Inchemistry, theamount of substance (symboln) in a given sample ofmatter is defined as a ratio (n =N/NA) between thenumber ofelementary entities (N) and theAvogadro constant (NA). The unit of amount of substance in theInternational System of Units is themole (symbol:mol), abase unit.[1] Since 2019, the mole has been defined such that the value of the Avogadro constantNA is exactly6.02214076×1023 mol−1, defining a macroscopic unit convenient for use in laboratory-scale chemistry. The elementary entities are usuallymolecules,atoms,ions, orion pairs of a specified kind. The particularsubstance sampled may be specified using a subscript or in parentheses, e.g., the amount ofsodium chloride (NaCl) could be denoted asnNaCl orn(NaCl). Sometimes, the amount of substance is referred to as thechemical amount or, informally, as the "number of moles" in a given sample of matter. The amount of substance in a sample can be calculated from measured quantities, such asmass orvolume, given themolar mass of the substance or themolar volume of an ideal gas at a giventemperature andpressure.
Because of the way themole and thedalton are defined, themass ingrams of one mole of achemical compound is numerically very nearly equal to themass of onemolecule orformula unit of the compound in daltons. For example, a single molecule ofwater has a mass of about 18.0153 daltons on average, whereas a mole of water (which contains6.02214076×1023 water molecules) has a mass of about 18.0153 grams on average. Themolar mass of anisotope in grams per mole is approximately equal to themass number. Before themole was redefined in 2019, this equality was exact by definition forcarbon-12.
In chemistry, because of thelaw of multiple proportions, it is often more convenient to work with amounts of substances denominated in moles, than with masses (grams) or volumes (liters). For example, the chemical fact "1 molecule ofoxygen (O 2) will react with 2 molecules ofhydrogen (H 2) to make 2 molecules of water (H2O)" can also be stated as "1 mole ofO2 will react with 2 moles ofH2 to form 2 moles of water". The same chemical fact, expressed in terms of masses, would be "32.0 g of oxygen (1 mole ofO 2) will react with approximately 4.0 g hydrogen (2 moles ofH 2) to make approximately 36.0 g of water (2 moles ofH2O)" (and the numbers would depend on theisotopic composition of the reagents). In terms of volume, the numbers would depend on the pressure and temperature of thereagents andproducts, although the volume of an ideal gas is proportional to the amount in moles or number of molecules at constant temperature and pressure. For the same reasons, the concentrations of reagents and products in solution are often specified inmoles per liter, rather thangrams per liter.
The amount of substance is also a convenient concept inthermodynamics. For example, the pressure of a certain quantity of anoble gas in a recipient of a given volume, at a given temperature, is directly related to the number of molecules in the gas (through theideal gas law), not to its mass.
This technical sense of the term "amount of substance" should not be confused with the general sense of "amount" in theEnglish language. The latter may refer to other measurements such as mass or volume,[2] rather than the number of particles. There are proposals to replace "amount of substance" with more easily-distinguishable terms, such asenplethy[3] andstoichiometric amount.[2]
TheIUPAC recommends that "amount of substance" should be used instead of "number of moles", just as the quantitymass should not be called "number of (kilo)grams".[3]
To avoid ambiguity, the nature of the particles should be specified in any measurement of the amount of substance: thus, a sample of 1 molof molecules ofoxygen (O 2) has a mass of about 32.00 g, whereas a sample of 1 molof atoms of oxygen (O) has a mass of about 16.00 g.[4][5]
The quotient of someextensive physical quantity of a homogeneous sample by its amount of substance is anintensive property of the substance, usually named by the prefix "molar" or the suffix "per mole".[6][7]
For example, the quotient of the mass of a sample by its amount of substance is itsmolar mass, for which the SI unit kilogram per mole or gram per mole may be used. This is about 18.015 g/mol for water, and 55.845 g/mol foriron. Similarly for volume, one gets themolar volume, which is about 18.069millilitres per mole for liquid water and 7.092 mL/mol for iron at room temperature. From theheat capacity, one gets themolar heat capacity, which is about 75.385 J/(K⋅mol) for water and about 25.10 J/(K⋅mol) for iron.
Themolar mass () of a substance is the ratio of themass () of a sample of that substance to its amount of substance ():. The amount of substance is given as the number ofmoles in the sample. For most practical purposes, the numerical value of the molar mass ingrams per mole is the same as that of the mean mass of one molecule or formula unit of the substance indaltons, as the mole was historically defined such that themolar mass constant was exactly 1 g/mol. Thus, given the molecular mass or formula mass in daltons, the same number in grams gives an amount very close to one mole of the substance. For example, the average molecular mass of water is about 18.015 Da and the molar mass of water is about 18.015 g/mol. This allows for accurate determination of the amount in moles of a substance by measuring its mass and dividing by the molar mass of the compound:.[8] For example, 100 g of water is about 5.5509 mol of water.
The molar mass of a substance depends not only on itsmolecular formula, but also on the distribution ofisotopes of each chemical element present in it. For example, the molar mass ofcalcium-40 is39.96259098(22) g/mol, whereas the molar mass ofcalcium-42 is41.95861801(27) g/mol, and ofcalcium with the normal isotopic mix is40.078(4) g/mol.
Another important derived quantity is themolar concentration () (also calledamount of substance concentration,[9]amount concentration, orsubstance concentration,[10] especially inclinical chemistry), defined as the amount in moles () of a specific substance (solute in a solution or component of a mixture), divided by the volume () of the solution or mixture:.
The standard SI unit of this quantity is mol/m3, although more practical units are commonly used, such as mole perliter (mol/L, equivalent to mol/dm3). For example, the amount concentration ofsodium chloride in ocean water is typically about 0.599 mol/L.
The denominator is the volume of the solution, not of the solvent. Thus, for example, one liter of standardvodka contains about 0.40 L ofethanol (315 g, 6.85 mol) and 0.60 L of water. The amount concentration of ethanol is therefore (6.85 mol of ethanol)/(1 L of vodka) = 6.85 mol/L, not (6.85 mol of ethanol)/(0.60 L of water), which would be 11.4 mol/L.
In chemistry, it is customary to read the unit "mol/L" asmolar, and denote it by the symbol "M" (both following the numeric value). Thus, for example, each liter of a "0.5 molar" or "0.5 M" solution ofurea (CH 4N 2O) in water contains 0.5 moles of that molecule. By extension, the amount concentration is also commonly called themolarity of the substance of interest in the solution. However, as of May 2007, these terms and symbols are not condoned by IUPAC.[11]
This quantity should not be confused with themass concentration, which is the mass of the substance of interest divided by the volume of the solution (about 35 g/L for sodium chloride in ocean water).
Confusingly, the amount (molar) concentration should also be distinguished from themolar fraction (also calledmole fraction oramount fraction) of a substance in a mixture (such as a solution), which 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 ofNaCl 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 ofNaCl will be0.34221/(0.34221 + 5.5509) = 0.05807.
In a mixture of gases, thepartial pressure of each component is proportional to its molar fraction.
Thealchemists, and especially the earlymetallurgists, probably had some notion of amount of substance, but there are no surviving records of any generalization of the idea beyond a set of recipes. In 1758,Mikhail Lomonosov questioned the idea that mass was the only measure of the quantity of matter,[12] but he did so only in relation to his theories ongravitation. The development of the concept of amount of substance was coincidental with, and vital to, the birth of modern chemistry.
1777:Wenzel publishesLessons on Affinity, in which he demonstrates that the proportions of the "base component" and the "acid component" (cation andanion in modern terminology) remain the same during reactions between two neutralsalts.[13]
1792:Richter publishes the first volume ofStoichiometry or the Art of Measuring the Chemical Elements (publication of subsequent volumes continues until 1802). The term "stoichiometry" is used for the first time. The first tables ofequivalent weights are published foracid–base reactions. Richter also notes that, for a given acid, the equivalent mass of the acid is proportional to the mass of oxygen in the base.[13]
1794:Proust'slaw of definite proportions generalizes the concept of equivalent weights to all types of chemical reaction, not simply acid–base reactions.[13]
1805:Dalton publishes his first paper on modernatomic theory, including a "Table of the relative weights of the ultimate particles of gaseous and other bodies".[15]
The concept of atoms raised the question of their weight. While many were skeptical about the reality of atoms, chemists quickly found atomic weights to be an invaluable tool in expressing stoichiometric relationships.
1808: Publication of Dalton'sA New System of Chemical Philosophy, containing the first table ofatomic weights (based on H = 1).[16]
1809:Gay-Lussac'slaw of combining volumes, stating an integer relationship between the volumes of reactants and products in the chemical reactions of gases.[17]
1811:Avogadro hypothesizes that equal volumes of different gases (at same temperature and pressure) contain equal numbers of particles, now known asAvogadro's law.[18]
1813/1814:Berzelius publishes the first of several tables of atomic weights based on the scale ofm(O) = 100.[13][19][20]
1815:Prout publishes hishypothesis that all atomic weights are integer multiple of the atomic weight of hydrogen.[21] The hypothesis is later abandoned given the observed atomic weight ofchlorine (approx. 35.5 relative to hydrogen).
Theideal gas law was the first to be discovered of many relationships between the number of atoms or molecules in a system and other physical properties of the system, apart from its mass. However, this was not sufficient to convince all scientists of the existence of atoms and molecules, many considered it simply being a useful tool for calculation.
1834:Faraday states hislaws of electrolysis, in particular that "the chemical decomposing action of a current isconstant for a constant quantity of electricity".[24]
1860: TheKarlsruhe Congress debates the relation between "physical molecules", "chemical molecules" and atoms, without reaching consensus.[27]
1865:Loschmidt makes the first estimate of the size of gas molecules and hence of number of molecules in a given volume of gas, now known as theLoschmidt constant.[28]
1886:van't Hoff demonstrates the similarities in behaviour between dilute solutions and ideal gases.
1887:Arrhenius describes the dissociation ofelectrolyte in solution, resolving one of the problems in the study of colligative properties.[29]
1893: First recorded use of the termmole to describe a unit of amount of substance byOstwald in a university textbook.[30]
1897: First recorded use of the termmole in English.[31]
By theturn of the twentieth century, the concept of atomic and molecular entities was generally accepted, but many questions remained, not least the size of atoms and their number in a given sample. The concurrent development ofmass spectrometry, starting in 1886, supported the concept of atomic and molecular mass and provided a tool of direct relative measurement.
1905:Einstein's paper onBrownian motion dispels any last doubts on the physical reality of atoms, and opens the way for an accurate determination of their mass.[32]
1921: Soddy receives the Nobel Prize in Chemistry "for his work on the chemistry of radioactive substances and investigations into isotopes".[38]
1922: Aston receives the Nobel Prize in Chemistry "for his discovery of isotopes in a large number of non-radioactive elements, and for his whole-number rule".[39]
1926: Perrin receives theNobel Prize in Physics, in part for his work in measuring the Avogadro constant.[40]
1959/1960: Unified atomic mass unit scale based onm(12C) = 12 u adopted byIUPAP andIUPAC.[41]
^Avogadro, Amedeo (1811). "Essai d'une maniere de determiner les masses relatives des molecules elementaires des corps, et les proportions selon lesquelles elles entrent dans ces combinaisons".Journal de Physique.73:58–76.English translation.
^Berzelius' first atomic weight measurements were published in Swedish in 1810:Hisinger, W.;Berzelius, J.J. (1810). "Forsok rorande de bestamda proportioner, havari den oorganiska naturens bestandsdelar finnas forenada".Afh. Fys., Kemi Mineral.3: 162.
