mole


 * Mole (unit) **
 * 

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 "elementary entities" (e.g. atoms, molecules, ions, electrons) as there are atoms in 12 g of carbon-12 (12C).[1]. A mole has 6.0221415×1023[6] atoms or molecules of the pure substance being measured. A mole will possess mass exactly equal to the substance's molecular/atomic weight 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/atomic weight.

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 (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 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] **  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 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. **
 * 

The second misconception, that the mole is simply a counting aid, has even found its way into elementary chemistry textbooks.[8] These books and others often contend that the mole is defined in terms of the Avogadro constant, rather than the other way around, and so is equal to 6.0221415×1023 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: **  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.
 * **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; **
 * **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">the definition of 12 g of carbon-12 atoms to be equivalent to one mole. **
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 18pt;">History **
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">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.

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. ** **<span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">Scale basis ** || **<span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">Scale basis relative to 12C = 12 ** || **<span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">Relative deviation from the 12C = 12 scale ** || <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 18pt;">
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">Atomic weight of hydrogen = 1 ** ||
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">1.007 ****<span style="color: #404040; font-family: "Cambria Math","serif"; font-size: 12pt;">  ****<span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">94(7) ** ||
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">−0.788% ** ||
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">Atomic weight of oxygen = 16 ** ||
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">15.9994(3) ** ||
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">+37.5 ppm ** ||
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">Relative atomic mass of 16O = 16 ** ||
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">15.994 ****<span style="color: #404040; font-family: "Cambria Math","serif"; font-size: 12pt;">  ****<span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">914 ****<span style="color: #404040; font-family: "Cambria Math","serif"; font-size: 12pt;">  ****<span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">6221(15) ** ||
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">+318 ppm ** ||
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">Relative atomic mass of 16O = 16 ** ||
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">15.994 ****<span style="color: #404040; font-family: "Cambria Math","serif"; font-size: 12pt;">  ****<span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">914 ****<span style="color: #404040; font-family: "Cambria Math","serif"; font-size: 12pt;">  ****<span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">6221(15) ** ||
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">+318 ppm ** ||
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 18pt;">Other units called "mole" **
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">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 (noted lb-mol or lbmol), which is defined is the number of entities in 12 lb of 12C. One //lb-mol// is equal to 453.59237 mol.[11]

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 12-C, and often referred to the mole as the gram-mole (noted 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, but whose name and symbol adopt the SI convention for standard multiples of metric units. ** <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 18pt;"> <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 13.5pt;">
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 18pt;">Proposed future definition **
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 13.5pt;">Kilogram **
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">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 ****<span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 14.5pt;">⁄ ****<span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">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. ** <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 18pt;"> <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 18pt;">
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 18pt;">Holiday **
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 12pt;">October the 23 (10/23) is the holiday, "Mole Day", honoring the unit. The day is used because of the unit in the equation of 10 to the 23rd power **
 * <span style="color: #404040; font-family: "Times New Roman","serif"; font-size: 18pt;">References **
 * 1) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ //**a**// //**b**// //**c**// //**d**// International Bureau of Weights and Measures (2006), //The International System of Units (SI)// (8th ed.), pp. 114–15, ISBN 92-822-2213-6, http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf  **
 * 2) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ ****<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Ostwald, Wilhelm (1893). //Hand- und Hilfsbuch zur ausführung physiko-chemischer Messungen//. Leipzig. p. 119.  **
 * 3) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ ****<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Helm, Georg (1897), //The Principles of Mathematical Chemistry: The Energetics of Chemical Phenomena//, transl. by Livingston, J.; Morgan, R., New York: Wiley, p. 6  **
 * 4) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ ****<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Some sources place the date of first usage in English as 1902. Merriam–Webster proposes an etymology from //Molekulärgewicht// (molecular weight). **
 * 5) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ //**a**// //**b**// //**c**// de Bièvre, P.; Peiser, H.S. (1992), "'Atomic Weight'—The Name, Its History, Definition, and Units", //Pure Appl. Chem.// 64 (10): 1535–43, doi:10.1351/pac199264101535, http://www.iupac.org/publications/pac/1992/pdf/6410x1535.pdf  **
 * 6) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ ****<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). "CODATA Recommended Values of the Fundamental Physical Constants: 2006". //Rev. Mod. Phys.// 80: 633–730. doi:10.1103/RevModPhys.80.633. http://physics.nist.gov/cuu/Constants/codata.pdf. Direct link to value.. **
 * 7) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ //**a**// //**b**// International Bureau of Weights and Measures. "Realising the mole." Retrieved 25 September 2008. **
 * 8) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ ****<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Kotz, John C.; Treichel, Paul M.; Townsend, John R. (2008), //Chemistry and Chemical Reactivity// (7th ed.), Brooks/Cole, ISBN 0495387037, http://cengagesites.com/academic/kotz.cfm?site=2719&section=home  **
 * 9) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ //**a**// //**b**// National Institute of Standards and Technology. "Atomic Weights and Isotopic Compositions for All Elements". http://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=&ascii=html&isotype=some. Retrieved 2008-09-25.  **
 * 10) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ ****<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> It should be emphasised that relative atomic masses are //measured// as ratios of the masses of two nuclides. They cannot be measured (at least not to this level of accuracy) as absolute values of the mass of each nuclide in yoctograms. **
 * 11) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ //**a**// //**b**// Himmelblau, David (1996). //Basic Principles and Calculations in Chemical Engineering// (6 ed.). p. 17-20. ISBN 0-13-305798-4.  **
 * 12) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ ****<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Mills, Ian M.; Mohr, Peter J.; Quinn, Terry J.; Taylor, Barry N.; Williams, Edwin R. (2005). "Redefinition of the kilogram: a decision whose time has come". //Metrologia// 42: 71–80. doi:10.1088/0026-1394/42/2/001. http://www.iop.org/EJ/article/0026-1394/42/2/001/met5_2_001.pdf. Abstract. **