The mole (symbol mol) is a unit of measurement, the base unit in the International System of Units (SI) for amount of substance. One mole is an aggregate of exactly 6.02214076×1023 elementary entities which can be atoms, molecules, ions, ion pairs, or other particles. This number of entities equals 602,214,076,000,000,000,000,000, approximately 602 sextillion or 602 billion multiplied by one trillion. 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. The relationship between the mole, Avogadro number, and Avogadro constant can be expressed in the following equation: 1 mol = N 0 N A = 6.02214076 × 10 23 N A {\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 12C, 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
As a set 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.
Relation to the Avogadro constant The number of entities (symbol N) in a one-mole sample equals the Avogadro number (symbol N0), a dimensionless quantity. The Avogadro constant (symbol NA) is given by the Avogadro number multiplied by the unit reciprocal mole (mol−1), i.e. NA = N0/mol. The ratio n = N/NA is a measure of the amount of substance (with the unit mole). The Avogadro constant was determined by a measurement of the number of 28Si atoms in a single crystalline sample.
Nature of the entities
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. The mole is an amount corresponding to a given count (an Avogadro number) of elementary entities. 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.
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