relative to 12C = 12Relative deviation

from the 12C = 12 scale

Atomic mass of hydrogen = 1 1.00794(7) −0.788%

Atomic mass of oxygen = 16 15.9994(3) +0.00375%

Relative atomic mass of 16O = 16 15.9949146221(15) +0.0318%

The name mole is an 1897 translation of the German unit Mol, coined by the chemistWilhelm Ostwald in 1894 from the German word Molekül (molecule).[8][9][10] However, the related concept of equivalent mass had been in use at least a century earlier.

The mole was made the seventh SI base unitin 1971 by the 14th CGPM.

Since its adoption into the International System of Units in 1971, numerous criticisms of the concept of the mole as a unit like the metre or the second have arisen:

the number of molecules, etc. in a given amount of material is a fixed dimensionless quantity that can be expressed simply as a number, not requiring a distinct base unit;[7]

the SI thermodynamic mole is irrelevant to analytical chemistry and could cause avoidable costs to advanced economies;

the mole is not a true metric (i.e. measuring) unit, rather it is a parametricunit and amount of substance is a parametric base quantity;

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.