The mole, symbol mol, is the unit of amount of substance in the International System of Units (SI). The quantity amount of substance is a measure of how many elementary entities of a given substance are in an object or sample. The mole is defined as containing exactly elementary entities. Depending on what the substance is, an elementary entity may be an

atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas ...

, a

molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bio ...

, an ion, an ion pair, or a subatomic particle such as an

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary partic ...

. For example, 10 moles of

water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...

chemical compound A chemical compound is a chemical substance composed of many identical molecules (or molecular entities) containing atoms from more than one chemical element held together by chemical bonds. A molecule consisting of atoms of only one ele ...

) and 10 moles of mercury (a

chemical element A chemical element is a species of atoms that have a given number of protons in their nuclei, including the pure substance consisting only of that species. Unlike chemical compounds, chemical elements cannot be broken down into simpler sub ...

), contain equal amounts of substance and the mercury contains exactly one atom for each molecule of the water, despite the two having different volumes and different masses. The number of elementary entities in one mole is known as the Avogadro number, which is the approximate number of

nucleon In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number (nucleon number). Until the 1960s, nucleons w ...

s ( protons or

neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behav ...

s) in one gram of ordinary

matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic par ...

. The previous definition of a mole was simply the number of elementary entities equal to that of 12

gram The gram (originally gramme; SI unit symbol g) is a unit of mass in the International System of Units (SI) equal to one one thousandth of a kilogram. Originally defined as of 1795 as "the absolute weight of a volume of pure water equal to ...

s of carbon-12, the most common isotope of carbon. The mole is widely used in chemistry as a convenient way to express amounts of reactants and products of chemical reactions. For example, the chemical equation can be interpreted to mean that for each 2 mol dihydrogen (H₂) and 1 mol

dioxygen There are several known allotropes of oxygen. The most familiar is molecular oxygen (O2), present at significant levels in Earth's atmosphere and also known as dioxygen or triplet oxygen. Another is the highly reactive ozone (O3). Others are: ...

(O₂) that react, 2 mol of water (H₂O) form. The

concentration In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', '' molar concentration'', '' number 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 moles per litre (mol/L). The term gram-molecule was formerly used for "mole of molecules", and gram-atom for "mole of atoms". For example, 1 mole of MgBr₂ is 1 gram-molecule of MgBr₂ but 3 gram-atoms of MgBr₂.

Concepts

Nature of the particles

The mole corresponds to a given count of particles. Usually the particles counted are chemically identical entities, individually distinct. For example, a solution may contain a certain number of dissolved molecules that are more or less independent of each other. However, in a solid the constituent particles 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 particles. In yet other cases, such as

diamond Diamond is a solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Another solid form of carbon known as graphite is the chemically stable form of carbon at room temperature and pressure, ...

, 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 particles of a substance, in other cases exact definitions may be specified. The 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.

Molar mass

The

molar mass In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecula ...

of a substance is the ratio of the

mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different element ...

of a sample of that substance to its amount of substance. The amount of substance is given as the number of moles in the sample. For most practical purposes, the numerical value of the molar mass expressed with the unit gram per mole is the same as that of the mean mass of one molecule of the substance expressed with the unit dalton. For example, the molar mass of water is 18.015 g/mol. International Bureau of Weights and Measures
Realising the mole
. Retrieved 25 September 2008. Other methods include the use of the molar volume or the measurement of

electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respecti ...

. The number of moles of a substance in a sample is obtained by dividing the mass of the sample by the molar mass of the compound. For example, 100 g of water is about 5.551 mol of water. The molar mass of a substance depends not only on its molecular formula, but also on the distribution of isotopes of each chemical element present in it. For example, the molar mass of calcium-40 is , whereas the molar mass of calcium-42 is , and of

calcium Calcium is a chemical element with the symbol Ca and atomic number 20. As an alkaline earth metal, calcium is a reactive metal that forms a dark oxide-nitride layer when exposed to air. Its physical and chemical properties are most similar t ...

with the normal isotopic mix is .

Molar concentration

The molar concentration, also called ''molarity'', of a solution of some substance is the number of moles per unit of volume of the final solution. In the SI its standard unit is mol/ m³, although more practical units, such as mole per litre (mol/L) are used.

Molar fraction

The molar fraction or mole fraction of a substance in a mixture (such as a solution) 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 of 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 of will be . In a mixture of gases, the partial pressure of each component is proportional to its molar ratio.

History

The history of the mole is intertwined with that of molecular mass,

atomic mass unit The dalton or unified atomic mass unit (symbols: Da or u) is a non-SI unit of mass widely used in physics and chemistry. It is defined as of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at r ...

s, 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 Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic ...

was defined as 1. These relative atomic masses were based on the

stoichiometric Stoichiometry refers to the relationship between the quantities of reactants and products before, during, and following chemical reactions. Stoichiometry is founded on the law of conservation of mass where the total mass of the reactants equ ...

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 Atomic theory is the scientific theory that matter is composed of particles called atoms. Atomic theory traces its origins to an ancient philosophical tradition known as atomism. According to this idea, if one were to take a lump of matter ...

(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.

Jöns Jacob Berzelius Baron Jöns Jacob Berzelius (; by himself and his contemporaries named only Jacob Berzelius, 20 August 1779 – 7 August 1848) was a Swedish chemist. Berzelius is considered, along with Robert Boyle, John Dalton, and Antoine Lavoisier, to be ...

(1779–1848) was instrumental in the determination of relative atomic masses to ever-increasing accuracy. He was also the first chemist to use

oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as we ...

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. 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 hydroge