"Nmol" redirects here. For the mathematical technique, seeMethod of lines.
mole
One mole is exactly6.02214076×1023 elementary entities, approximately equivalent to the number of atoms in 12 grams of carbon-12 in the historical definition
Themole (symbolmol) is aunit of measurement, thebase unit in theInternational System of Units (SI) foramount of substance, an SI base quantity proportional to thenumber of elementary entities of a substance. One mole is an aggregate of exactly6.02214076×1023 elementary entities (approximately 602sextillion or 602 billion times a trillion), which can beatoms,molecules,ions,ion pairs, or otherparticles. The number of particles in a mole is theAvogadro number (symbolN0) and the numerical value of theAvogadro constant (symbolNA) has units ofmol−1.[1] The relationship between the mole, Avogadro number, and Avogadro constant can be expressed in the following equation:[1]The current SI value of the mole is based on the historical definition of the mole as the amount of substance that corresponds to the number of atoms in 12 grams of12C,[1] which made themolar mass of a compound in grams per mole, numerically equal to the averagemolecular mass or formula mass of the compound expressed indaltons. With the2019 revision of the SI, the numerical equivalence is now only approximate, but may still be assumed with high accuracy.
Conceptually, the mole is similar to the concept ofdozen or other convenient grouping used to discuss collections of identical objects. Because laboratory-scale objects contain a vast number of tiny atoms, the number of entities in the grouping must be huge to be useful for work.
The mole is widely used inchemistry as a convenient way to express amounts ofreactants and amounts ofproducts ofchemical reactions. For example, the chemical equation2 H2 + O2 → 2 H2O can be interpreted to mean that for each 2 molmolecular hydrogen (H2) and 1 molmolecular oxygen (O2) that react, 2 mol of water (H2O) form. Theconcentration of a solution is commonly expressed by itsmolar concentration, defined as the amount of dissolved substance per unit volume of solution, for which the unit typically used is mole perlitre (mol/L).
Conceptually a mole is similar to words like "pair" or "dozen". These words describe a set of identical objects—i.e. a collection or aggregate of the objects themselves, not the numbers 2 or 12. The unusual and daunting aspect of a mole is that the number of objects in the set, given by the Avogadro number, is difficult to comprehend. To be useful as a unit, the mole needs to describe the amount in a sample containing a number of atoms (or other elementary entities) that can be manipulated in an ordinary chemistry lab. Atoms are so small that not just trillions but trillions-of-trillions of atoms are needed to create an aggregate large enough to work with.[2]
Thenumber of entities (symbolN) in a one-mole sample equals theAvogadro number (symbolN0), adimensionless quantity.[1] TheAvogadro constant (symbolNA) is given by the Avogadro number multiplied by the unitreciprocal mole (mol−1), i.e.NA =N0/mol.[3] The ration =N/NA is a measure of theamount of substance (with the unitmole).[3][4]The Avogadro constant was determined by a measurement of the number of28Si atoms in a single crystalline sample.[5]
Depending on the nature of the substance, anelementary entity may be an atom, a molecule, an ion, an ion pair, or asubatomic particle such as aproton. For example, 10 moles ofwater (achemical compound) and 10 moles ofmercury (achemical element) contain equal numbers of particles of each substance, with one atom of mercury for each molecule of water, despite the two quantities having different volumes and different masses.[citation needed]
The mole is an amount corresponding to a given count (an Avogadro number) of elementary entities.[6] Usually, the entities counted are chemically identical and individually distinct. For example, a solution may contain a certain number of dissolved molecules that are more or less independent of each other. However, the constituent entities in a solid 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 entities. In yet other cases, such asdiamond, 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 molecules. Thus, common chemical conventions apply to the definition of the constituent entities of a substance, in other cases exact definitions may be specified. Themolar mass of a substance is equal to itsrelative atomic (or molecular) mass multiplied by themolar mass constant, which is almost exactly 1 g/mol.[citation needed]
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, as. Chemical engineers once used thekilogram-mole (notationkg-mol), which is defined as the number of entities in 12 kg of12C, and often referred to the mole as thegram-mole (notationg-mol), then defined as the number of entities in 12 g of12C, when dealing with laboratory data.[7]
Late 20th-century chemical engineering practice came to use thekilomole (kmol), which was numerically identical to the kilogram-mole (until the2019 revision of the SI, which redefined the mole by fixing the value of the Avogadro constant, making it very nearly equivalent to but no longer exactly equal to the gram-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 systemscoherent. For example, the conversion of a flowrate of kg/s to kmol/s only requires dividing by the molar mass in kg/kmol (which is equivalent to g/mol, as) without multiplying by 1000 unless the basic SI unit of mol/s were to be used, which would otherwise require the molar mass to be converted to kg/mol.
For convenience in avoiding conversions in theimperial (orUS customary units), some engineers adopted thepound-mole (notationlb-mol orlbmol), which is defined as the number of entities in 12 lb of12C. One lb-mol is equal to453.59237 g‑mol,[7] which is the same numerical value as the number of grams in aninternational avoirdupois pound.
Greenhouse and growth chamber lighting for plants is sometimes expressed in micromoles per square metre per second, where 1 mol photons ≈6.02×1023 photons.[8] The obsolete uniteinstein is variously defined as the energy in one mole of photons and also as simply one mole of photons.
One femtomole is exactly602214076 molecules; attomole and smaller quantities do not correspond to a whole number of entities. The yoctomole, equal to around 0.6 of an individual molecule, did make appearances in scientific journals in the year the yocto- prefix was officially implemented.[9]
The first table ofstandard atomic weight was published byJohn Dalton (1766–1844) in 1805, based on a system in which the relative atomic mass ofhydrogen was defined as 1. These relative atomic masses were based on thestoichiometric proportions of chemical reaction and compounds, a fact that greatly aided their acceptance: It was not necessary for a chemist to subscribe toatomic 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) andequivalent 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.[citation needed]
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 useoxygen as the standard to which other masses were referred. Oxygen is a useful standard, as, unlike hydrogen, it forms compounds with most other elements, especiallymetals. However, he chose to fix the atomic mass of oxygen as 100, which did not catch on.[citation needed]
Charles Frédéric Gerhardt (1816–56),Henri Victor Regnault (1810–78) andStanislao 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 theKarlsruhe 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.[citation needed]
In chemistry, it has been known sinceProust'slaw of definite proportions (1794) that knowledge of the mass of each of the components in a chemicalsystem 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 byDalton'slaw 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 theideal gas law (where the relationship was first demonstrated in 1857). The term "mole" was first used in a textbook describing thesecolligative properties.[14]
Developments inmass spectrometry led to the adoption ofoxygen-16 as the standard substance, in lieu of natural oxygen.[15]
The oxygen-16 definition was replaced with one based on carbon-12 during the 1960s. The International Bureau of Weights and Measures defined the mole as "the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilograms of carbon-12." Thus, by that definition, one mole of pure12C had a mass ofexactly 12 g.[16][6] The four different definitions were equivalent to within 1%.
Scale basis
Scale basis relative to12C = 12
Relative deviation from the12C = 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 of16O = 16
15.9949146221(15)
+0.0318%
Because adalton, a unit commonly used to measureatomic mass, is exactly 1/12 of the mass of a carbon-12 atom, this definition of the mole 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 anucleon (i.e. aproton orneutron) is approximately 1 dalton and the nucleons in an atom's nucleus make up the overwhelming majority of its mass, this 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.
Since the definition of the gram was not mathematically tied to that of the dalton, the number of molecules per moleNA (the Avogadro constant) had to be determined experimentally. The experimental value adopted byCODATA in 2010 isNA =6.02214129(27)×1023 mol−1.[17]In 2011 the measurement was refined to6.02214078(18)×1023 mol−1.[18]
The mole was made the seventhSI base unit in 1971 by the 14th CGPM.[19]
Before the2019 revision of the SI, the mole was defined as the amount of substance of a system that contains as many elementary entities as there are atoms in 12 grams ofcarbon-12 (the most commonisotope of carbon).[20]The termgram-molecule was formerly used to mean one mole of molecules, andgram-atom for one mole of atoms.[16] For example, 1 mole ofMgBr2 is 1 gram-molecule of MgBr2 but 3 gram-atoms of MgBr2.[21][22]
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 byphysical constants that are, in their nature, exact.[4]
Such changes officially came into effect on 20 May 2019. Following such changes, "one mole" of a substance was redefined as containing "exactly6.02214076×1023 elementary entities" of that substance.[23][24]
Since its adoption into theInternational System of Units in 1971, numerous criticisms of the concept of the mole as a unit like themetre or thesecond have arisen:
the number of molecules, etc. in a given amount of material is a fixeddimensionless quantity that can be expressed simply as a number, not requiring a distinct base unit;[6][25]
The SI thermodynamic mole is irrelevant to analytical chemistry and could cause avoidable costs to advanced economies[26]
The mole is not a true metric (i.e. measuring) unit, rather it is aparametric unit, and amount of substance is aparametric base quantity[27]
the SI defines numbers of entities as quantities of dimension one, and thus ignores the ontological distinction betweenentities andunits of continuous quantities[28]
the mole is often used interchangeably and inconsistently to refer to both a unit and a quantity without appropriate use of amount of substance potentially causing confusion for novice chemistry students.[29]
^Chen, Da Yong; et al. (1991). "Low-cost, high-sensitivity laser-induced fluorescence detection for DNA sequencing by capillary gel electrophoresis".Journal of Chromatography.559 (1–2):237–246.doi:10.1016/0021-9673(91)80074-Q.PMID1761625.
^Ostwald, Wilhelm (1893).Hand- und Hilfsbuch zur Ausführung Physiko-Chemischer Messungen [Handbook and Auxiliary Book for Conducting Physico-Chemical Measurements]. Leipzig, Germany: Wilhelm Engelmann. p. 119. From p. 119:"Nennen wir allgemein das Gewicht in Grammen, welches dem Molekulargewicht eines gegebenen Stoffes numerisch gleich ist, ein Mol, so ... " (If we call in general the weight in grams, which is numerically equal to the molecular weight of a given substance, a "mol", then ... )
^Barański, Andrzej (2012). "The Atomic Mass Unit, the Avogadro Constant, and the Mole: A Way to Understanding".Journal of Chemical Education.89 (1):97–102.Bibcode:2012JChEd..89...97B.doi:10.1021/ed2001957.
^Price, Gary (2010). "Failures of the global measurement system. Part 1: the case of chemistry".Accreditation and Quality Assurance.15 (7):421–427.doi:10.1007/s00769-010-0655-z.S2CID95388009.
^Rees, S. W.; Bruce, M. (2022). "Inconsistent language use in online resources explaining the mole has implications for students' understanding".Journal of Chemical Education.99 (7):2446–2450.doi:10.1021/acs.jchemed.2c00199.
