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mole
One mole is exactly 6.02214076×1023 elementary entities, approximately equivalent to the number of atoms in 12 grams of carbon-12 in the historical definition
General information
Unit systemSI
Unit ofamount of substance
Symbolmol

The mole (symbol mol) is a unit of measurement, the base unit in the International System of Units (SI) for amount of substance, an SI base quantity proportional to the number of elementary entities of a substance. One mole is an aggregate of exactly 6.02214076×1023 elementary entities (approximately 602 sextillion or 602 billion times a trillion), which can be atoms, molecules, ions, ion pairs, or other particles. The number of particles in a mole is the Avogadro number (symbol N0) and the numerical value of the Avogadro constant (symbol NA) has units of mol−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 of 12C,[1] which made the molar mass of a compound in grams per mole, numerically equal to the average molecular mass or formula mass of the compound expressed in daltons. With the 2019 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 of dozen 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 in chemistry as a convenient way to express amounts of reactants and amounts of products of chemical reactions. For example, the chemical equation 2 H2 + O2 → 2 H2O can be interpreted to mean that for each 2 mol molecular hydrogen (H2) and 1 mol molecular oxygen (O2) that react, 2 mol of water (H2O) form. The concentration of a solution is commonly expressed by its molar concentration, defined as the amount of dissolved substance per unit volume of solution, for which the unit typically used is mole per litre (mol/L).

Concepts

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As a set

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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]

Relation to the Avogadro constant

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The number of entities (symbol N) in a one-mole sample equals the Avogadro number (symbol N0), a dimensionless quantity.[1] The Avogadro constant (symbol NA) is given by the Avogadro number multiplied by the unit reciprocal mole (mol−1), i.e. NA = N0/mol.[3] The ratio n = N/NA is a measure of the amount of substance (with the unit mole).[3][4] The Avogadro constant was determined by a measurement of the number of 28Si atoms in a single crystalline sample.[5]

Nature of the entities

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Main article: Molecular entity
See also: Amount of substance § Nature of the particles

Depending on the nature of the substance, an elementary entity may be an atom, a molecule, an ion, an ion pair, or a subatomic particle such as a proton. For example, 10 moles of water (a chemical compound) and 10 moles of mercury (a chemical 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 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 molecules. Thus, common chemical conventions apply to the definition of the constituent entities of a substance, in other cases exact definitions may be specified. The molar mass of a substance is equal to its relative atomic (or molecular) mass multiplied by the molar mass constant, which is almost exactly 1 g/mol.[citation needed]

Similar units

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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 the kilogram-mole (notation 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 (notation g-mol), then defined as the number of entities in 12 g of 12C, when dealing with laboratory data.[7]

Late 20th-century chemical engineering practice came to use the kilomole (kmol), which was numerically identical to the kilogram-mole (until the 2019 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 systems coherent. 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 the imperial (or US 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 12C. One lb-mol is equal to 453.59237 g‑mol,[7] which is the same numerical value as the number of grams in an international 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 unit einstein is variously defined as the energy in one mole of photons and also as simply one mole of photons.

Derived units and SI multiples

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The only SI derived unit with a special name derived from the mole is the katal, defined as one mole per second of catalytic activity. Like other SI units, the mole can also be modified by adding a metric prefix that multiplies it by a power of 10:

SI multiples of mole (mol)
Submultiples Multiples
Value SI symbol Name Value SI symbol Name
10−1 mol dmol decimole 101 mol damol decamole
10−2 mol cmol centimole 102 mol hmol hectomole
10−3 mol mmol millimole 103 mol kmol kilomole
10−6 mol μmol micromole 106 mol Mmol megamole
10−9 mol nmol nanomole 109 mol Gmol gigamole
10−12 mol pmol picomole 1012 mol Tmol teramole
10−15 mol fmol femtomole 1015 mol Pmol petamole
10−18 mol amol attomole 1018 mol Emol examole
10−21 mol zmol zeptomole 1021 mol Zmol zettamole
10−24 mol ymol yoctomole 1024 mol Ymol yottamole
10−27 mol rmol rontomole 1027 mol Rmol ronnamole
10−30 mol qmol quectomole 1030 mol Qmol quettamole

One femtomole is exactly 602214076 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]

History

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Avogadro, who inspired the Avogadro constant

The history of the mole is intertwined with that of units of molecular mass, and the Avogadro constant.

The first table of standard 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.[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 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.[citation needed]

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.[citation needed]

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).[10][11][12] The related concept of equivalent mass had been in use at least a century earlier.[13]

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.[14]

Standardization

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Developments in mass spectrometry led to the adoption of oxygen-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 pure 12C had a mass of exactly 12 g.[16][6] The four different definitions were equivalent to within 1%.

Scale basis Scale basis
relative to 12C = 12 		Relative 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%

Because a dalton, a unit commonly used to measure atomic 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 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, 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 mole NA (the Avogadro constant) had to be determined experimentally. The experimental value adopted by CODATA in 2010 is NA = 6.02214129(27)×1023 mol−1.[17] In 2011 the measurement was refined to 6.02214078(18)×1023 mol−1.[18]

The mole was made the seventh SI base unit in 1971 by the 14th CGPM.[19]

2019 revision of the SI

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Before the 2019 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 of carbon-12 (the most common isotope of carbon).[20] The term gram-molecule was formerly used to mean one mole of molecules, and gram-atom for one mole of atoms.[16] For example, 1 mole of MgBr2 is 1 gram-molecule of MgBr2 but 3 gram-atoms of MgBr2.[21][22]

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 physical 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 "exactly 6.02214076×1023 elementary entities" of that substance.[23][24]

Criticism

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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;[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 a parametric unit, and amount of substance is a parametric base quantity[27]
  • the SI defines numbers of entities as quantities of dimension one, and thus ignores the ontological distinction between entities and units of continuous quantities[28]
  • the mole is often used interchangeably and inconsistently in online sources to refer to both a unit and a quantity without appropriate use of amount of substance causing confusion for novice chemistry students.[29]

Mole Day

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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 6.022×1023. It starts at 6:02 a.m. and ends at 6:02 p.m. Alternatively, some chemists celebrate June 2 (06/02), June 22 (6/22), or 6 February (06.02), a reference to the 6.02 or 6.022 part of the constant.[30][31]

See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Mole (unit)

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from Grokipedia
The mole, symbol mol, is the base unit in the International System of Units (SI) for measuring amount of substance. It quantifies the number of specified elementary entities—such as atoms, molecules, ions, electrons, or other particles or groups of such particles—in a given system. By definition, one mole contains exactly 6.02214076×10236.02214076 \times 10^{23} elementary entities, a fixed value equal to the Avogadro constant NAN_A. The concept of the mole emerged in the late amid advances in atomic theory and chemical , providing a means to count vast numbers of microscopic particles through macroscopic like . The term "mole" derives from the German "Mol," introduced by chemist around 1893 to denote the molecular weight of a substance in grams. It was formally established as the seventh in 1971 by the 14th General Conference on Weights and Measures (CGPM), initially defined relative to the number of atoms in 0.012 kg of carbon-12. This definition was revised in 2019 by the 26th CGPM to anchor the mole directly to the exact value of the , eliminating reliance on physical artifacts and enhancing precision across scientific disciplines. In chemistry and related fields, the mole serves as a critical bridge between observable quantities—such as mass, volume, and concentration—and the atomic scale, enabling calculations of chemical reactions, equilibria, and material properties. For instance, the molar mass of an element or compound, expressed in grams per mole, directly links the mole to the gram, facilitating practical laboratory measurements. Its adoption has standardized global scientific communication, supporting advancements in fields from pharmaceuticals to materials science.

Core Concepts

Definition of the Mole

The mole, symbol mol, is the SI unit of amount of substance in the International System of Units (SI). It is defined as the amount of substance that contains exactly 6.02214076×10236.02214076 \times 10^{23} elementary entities, where this fixed numerical value is the Avogadro constant expressed in units of mol−1^{-1}. This definition, adopted in the 2019 revision of the SI, ensures a precise and universal standard for quantifying substance amounts independent of specific measurement artifacts. This large number of entities in one mole provides a bridge between the microscopic scale of individual particles and macroscopic quantities, analogous to everyday counting units like the dozen (12 items) or gross (144 items). Specifically, one mole corresponds to the number of atoms present in exactly 12 grams (0.012 kilograms) of the carbon-12 isotope, making it a practical scale for handling vast numbers of particles in bulk samples. This equivalence facilitates direct comparisons and conversions in scientific work, emphasizing the mole's role as a standardized "package" for entities such as atoms, molecules, or ions. In chemistry and physics, the mole serves as a fundamental measure for amount of substance, enabling stoichiometric calculations in chemical reactions, determination of concentrations in solutions, and analysis of gas volumes under standard conditions. It connects mass measurements to particle counts, which is essential for predicting reaction yields, formulating solutions, and applying laws like the ideal gas law. By quantifying substance in moles, scientists can scale experiments reproducibly across laboratories worldwide. The MM of a substance is defined as the mm of a sample divided by its nn (in moles), expressed as M=m/nM = m / n. This relationship derives from the mole's definition: since one mole contains a fixed number of entities (NA=6.02214076×1023N_A = 6.02214076 \times 10^{23} mol−1^{-1}), the of one mole of a substance equals the of NAN_A entities, or equivalently, the total divided by the number of moles present. For example, the of carbon-12 is exactly 0.012 kg mol−1^{-1}, providing a reference for other elements and compounds whose are typically reported in grams per mole (g mol−1^{-1}) for convenience in chemical applications. This formula allows straightforward conversion between and amount, underpinning quantitative analysis in experimental science.

Relation to Avogadro Constant

The Avogadro constant, denoted NAN_A, is defined as exactly 6.02214076×10236.02214076 \times 10^{23} mol−1^{-1}, representing the number of specified elementary entities (such as atoms, molecules, ions, or other particles) in one mole of a substance. This fixed value was established in the 2019 revision of the International System of Units (SI), making NAN_A a defining constant that precisely links the microscopic scale of individual particles to the macroscopic scale of chemical amounts. The fundamental relation between the amount of substance and the number of entities is given by the equation n=NNAn = \frac{N}{N_A}, where nn is the amount of substance in moles (mol), NN is the number of entities (dimensionless), and NAN_A is the Avogadro constant in mol−1^{-1}. This equation allows for the direct conversion between the count of discrete particles and the standardized unit of amount, ensuring consistency in quantitative chemistry and physics. Through this relation, NAN_A enables the connection between particle counts and measurable properties like and volume. For instance, the molar MM of a substance is M=mn=mNANM = \frac{m}{n} = \frac{m N_A}{N}, where mm is the in kilograms, bridging the total of a sample to the number of constituent entities and the atomic mass unit. In the of gases, the PV=nRTPV = nRT incorporates NAN_A via the R=NAkBR = N_A k_B, where kBk_B is the , thus relating macroscopic pressure PP, volume VV, and temperature TT to the kinetic behavior of N=nNAN = n N_A individual particles. This linkage facilitates derivations in , where the pressure arises from particle collisions. Prior to the 2019 SI revision, the was not fixed but determined experimentally, with values refined through precision measurements such as those in the International Avogadro Project using silicon-28 spheres to relate to macroscopic . The adoption of the exact value in 2019 eliminated uncertainties from such measurements, enhancing the stability of the mole as a base unit.

Nature of the Entities

The elementary entities counted by the mole are the specified particles in a given system of substance, which may include atoms, molecules, ions, electrons, or other particles, or specified groups thereof. When the mole is used, these entities must be explicitly identified to ensure precise measurement of the amount of substance. For instance, one mole of helium consists of exactly 6.02214076×10236.02214076 \times 10^{23} helium atoms. Similarly, one mole of water (H₂O) comprises exactly 6.02214076×10236.02214076 \times 10^{23} water molecules, which collectively contain 3×6.02214076×10233 \times 6.02214076 \times 10^{23} atoms (two hydrogen atoms and one oxygen atom per molecule). In usage, the elementary entities for a mole must be of the same specified type to maintain consistency, avoiding mixtures of distinct particle kinds within a single measurement; this ensures the entities are indistinguishable for counting purposes. The mole plays a central role in stoichiometry by allowing chemical reactions to be quantified through proportional relationships among these entities, facilitating predictions of reactant and product quantities. The relation to chemical is : the of a substance defines the elementary entity being counted, such that one mole corresponds to the number of those entities—for example, one mole of (NaCl) contains exactly 6.02214076×10236.02214076 \times 10^{23} units, each comprising one sodium ion and one chloride ion. This scaling by the links microscopic particle counts to macroscopic amounts in chemical analysis.

Units and Measurements

Similar Units

The mole, as a unit of , shares conceptual similarities with other counting units that denote fixed numbers of entities, but it is uniquely scaled to accommodate the vast quantities involved in atomic and molecular scales. Everyday counting units, such as the (representing 12 items, like eggs or doughnuts), the gross (144 items, or 12 , often used for small hardware like screws), and the (typically 500 sheets of ), facilitate practical of macroscopic objects by grouping them into manageable sets. These units are arbitrary in their numerical basis and suited to human-scale handling, whereas the mole's fixed count of exactly 6.02214076×10236.02214076 \times 10^{23} entities aligns with the enormous populations required for measurable masses of microscopic particles, making direct counting infeasible. In scientific contexts beyond chemistry, analogous units exist but lack the mole's formal standardization within the International System of Units (SI). For instance, a pair denotes exactly two entities, such as an electron-positron pair in particle physics processes like pair production, providing a simple grouping for binary interactions without being an SI base unit. Historically, chemistry employed precursors like the gram-atom, which referred to the amount of an element with a mass in grams equal to its atomic weight, effectively counting entities on a scale similar to the modern mole but without a fixed universal number. These units served early stoichiometric needs but were eventually unified under the mole for precision and consistency across disciplines. Non-metric systems, such as the centimeter-gram-second (CGS) and foot-pound-second (FPS, or imperial) frameworks, incorporate units for , , and time but lack a dedicated base unit equivalent to the mole for . In CGS, chemical quantities were often expressed using gram-atoms or similar measures, while imperial systems, focused on applications, do not define at all, requiring to adopt the SI mole for chemical work. This absence underscores the mole's role as a specialized SI unit tailored for chemistry and related fields. The mole's distinctiveness arises from its calibration to microscopic scales, enabling practical measurements of substances where individual entities are invisible and their numbers immense, unlike the macroscopic focus of traditional units. By linking a specific large count to observable properties like , the mole bridges quantum-scale phenomena with quantities, a functionality not replicated in other systems.

Derived Units and SI Multiples

The mole is the SI base unit for , from which several derived units arise to quantify compositions and concentrations in chemical systems. Mole fraction, also known as amount fraction and denoted xix_i, is a dimensionless derived quantity that expresses the proportion of a component in a mixture as the ratio of its amount of substance nin_i to the total amount nn: xi=nin.x_i = \frac{n_i}{n}. This unit is particularly useful for describing the composition of gas mixtures and calculating partial pressures via Dalton's law. Molality, denoted mm or bb, is defined as the amount of solute nn divided by the mass of the solvent msm_s, with the SI unit mol/kg: m=nms.m = \frac{n}{m_s}. Unlike volume-based measures, molality remains constant with temperature changes, making it ideal for studies of colligative properties such as boiling point elevation. Amount concentration, commonly called molarity and denoted cc, represents the amount of substance nn per unit volume VV of the solution, with the SI unit mol/dm³ (equivalent to mol/L): c=nV.c = \frac{n}{V}. It is essential for stoichiometric calculations in reactions involving solutions, such as determining reactant quantities in titrations. For ideal gases, molar volume VmV_m is a key derived quantity, defined as the volume occupied by one mole at specified conditions. According to IUPAC recommendations, at standard temperature and pressure (STP: 0 °C and 100 kPa), Vm=22.711V_m = 22.711 L/mol, derived from the ideal gas law Vm=RT/PV_m = RT / P where RR is the gas constant. (The traditional value at 0 °C and 1 atm is 22.414 L/mol.) This value facilitates conversions between gas volumes and amounts of substance in chemical analyses. SI prefixes scale the mole unit for practical scales in experiments and processes. The kilomole (kmol = 10310^3 mol) applies to large-scale industrial reactions, such as ammonia synthesis, while the millimole (mmol = 10−310^{-3} mol) suits routine laboratory dilutions, and the micromole (μmol = 10−610^{-6} mol) is standard in biochemistry for quantifying metabolites or nucleic acids. These derived units and prefixes support accurate chemical practice by enabling reproducible solution preparation—e.g., using molarity to mix reagents—and reliable prediction of reaction yields through stoichiometric balancing with mole-based quantities.

Historical Development

Early Concepts and Standardization

The concept of the mole originated in the early with Amedeo Avogadro's , which posited that equal volumes of different gases, under the same conditions of and , contain an equal number of molecules, thereby linking macroscopic gas volumes to the number of microscopic particles. This idea laid the groundwork for quantifying amounts of substances in terms of particle numbers, though it was initially met with skepticism and not widely accepted until later. Building on Avogadro's work, in 1858 developed the notion of the "gram-molecular weight," defined as the mass in grams numerically equal to the molecular weight of a substance, allowing chemists to determine relative atomic and molecular masses through vapor measurements and chemical reactions. In the late , the term "mole" emerged to streamline these concepts. introduced the German term "Mol" in 1893 in his on physicochemical measurements, using it to denote the molecular in grams of a substance, initially as a practical for stoichiometric calculations amid debates over atomic theory. By 1900, Ostwald further popularized "mole" in his as an alternative to cumbersome phrases like "gram-molecular weight," reflecting a shift toward macroscopic equivalents in chemistry while navigating naming controversies, such as distinguishing "gram-atom" for elements (the atomic weight in grams) from "gram-molecule" for compounds. These terms resolved inconsistencies in early 20th-century nomenclature, with "Mol" gaining traction in German literature and influencing international usage, though English texts often retained "gram-molecule" until mid-century. Standardization accelerated in the mid-20th century through international bodies. In 1961, the International Union of Pure and Applied Chemistry (IUPAC) and the International Union of Pure and Applied Physics (IUPAP) recommended defining the mole as the amount of substance containing as many entities as atoms in exactly 12 grams of carbon-12, tying it to a specific isotope for precision. This was formalized by the International Committee for Weights and Measures (CIPM) in 1967, establishing the mole's definition based on 0.012 kilograms of unbound carbon-12 atoms at rest in their ground state. The 14th CGPM in 1971 then officially recognized the mole as the seventh base unit of the International System of Units (SI), symbol mol, integrating it into the global measurement framework alongside units like the meter and kilogram. The value of the Avogadro constant (N_A), central to the mole's particle count, was experimentally determined through methods like , first proposed by in 1913 for measuring crystal lattice parameters to link atomic-scale structures to macroscopic densities. This technique, refined over decades using crystals and precise density measurements, provided key validations for the mole's , with early estimates in the early confirming N_A around 6.02 × 10^{23} mol^{-1} and supporting the linkage.

2019 SI Revision

The 2019 revision of the (SI) marked a fundamental shift by defining all base units in terms of seven fixed defining constants of nature, ensuring long-term stability and universality in measurements. These constants include the c, the h, the k, the e, the caesium hyperfine transition frequency Δν_Cs, the K_cd, and the N_A. This approach eliminated reliance on physical artifacts or specific materials, promoting consistency across scientific disciplines and . For the mole specifically, the revision fixed the at an exact value of N_A = 6.02214076 × 10²³ mol⁻¹, redefining the mole as the containing exactly this number of elementary entities, such as atoms, molecules, or ions. Prior to 2019, from 1971 onward, the mole had been defined as the containing the same number of elementary entities as there are atoms in exactly 0.012 of the , linking it indirectly to the artifact and introducing potential uncertainties from mass measurements. The new definition severs this dependence on the mass standard, enhancing precision by anchoring the unit directly to a universal constant determined through advanced experimental methods like the Avogadro experiment and measurements. The redefinition was approved unanimously by the 26th General Conference on Weights and Measures (CGPM) in November 2018, following decades of preparatory work including CODATA evaluations of constant values, and took effect on 20 May 2019, coinciding with World Metrology Day. This process built on earlier SI resolutions, such as the 2011 proposal and 2014 confirmation of metrological conditions, to ensure the fixed value of N_A aligned with the best available measurements at the time. The impacts of this change are profound for , reducing in linking atomic and macroscopic scales—for instance, the relative uncertainty in the molar mass of ¹²C dropped to 2.5 × 10⁻¹⁰—while more accurate realizations in fields like and isotope through improved to fundamental constants. However, for most practical calculations in chemistry and everyday applications, the revision introduces no noticeable changes, as the numerical value of N_A remains effectively the same, with differences appearing only in the ninth decimal place.

Critical and Cultural Aspects

Criticism of the Mole

The mole unit has faced conceptual criticism for its immense scale, defined by the Avogadro constant of approximately 6.022 × 10²³ entities per mole, which renders it nearly impossible for individuals to visualize or intuitively grasp the quantity of particles involved. This abstraction often leads to a disconnect between the unit's numerical representation and its physical reality, as the number far exceeds everyday scales like grains of sand on Earth. Critics argue that this scale exacerbates the challenge of understanding amount of substance as a fundamental property, making it harder to relate to tangible chemical processes. Practically, the mole contributes to widespread student misconceptions, such as equating one mole directly with one molecule or confusing it with molar mass, where learners might calculate molar masses incorrectly by incorporating stoichiometric coefficients rather than atomic weights. Studies show that up to 40% of students misapply these concepts in stoichiometry problems, often due to the unit's dual role as both a counting device and a measure of substance portion. Proposals for alternatives include redefining the mole as exactly the Avogadro number of entities and renaming "amount of substance" to "number of entities" for clarity in teaching and practice. Philosophically, debates within IUPAC during the 1990s questioned whether qualifies as a true base quantity akin to or , arguing that the mole functions more as a dimensionless count of discrete entities rather than a continuous measurable , which undermines its status in the SI system. Some contended that this reinforces unexamined assumptions of atomic theory by prioritizing particulate models over continuum views of matter, and that the unit lacks direct comparability via instruments, unlike other base units. These critiques, voiced in IUPAC discussions around the atomic weight standard, highlighted inconsistencies in treating the mole as both a scaling factor and a standard unit. Defenders of the mole counter that, despite its abstractness, the unit's utility in —enabling precise predictions of reaction yields and balances—far outweighs philosophical drawbacks, as it provides a standardized bridge between microscopic particle counts and macroscopic measurements. IUPAC has addressed concerns by clarifying definitions and supporting its retention as a base unit, emphasizing that remains a valid metrological process in quantum-based systems. While renaming suggestions like "number of entities" persist, the consensus affirms the mole's practical indispensability in chemistry.

Mole Day

Mole Day is an annual educational and celebratory event observed by chemists, students, and enthusiasts to honor the mole as a fundamental unit in chemistry. Established on , by Maurice Oehler, a high school chemistry teacher at Prairie du Chien High School in , the holiday was formalized through the founding of the National Mole Day Foundation to foster for the subject. The observance takes place on from 6:02 a.m. to 6:02 p.m., deliberately chosen to evoke the approximate value of Avogadro's constant, 6.02×10236.02 \times 10^{23}, which defines the number of entities in one mole. Typical activities during emphasize and , including school-based chemistry demonstrations, hands-on experiments, and creative projects such as mole-themed puzzles, posters, and inspired by chemical . Organizations like the (ACS) provide resources, including lab activities and lesson plans tailored for high school students to explore the mole's role in measurements. An extension known as "Extended Mole Day" occurs on from 10:23 a.m. to 10:23 p.m., aligning with the date format 6/02 and the exponent 102310^{23} for a more complete representation of Avogadro's constant. The event has grown into a global tradition that promotes chemistry education by connecting the mole to Amedeo Avogadro's foundational contributions to molecular theory. Celebrations extend beyond the United States to schools and communities worldwide, often coinciding with ACS's National Chemistry Week to highlight the unit's practical importance in science. Following the 2019 revision of the International System of Units (SI), which fixed the Avogadro constant at exactly 6.02214076×10236.02214076 \times 10^{23}, observances have retained the traditional timing based on the approximate value.

References

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