Avogadro constant in the context of Reciprocal mole

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 6.02214076×10 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 N_A) has units of mol. The relationship between the mole, Avogadro number, and Avogadro constant can be expressed in the following equation:$${\displaystyle 1{\text{ mol}}={\frac {N_{0}}{N_{\text{A}}}}={\frac {6.02214076\times 10^{23}}{N_{\text{A}}}}}$$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 C, 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.

In chemistry, the amount of substance (symbol n) in a given sample of matter is defined as a ratio (n = N/N_A) between the number of elementary entities (N) and the Avogadro constant (N_A). The unit of amount of substance in the International System of Units is the mole (symbol: mol), a base unit. Since 2019, the mole has been defined such that the value of the Avogadro constant N_A is exactly 6.02214076×10 mol, defining a macroscopic unit convenient for use in laboratory-scale chemistry. The elementary entities are usually molecules, atoms, ions, or ion pairs of a specified kind. The particular substance sampled may be specified using a subscript or in parentheses, e.g., the amount of sodium chloride (NaCl) could be denoted as n_NaCl or n(NaCl). Sometimes, the amount of substance is referred to as the chemical amount or, informally, as the "number of moles" in a given sample of matter. The latter term is deprecated by the IUPAC because, for a substance X, the correct meaning of "number of moles" is n(X)/mol. The amount of substance in a sample can be calculated from measured quantities, such as mass or volume, given the molar mass of the substance or the molar volume of an ideal gas at a given temperature and pressure.

In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artefacts such as the standard kilogram. Effective 20 May 2019, the 144th anniversary of the Metre Convention, the kilogram, ampere, kelvin, and mole are defined by setting exact numerical values, when expressed in SI units, for the Planck constant (h), the elementary electric charge (e), the Boltzmann constant (k_B), and the Avogadro constant (N_A), respectively. The second, metre, and candela had previously been redefined using physical constants. The four new definitions aimed to improve the SI without changing the value of any units, ensuring continuity with existing measurements. In November 2018, the 26th General Conference on Weights and Measures (CGPM) unanimously approved these changes, which the International Committee for Weights and Measures (CIPM) had proposed earlier that year after determining that previously agreed conditions for the change had been met. These conditions were satisfied by a series of experiments that measured the constants to high accuracy relative to the old SI definitions, and were the culmination of decades of research.

The previous major change of the metric system occurred in 1960 when the International System of Units (SI) was formally published. At this time the metre was redefined: the definition was changed from the prototype of the metre to a certain number of wavelengths of a spectral line of a krypton-86 radiation, making it derivable from universal natural phenomena. The kilogram remained defined by a physical prototype, leaving it the only artefact upon which the SI unit definitions depended. At this time the SI, as a coherent system, was constructed around seven base units, powers of which were used to construct all other units. With the 2019 redefinition, the SI is constructed around seven defining constants, allowing all units to be constructed directly from these constants. The designation of base units is retained but is no longer essential to define the SI units.

The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol R or R. It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per amount of substance, rather than energy per temperature increment per particle. The constant is also a combination of the constants from Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. It is a physical constant that is featured in many fundamental equations in the physical sciences, such as the ideal gas law, the Arrhenius equation, and the Nernst equation.

The gas constant is the constant of proportionality that relates the energy scale in physics to the temperature scale and the scale used for amount of substance. Thus, the value of the gas constant ultimately derives from historical decisions and accidents in the setting of units of energy, temperature and amount of substance. The Boltzmann constant and the Avogadro constant were similarly determined, which separately relate energy to temperature and particle count to amount of substance.