Mole (unit)
The mole, symbol mol, is the SI base unit of amount of substance. The quantity amount of substance is a measure of how many elementary entities of a given substance are in an object or sample. Depending on what the substance is, an elementary entity may be an atom, a molecule, an ion, an ion pair, or a subatomic particle such as an electron. For example, if beaker A contains 10 moles of water (a chemical compound) and beaker B contains 10 moles of mercury (a chemical element), they contain equal amounts of substance and beaker B contains  exactly 1 atom of mercury for each molecule of water in beaker A, despite the 2 beakers containing different volumes and very different masses of liquid. The mole is defined as exactly elementary entities. This definition was adopted in November 2018 and came into force on the 20 May 2019, superseding the previous definition of the mole as a number of elementary entities equal to that in 12 grams of carbon-12, the most common isotope of carbon. Because a dalton, a unit commonly used to measure atomic mass, is exactly 1/12 of the mass of a carbon-12 atom, the definition  of the mole in place before 2019 entailed that the mass of one mole of a compound or element in grams was numerically equal to the average mass of one molecule or atom of the substance in daltons and that the number of daltons in a gram was equal to the number of elementary entities in a mole. Because the mass of a nucleon (i.e. a proton or neutron) is approximately 1 dalton and the nucleons in an atom's nucleus make up the overwhelming majority of its mass, the pre-2019 definition also entailed that the mass of one mole  of a substance was roughly equivalent to the number of nucleons in one atom or molecule of that substance. For example, a water molecule formed from the most common isotope of oxygen and of hydrogen contains 10 protons and 8 neutrons and has a total mass of 18.015 daltons, meaning a mole of water has a mass of 18.015 grams, while an atom of the only stable isotope of gold contains 79 protons and 118 neutrons and has a mass of daltons, meaning a mole of gold has a mass of grams. The number of elementary entities in 1 mole  is known as the Avogadro number. Prior to 2019, it could only be estimated based on experimental data. The value was adopted based on the best estimates available in 2018, allowing the new definition to very closely approximate the earlier definition and avoid the need to recalibrate measuring equipment or update published data tables. 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 can be interpreted to mean that for each 2 mol dihydrogen (H) and 1 mol dioxygen (O) that react, 2  mol of water (HO) form. The mole may also be used to measure the amount of atoms, ions, electrons, or other entities. The concentration of a solution is commonly expressed by its molarity, defined as the amount of dissolved substance in mole(s) per unit volume of solution, for which the unit typically used is moles per litre (mol/L), commonly abbreviated M. The term gram-molecule (g mol) was formerly used for "mole of molecules", and gram-atom (g atom) for "mole of atoms". For example, 1 mole of MgBr is 1 gram-molecule of MgBr but 3 gram-atoms  of MgBr. Concepts. Nature of the particles. The mole is essentially a count of particles. Usually the particles counted are chemically identical entities, individually distinct. For example, a solution may contain a certain number of dissolved molecules that are more or less independent of each other. However, in a solid the constituent particles are fixed and bound in a lattice arrangement, yet they may be separable without losing their chemical identity. Thus the solid is composed of a certain number of moles of such particles. In yet other cases, such as diamond, where the entire crystal is essentially a single  molecule, the mole is still used to express the number of atoms bound together, rather than a count of multiple molecules. Thus, common chemical conventions apply to the definition of the constituent particles of a substance, in other cases exact definitions may be specified. The mass of 1 mole of a substance is equal to its relative atomic or molecular mass in grams. Molar mass. The molar mass of a substance is the mass of 1 mole of that substance, in multiples of the gram. The amount of substance is the number of moles in the sample. For most practical  purposes, the magnitude of molar mass is numerically the same as that of the mean mass of one molecule, expressed in daltons. For example, the molar mass of water is 18.015 g/mol. Other methods include the use of the molar volume or the measurement of electric charge. The number of moles of a substance in a sample is obtained by dividing the mass of the sample by the molar mass of the compound. For example, 100 g of water is about 5.551 mol of water. The molar mass of a substance depends not only on its molecular formula, but  also on the distribution of isotopes of each chemical element present in it. For example, the mass of one mole of calcium-40 is , whereas the mass of one mole of calcium-42 is , and of one mole of calcium with the normal isotopic mix is . Molar concentration. The molar concentration, also called "molarity", of a solution of some substance is the number of moles per unit of volume of the final solution. In the SI its standard unit is mol/m, although more practical units, such as mole per litre (mol/L) are used. Molar fraction. The molar fraction or mole  fraction of a substance in a mixture (such as a solution) is the number of moles of the compound in one sample of the mixture, divided by the total number of moles of all components. For example, if 20 g of is dissolved in 100 g of water, the amounts of the two substances in the solution will be (20 g)/(58.443 g/mol) = 0.34221 mol and (100 g)/(18.015 g/mol) = 5.5509 mol, respectively; and the molar fraction of will be 0.34221/(0.34221 + 5.5509) = 0.05807. In a mixture of gases, the partial pressure of each component is proportional  to its molar ratio. History. The history of the mole is intertwined with that of molecular mass, atomic mass units, and the Avogadro number. The first table of standard atomic weight (atomic mass) 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 oxygen as 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. The name "mole" is an 1897 translation of the German unit "Mol", coined by the chemist Wilhelm Ostwald in 1894 from the German word "Molekül" (molecule). The related concept of equivalent mass had been in use at least a century earlier. Standardization. Developments in mass spectrometry led to the adoption of oxygen-16 as the standard substance, in lieu of natural oxygen. The oxygen-16 definition was replaced with  one based on carbon-12 during the 1960s. The mole was defined by International Bureau of Weights and Measures as "the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12." Thus, by that definition, one mole of pure C had a mass of "exactly" 12 g. The four different definitions were equivalent to within 1%. Since the definition of the gram was not mathematically tied to that of the dalton, the number of molecules per mole "N" (the Avogadro constant) had to be determined experimentally. The experimental value adopted  by CODATA in 2010 is . In 2011 the measurement was refined to . The mole was made the seventh SI base unit in 1971 by the 14th CGPM. 2019 redefinition of SI base units. In 2011, the 24th meeting of the General Conference on Weights and Measures (CGPM) agreed to a plan for a possible revision of the SI base unit definitions at an undetermined date. On 16 November 2018, after a meeting of scientists from more than 60 countries at the CGPM in Versailles, France, all SI base units were defined in terms of physical constants. This meant that each  SI unit, including the mole, would not be defined in terms of any physical objects but rather they would be defined by constants that are, in their nature, exact. Such changes officially came into effect on 20 May 2019. Following such changes, "one mole" of a substance was redefined as containing "exactly elementary entities" of that substance. Criticism. 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: 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. Similar units. Like chemists, chemical engineers use the unit mole extensively, but different unit multiples may be more suitable for industrial use. For example, the SI unit for volume is the cubic metre, a much larger unit than the commonly used litre in the chemical laboratory. When amount of substance is also expressed in kmol (1000 mol) in industrial-scaled processes, the numerical value of molarity remains the same. For convenience in avoiding conversions in the imperial (or  American customary units), some engineers adopted the "pound-mole" (notation "lb-mol" or "lbmol"), which is defined as the number of entities in 12 lb of C. One lb-mol is equal to , which value is the same as the number of grams in an international avoirdupois pound. In the metric system, chemical engineers once used the "kilogram-mole" (notation "kg-mol"), which is defined as the number of entities in 12 kg of C, and often referred to the mole as the "gram-mole" (notation "g-mol"), when dealing with laboratory data. Late 20th-century chemical engineering practice came  to use the "kilomole" (kmol), which is numerically identical to the kilogram-mole, but whose name and symbol adopt the SI convention for standard multiples of metric units – thus, kmol means 1000 mol. This is equivalent to the use of kg instead of g. The use of kmol is not only for "magnitude convenience" but also makes the equations used for modelling chemical engineering systems coherent. For example, the conversion of a flowrate of kg/s to kmol/s only requires the molecular mass without the factor 1000 unless the basic SI unit of mol/s were to be used . Greenhouse and growth chamber lighting for plants is sometimes expressed in micromoles per square metre per second, where 1 mol photons = photons. Multiples. Like other SI units, the mole can modified by adding a prefix that multiplies it by a power of 10. Yoctomole. A yoctomole (ymol) is one septillionth of a mole (). It is equal to elementary entities. While the metric prefix system entails the existence of this unit, in practice it would be more convenient to simply express such extremely small quantities of amount of substance by stating the number of elementary entities directly. Zeptomole. A zeptomole  (zmol) is one sextillionth of a mole (). It is equal to elementary entities. Attomole. An attomole (amol) is one quintillionth of a mole (). It is equal to 602,214.076 elementary entities. Femtomole. A femtomole (fmol) is one quadrillionth of a mole (). It is equal to 602,214,076 elementary entities. Picomole. A picomole (pmol) is one trillionth of a mole (). It is equal to 602,214,076,000 elementary entities. Nanomole. A nanomole (nmol) is one billionth of a mole (). It is equal to 602,214,076,000,000 or elementary entities. Micromole. A micromole (μmol) is one millionth of a mole (). It is equal to 602,214,076,000,000,000 or elementary entities , the approximate number of elementary charges in coulombs. Millimole. A millimole (mmol) is one one thousandth of a mole (0.001 mol or ). It is equal to elementary entities, the approximate number of atoms in 1/5 of a gram of mercury. Centimole. A centimole (cmol) is one one hundredth of a mole (0.01 mol or ). It is equal to elementary entities, slightly more than the number of atoms in a gram of ruthenium metal. Decimole. A decimole (dmol) is one tenth of a mole (0.1 mol or ). It is equal to elementary entities, somewhat more than the number of atoms in  a gram of boron and somewhat less than the number of atoms in a gram of beryllium. Decamole. A decamole (damol) is ten moles (10 mol or ). It is equal to elementary entities, the approximate number of molecules in a 180 ml glass of water. Hectomole. A hectomole (hmol) is one hundred moles (100 mol or ). It is equal to elementary entities. Kilomole. A kilomole (kmol) is one thousand moles (1000 mol or ). It is equal to elementary entities, the approximate number of molecules in an 18 litre (4.755 US gallon) tub of water. Megamole. A megamole (Mmol) is one  million moles (). It is equal to elementary entities, the approximate number of water molecules in an 18 cubic metre pond. Gigamole. A gigamole (Gmol) is one billion moles (). It is equal to elementary entities, the approximate number of water molecules in an 18,000 cubic metre lake. Teramole. A teramole (Tmol) is one trillion moles (). It is equal to elementary entities, the approximate number of water molecules in Blithfield Reservoir in Staffordshire, United Kingdom, when full to capacity. Petamole. A petamole (Pmol) is one quadrillion moles (). It is equal to elementary entities, a little less than the number of water molecules  in Crater Lake, Oregon, the deepest lake in the United States. Examole. An examole (Emol) is one quintillion moles (). It is equal to elementary entities, a little less than the number of water molecules in Lake Tanganyika, the largest lake in Africa and the third largest in the world by volume. Zettamole. A zettamole (Zmol) is one sextillion moles (). It is equal to elementary entities, a little less than the number of water molecules in the Arctic Ocean. Yottamole. A yottamole (Ymol) is one septillion moles (). It is equal to elementary entities, approximately 13.5 times the number of water molecules  in all oceans on Earth. Mole Day. October 23, denoted 10/23 in the US, is recognized by some as Mole Day. It is an informal holiday in honor of the unit among chemists. The date is derived from the Avogadro number, which is approximately . It starts at 6:02 a.m. and ends at 6:02 p.m. Alternatively, some chemists celebrate June 2 (), June 22 (), or 6 February (), a reference to the 6.02 or 6.022 part of the constant.