Amount of substance
In chemistry, the amount of substance "n" in a given sample of matter is defined as the quantity or number of discrete atomic-scale particles in it divided by the Avogadro constant "N". The particles or entities may be molecules, atoms, ions, electrons, or other, depending on the context, and should be specified (e.g. amount of sodium chloride "n"). The value of the Avogadro constant "N" has been defined as . The mole (symbol: mol) is a unit of amount of substance in the International System of Units, defined (since 2019) by fixing the Avogadro constant at the  given value. Sometimes, the amount of substance is referred to as the chemical amount. Role of amount of substance and its unit mole in chemistry. Historically, the mole was defined as the amount of substance in 12 grams of the carbon-12 isotope. As a consequence, the mass of one mole of a chemical compound, in grams, is numerically equal (for all practical purposes) to the mass of one molecule of the compound, in daltons, and the molar mass of an isotope in grams per mole is equal to the mass number. For example, a molecule of water has a mass  of about 18.015  daltons on average, whereas a mole of water (which contains water molecules) has a total mass of about 18.015 grams. In chemistry, because of the law of multiple proportions, it is often much more convenient to work with amounts of substances (that is, number of moles or of molecules) than with masses (grams) or volumes (liters). For example, the chemical fact "1 molecule of oxygen () will react with 2 molecules of hydrogen () to make 2 molecules of water ()" can also be stated as "1 mole of will react with 2 moles of to form 2 moles of  water". The same chemical fact, expressed in terms of masses, would be "32 g (1 mole) of oxygen will react with approximately 4.0304 g (2 moles of ) hydrogen to make approximately 36.0304 g (2 moles) of water" (and the numbers would depend on the isotopic composition of the reagents). In terms of volume, the numbers would depend on the pressure and temperature of the reagents and products. For the same reasons, the concentrations of reagents and products in solution are often specified in moles per liter, rather than grams per liter. The amount of substance is also a convenient concept  in thermodynamics. For example, the pressure of a certain quantity of a noble gas in a recipient of a given volume, at a given temperature, is directly related to the number of molecules in the gas (through the ideal 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 the English language. The latter may refer to other measurements such as mass or volume, rather than the number of particles. There are proposals to replace "amount of substance" with more easily-distinguishable terms, such  as enplethy and stoichiometric amount. The IUPAC recommends that "amount of substance" should be used instead of "number of moles", just as the quantity mass should not be called "number of kilograms". Nature of the particles. To avoid ambiguity, the nature of the particles should be specified in any measurement of the amount of substance: thus, a sample of 1 mol "of molecules" of oxygen () has a mass of about 32 grams, whereas a sample of 1 mol "of atoms" of oxygen () has a mass of about 16 grams. Derived quantities. Molar quantities (per mole). The quotient of some extensive  physical quantity of a homogeneous sample by its amount of substance is an intensive property of the substance, usually named by the prefix molar. For example, the ratio of the mass of a sample by its amount of substance is the molar mass, whose SI unit is kilograms (or, more usually, grams) per mole; which is about 18.015 g/mol for water, and 55.845 g/mol for iron. From the volume, one gets the molar volume, which is about 17.962 milliliter/mol for liquid water and 7.092 mL/mol for iron at room temperature. From the heat capacity, one gets  the molar heat capacity, which is about 75.385 J/K/mol for water and about 25.10 J/K/mol for iron. Amount concentration (moles per liter). Another important derived quantity is the amount of substance concentration (also called "amount concentration", or "substance concentration" in clinical chemistry; which is defined as the amount of a specific substance in a sample of a solution (or some other mixture), divided by the volume of the sample. The SI unit of this quantity is the mole (of the substance) per liter (of the solution). Thus, for example, the amount concentration of sodium 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 standard vodka contains about 0.40 L of ethanol (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" as molar, 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 of urea () in water contains 0.5 moles of that molecule. By extension, the amount concentration is also commonly called the molarity of the substance of interest in the solution. However, as of May 2007, these terms and symbols are not condoned by IUPAC. This quantity should not be confused with the mass 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). Amount fraction (moles per mole). Confusingly, the amount  concentration, or "molarity", should also be distinguished from "molar concentration", which should be the number of moles (molecules) of the substance of interest divided by the total number of moles (molecules) in the solution sample. This quantity is more properly called the amount fraction. History. The alchemists, and especially the early metallurgists, 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, but he did so only  in relation to his theories on gravitation. The development of the concept of amount of substance was coincidental with, and vital to, the birth of modern chemistry.